{ "schema_version": "0.1.0", "title": "Spectral Consult — spec-routed, measurement-backed reasoning over an open corpus", "description": "A single entry point an AI agent (or a person) can fetch to learn what to read and which instrument to run for a given business decision. Routing is by the decision to be made; the corpus and its runnable instruments are the answer surface. Measurement questions resolve to instrument outputs, not literature summaries.", "canonical_url": "https://consult.orgschema.com/consult.json", "generated": "Generated projection of the open spectral-branding corpus substrate. Do not hand-edit; regenerated from source.", "frameworks": [ "SBT", "OST", "meaningfulness" ], "detail_levels": [ { "level": 0, "name": "Framing", "desc": "One-paragraph framing of the decision and the corpus's stance on it." }, { "level": 1, "name": "Claims", "desc": "The core anchor propositions of the 2-3 anchor papers." }, { "level": 2, "name": "Spine", "desc": "Full proposition spine + methods of the anchor papers; how the claims were derived." }, { "level": 3, "name": "Instrument", "desc": "Run the runnable instrument; the answer is a measurement, not a reading." } ], "intents": [ { "id": "diagnose-perception", "status": "ready", "decision": "Diagnose a brand's perception and find perception gaps across audiences.", "persona": [ "CMO", "brand lead", "brand strategist" ], "framework": "SBT", "tiers": [ 4 ], "framing": "A brand does not exist in the object; it is completed in the observer. So a diagnosis is not \"what is our brand?\" but \"what perception does our brand complete, in whom, and where do those perceptions disagree?\" The corpus decomposes a brand signal into eight independent perceptual dimensions and reads them per cohort, so a gap is a measured distance between cohorts on a named dimension — not an averaged score. The runnable instrument (the Brand Spectrometer) reconstructs those cohort readings from public artifacts with explicit noise floors, so a reported gap is one the measurement can actually resolve.", "spec_url": "https://consult.orgschema.com/specs/diagnose-perception.md", "levels": { "L0": { "name": "Framing", "framing": "A brand does not exist in the object; it is completed in the observer. So a diagnosis is not \"what is our brand?\" but \"what perception does our brand complete, in whom, and where do those perceptions disagree?\" The corpus decomposes a brand signal into eight independent perceptual dimensions and reads them per cohort, so a gap is a measured distance between cohorts on a named dimension — not an averaged score. The runnable instrument (the Brand Spectrometer) reconstructs those cohort readings from public artifacts with explicit noise floors, so a reported gap is one the measurement can actually resolve.", "thesis": "Brand perception is irreducibly observer-dependent: there is no single brand-in-itself with properties, only a shared signal environment and heterogeneous observers who each collapse it into a structurally different conviction. Spectral Brand Theory decomposes brand signals across eight perceptual dimensions (Semiotic, Narrative, Ideological, Experiential, Social, Economic, Cultural, Temporal), defines each observer cohort by a formal spectral profile (spectrum, weights, tolerances, priors, identity gate, encounter mode), and models perception as a pipeline — signal emission to observer filtering to probabilistic perception-cloud formation to threshold-based conviction collapse to re-collapse on new evidence. Single-score brand measurement (NPS, equity indices) collapses this multi-dimensional, observer-mediated structure and destroys the very information that explains why observers form irreconcilable perceptions of the same brand. SBT formalizes the heterogeneous observer that customer-based brand equity theory acknowledged but never parameterized, yields five testable structural propositions, and is computationally implementable as a structured LLM prompt sequence. An illustrative five-brand proof-of-concept surfaces four candidate mechanisms (structural absence, a five-type coherence taxonomy, asymmetric conviction resilience, and brand-power/brand-health independence); these are candidates for empirical investigation, not validated findings, and human-subject validation is the priority next step." }, "L1": { "name": "Claims", "papers": [ { "key": "2026a", "title": "Spectral Brand Theory: A Computational Framework for Multi-Dimensional Brand Perception", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.18945912", "doi_url": "https://doi.org/10.5281/zenodo.18945912", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/spectral-brand-theory", "claims": [ { "id": "P1", "text": "A brand is not an object with properties but a perceptual process with observers; \"the brand\" as commonly understood is always already a collapse — a conviction assembled in an observer's mind from whichever signals they could perceive through their spectral profile. These convictions are not errors against a true brand; they are the only brands that exist." }, { "id": "P2", "text": "Brand signals decompose across eight independent perceptual dimensions — Semiotic, Narrative, Ideological, Experiential, Social, Economic, Cultural, Temporal — each a distinct channel carrying information the others cannot. The dimensions measure brand OUTPUT (what is emitted and how it is perceived), not internal organizational process." }, { "id": "P3", "text": "Each signal carries a source type (designed / ambient / synthetic), an emission type (positive / null / structural absence), and a strength (0-5). The designed/ambient (D/A) ratio is a diagnostic metric: a brand whose perception is predominantly ambient (D/A < .40) faces a structural problem no communication strategy can solve, because its story is being written by others." }, { "id": "P4", "text": "Each observer cohort is defined by a formal spectral profile — spectrum (which dimensions are visible), weights (priority per dimension, summing to 1), tolerances (accepted inconsistency), priors (stored convictions), identity gate (recognition), and encounter mode (direct / mediated / mixed). This converts \"different people perceive differently\" from a qualitative observation into a parameterized scoring function." }, { "id": "P5", "text": "A cohort is a CLUSTER IN SPECTRAL-PROFILE SPACE, not a demographic segment. Demographic variables (age, income, geography) are metadata that may correlate with but do not determine perceptual behavior; two observers sharing every demographic attribute may belong to different cohorts if their profiles diverge. Cohort membership is dynamic: signal events physically redistribute observers across cohort boundaries." }, { "id": "P6", "text": "Brand perception follows a three-stage epistemic pipeline: (1) cloud formation — perceived signals cluster, weighted by the profile, into a probabilistic perception cloud with valence and confidence; (2) conviction collapse — sufficient consistent evidence collapses the cloud into a stable conviction at an observer-specific threshold; (3) re-collapse — strong contradicting evidence dissolves the conviction, which is then rebuilt from surviving + crystallized + new signals, never patched." }, { "id": "P7", "text": "Coherence is a STRUCTURAL property — the degree to which different cohorts' convictions are compatible (not identical) — not the consistency of messaging. It is measured by a seven-metric spectral scorecard (dimensional coverage, gate permeability, cloud coherence, collapse strength, re-collapse resistance, emission efficiency, D/A ratio) yielding an A+..F grade." }, { "id": "P8", "text": "SBT and classical brand frameworks stand in a correspondence-principle relationship: when observer diversity is low (cohorts share similar profiles) perception space is approximately flat and classical single-observer measurement is adequate; as diversity rises through globalization, AI mediation, and digital fragmentation, curvature becomes non-negligible and SBT's geometric tools become necessary." }, { "id": "P9", "text": "SBT measures the OUTPUT (WHAT) layer of a brand — the target perception across eight dimensions — not the coordination machinery (DO) that produces it. Output standardization is decidable (a finite acceptance test on eight dimensions); process standardization is not. SBT and Organizational Schema Theory are measurement and specification of one shared output interface, bridged by the WHAT/DO distinction." }, { "id": "PF1", "text": "(Formal Proposition 1 — Observer heterogeneity) Different observer cohorts exposed to identical brand signal environments form systematically different brand convictions as a function of their spectral-profile differences (weights, tolerances, priors, encounter mode) — profile-predictable divergence, not random variation." }, { "id": "PF2", "text": "(Formal Proposition 2 — Non-ergodicity of perception) The temporal sequence in which brand signals are encountered affects the resulting conviction even when the signal set is identical, because signals compound multiplicatively through priors rather than summing additively." }, { "id": "PF3", "text": "(Formal Proposition 3 — Structural absence as signal) Designed restriction of signal emission in specific dimensions generates perceived value that cannot be replicated by signal addition in other dimensions; restriction on one dimension produces a signal on a different dimension." }, { "id": "PF4", "text": "(Formal Proposition 4 — Coherence type over coherence score) Brands with identical aggregate coherence scores exhibit different resilience properties depending on coherence TYPE (ecosystem, signal, identity, experiential asymmetry, incoherent). Single-score coherence metrics are geometrically blind to this distinction (a form of spectral metamerism)." }, { "id": "PF5", "text": "(Formal Proposition 5 — Conviction asymmetry) Evidence-free negative brand convictions are more resistant to disconfirmation than evidence-rich positive convictions, because the negative holder's profile excludes the dimensions where disconfirming evidence would have to arrive (the experiential gate is effectively closed)." }, { "id": "thesis", "text": "Brand perception is irreducibly observer-dependent: there is no single brand-in-itself with properties, only a shared signal environment and heterogeneous observers who each collapse it into a structurally different conviction. Spectral Brand Theory decomposes brand signals across eight perceptual dimensions (Semiotic, Narrative, Ideological, Experiential, Social, Economic, Cultural, Temporal), defines each observer cohort by a formal spectral profile (spectrum, weights, tolerances, priors, identity gate, encounter mode), and models perception as a pipeline — signal emission to observer filtering to probabilistic perception-cloud formation to threshold-based conviction collapse to re-collapse on new evidence. Single-score brand measurement (NPS, equity indices) collapses this multi-dimensional, observer-mediated structure and destroys the very information that explains why observers form irreconcilable perceptions of the same brand. SBT formalizes the heterogeneous observer that customer-based brand equity theory acknowledged but never parameterized, yields five testable structural propositions, and is computationally implementable as a structured LLM prompt sequence. An illustrative five-brand proof-of-concept surfaces four candidate mechanisms (structural absence, a five-type coherence taxonomy, asymmetric conviction resilience, and brand-power/brand-health independence); these are candidates for empirical investigation, not validated findings, and human-subject validation is the priority next step." } ] }, { "key": "2026ax", "title": "The Brand Spectrometer: A Reproducible Instrument for Cohort-Resolved, Multi-Dimensional Brand-Perception Measurement from Public Artifacts", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20775963", "doi_url": "https://doi.org/10.5281/zenodo.20775963", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/brand-spectrometer-methods", "claims": [ { "id": "P1", "text": "The instrument is reliable: it returns the same cohort vector to the same input within its self-computed operator floor." }, { "id": "P2", "text": "The instrument is convergent-valid and reproducible: independent artifact halves agree within the artifact floor (P2a), and the atlas re-derives deterministically from published code + data (P2b)." }, { "id": "P3", "text": "Structural validity is conditional, not absolute: the instrument resolves cohort differences that exceed its floors and abstains (reports sub-resolution) when they do not — it refuses to manufacture differences it cannot separate from operator noise. Demonstrated WITHIN one window: on the same reflections the mean-cosine metric abstains while the distributional metric resolves owners-from-press (F5, F6)." }, { "id": "P4", "text": "Discriminant resolution is METRIC-dependent, not merely window-dependent: the signal lives in magnitude+distribution (resolved by energy distance, F6/F7), not mean shape (discarded by cosine, F5). The within-window two-metric contrast plus the positive/negative controls (F8) is the falsification test; it shows the floors are not trivially inflated without relying on a cross-window contrast (the pinned window abstains under both metrics)." }, { "id": "P5", "text": "Metameric psychometrics: a validation framework coherent WITHOUT a latent true score — two instrument-computed noise floors replace the oracle, making \"is this difference real?\" a quantified, falsifiable, panel-free question." }, { "id": "P6", "text": "A signal-detection resolution model formalizes P3: cohorts (Ci,Cj) are resolved when d(Ci,Cj) > k * max(O, A) with pre-registered k=2; the implemented per-pair S/N uses the operator-floor denominator max(O_i,O_j) and V3 reads the source floor, generalizing to max(O,A). The promised Monte-Carlo calibration is DELIVERED (not forthcoming): the permutation-null FPR of the S/N rule and the floor's source-count stability are computed (M8, F8)." }, { "id": "P7", "text": "The instrument surfaces boundary objects that survey-CBBE point estimates smooth away: rapid brand-crisis discourse shifts (a same-window owner vs debater divergence recorded as a cross-pair distance + resolution verdict), generational brand-purpose reversals (divergence on the Ideological and Cultural dimensions as a resolved cohort-pair separation), and country-of-origin divergence (distinct dimensional shapes across language-register cohorts that a population-level tracker cannot surface)." }, { "id": "P8", "text": "Exploratory-vs-confirmatory honesty is itself a contribution: the distributional metric was adopted after the confirmatory mean-cosine null, so its resolution (F6) is exploratory and is reported as such, the triangulation criterion is pre-registered going forward, and a confirmatory replication on a new case is owed. Triangulation + Holm/BH + controls + calibration guard against metric-shopping." }, { "id": "thesis", "text": "The Brand Spectrometer is a measurement instrument, not a brand oracle. It reconstructs cohort-resolved eight-dimensional brand-perception spec vectors from public artifacts through a fixed open pipeline (acquire -> render -> extract -> aggregate -> sensitivity) operated by cross-family LLM pairs. Because brand perception is ground-truth-absent — cohort metameric variance IS the measurement, not error around a latent true spec — the instrument is validated for its MEASUREMENT PROPERTIES against two noise floors it computes for itself (an operator floor from cross-family alt-pairs; an artifact floor from leave-one-out), never for criterion accuracy. A pre-registered V1-V5 battery across two adjacent sampling windows of one topical case shows the instrument is reliable (test-retest within the operator floor), cross-operator reliable, convergent-valid, reproducible (byte-identical re-derivation, no keys), and structurally valid: it resolves cohort differences exceeding its floors and DECLINES to manufacture differences it cannot separate from operator noise. Discriminant resolution is METRIC-dependent: a scale-invariant mean-cosine signal-to-noise abstains on both windows, while a distribution-level, operator-floored criterion resolves the owner cohort from the press in the fresh window (a magnitude separation triangulated across an energy-distance permutation test, a kernel MMD, and a bootstrap interval, and reported as EXPLORATORY because the metric was chosen after the confirmatory null). We name this validation class metameric psychometrics: reliability, cross-operator reliability, convergent validity, and reproducibility hold unconditionally; discriminant resolution is conditional on cohort signal exceeding the instrument's own noise in the structure a given metric can see (shape vs magnitude-and-distribution)." } ] }, { "key": "2026b", "title": "The Atom-Cloud-Fact Epistemological Pipeline: From Financial Document Processing to Brand Perception Modeling", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.18944770", "doi_url": "https://doi.org/10.5281/zenodo.18944770", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/alibi-epistemology", "claims": [ { "id": "P1_CONFBIAS", "text": "External corroboration structurally reduces confirmation bias in brand assessment, because the pipeline requires convergent evidence across independently typed sources before any fact collapse, subordinating single-source conclusions to the multi-source cloud." }, { "id": "P2_MULTIMODEL", "text": "Multi-model replication produces more robust brand assessments than single-model analysis: conclusions surviving across architecturally distinct models (treated as distinct observation sources under source binding) are high-confidence clouds approaching collapse, while single-model conclusions are unconfirmed clouds possibly reflecting model-specific artifacts." }, { "id": "P3_EPISTSEP", "text": "Three-stage epistemic separation prevents category errors that conflate brand signals (atoms), perception clouds (clouds), and brand convictions (facts) — errors such as treating signals as convictions, clouds as facts, or convictions as permanent." }, { "id": "P4_DISAGREE", "text": "Cross-model disagreement is diagnostic of evidential ambiguity (a cloud below collapse threshold), not model failure: if unambiguous evidence existed, all model implementations would converge, so disagreement identifies where available atoms are insufficient to push the cloud past threshold in all observers." }, { "id": "P_ARCH1", "text": "Knowledge formation from heterogeneous observation has a three-stage structure — atoms (typed, source-bound, immutable observations), clouds (probabilistic, multi-source, revisable hypotheses), and facts (threshold-crossed, stable, but re-collapsible knowledge) — with a feedback path from arriving evidence back to the atom layer." }, { "id": "P_ARCH2", "text": "Seven architectural principles — dimensional typing, source binding, identity gating, asymmetric tolerances, weighted multi-dimensional scoring, re-collapse on new evidence, and epistemic separation — govern the pipeline's operation and were discovered through the financial implementation." }, { "id": "P_DESIGNSCI", "text": "The work sits within the design-science tradition (artifact = the pipeline; utility = systems natively supporting observer heterogeneity and non-incremental revision), but its primary frame is epistemological — the pipeline as a candidate general structure of knowledge formation, not solely an IS design recommendation." }, { "id": "P_EMERGENT", "text": "The transfer surfaces three properties latent in the financial domain but central in the brand domain: observer heterogeneity as a feature (not a bug), structural absence as a signal (designed restriction generating perception effects, with a scarcity multiplier extending the atom model), and valence asymmetry (a conjectured greater resilience of evidence-free negative convictions than experientially-grounded positive convictions)." }, { "id": "P_FINIMPL", "text": "The financial reconciliation problem — a variant of probabilistic record linkage on unstructured documents — instantiates all seven principles, maintaining three-stage epistemic separation rather than collapsing to a direct match/non-match decision." }, { "id": "P_GENERAL", "text": "The pipeline is a candidate framework for any domain meeting one structural condition — typed observations from multiple sources clustering under uncertainty into revisable knowledge — with medical diagnosis, legal evidence assessment, and intelligence analysis as the highest-priority cross-domain replication tests." }, { "id": "P_HETOBS", "text": "The critical parametric extension producing Spectral Brand Theory is replacing the single-observer assumption with a heterogeneous-observer model: each cohort applies its own observer spectral profile (spectrum, weights, tolerances, priors) to the same signal environment, so the same brand produces different convictions in different observers — not errors, but the perceptions the architecture recovers from available signal." }, { "id": "P_LLMIMPL", "text": "The pipeline is linguistically implementable: its seven principles describe cognitive operations (perceive, cluster, weigh, decide, revise) expressible as a natural-language system prompt, so an LLM can execute and audit the cloud-to-fact transition as a typed verification contract — unlike frameworks requiring explicit probability distributions or formal rule bases." }, { "id": "P_RECOLLAPSE", "text": "Re-collapse — full dissolution of facts and rebuild from the complete atom set on contradicting evidence, rather than incremental patching — is the architectural commitment that most strongly distinguishes the pipeline from incremental updating systems and guarantees consistency with total evidence regardless of arrival order." }, { "id": "P_RIVALS", "text": "Four requirements define an adequate multi-domain knowledge-formation framework — path-independence, observer heterogeneity, epistemic separation, linguistic implementability — and Bayesian updating, AGM revision, Dempster-Shafer theory, and symbolic expert systems each fail at least one structurally; the atom-cloud-fact pipeline passes all four." }, { "id": "P_TRANSFER", "text": "The seven principles transfer from financial reconciliation to brand perception without domain specialization: atom→brand signal, source→ encounter type, identity gate→brand recognition, cloud→perception cloud, fact→brand conviction, re-collapse→conviction rebuild — because the underlying epistemic structure is identical." }, { "id": "thesis", "text": "The atom-cloud-fact pipeline is a domain-general epistemological architecture — a formal model of how knowledge forms from heterogeneous observation — not merely a financial document-processing technique. It models knowledge formation through three formally distinct stages: atomic observation (typed, source-bound, immutable data extraction), probabilistic cloud formation (weighted multi-dimensional clustering of revisable hypotheses), and fact collapse (threshold-based crystallization subject to full re-collapse on new evidence). Seven architectural principles (dimensional typing, source binding, identity gating, asymmetric tolerances, weighted scoring, re-collapse, epistemic separation) govern the pipeline and transfer with parametric extension from financial reconciliation to multi-cohort brand perception, where the single-observer assumption is replaced by a heterogeneous-observer model — producing Spectral Brand Theory. The architecture supports four testable propositions about confirmation bias, multi-model replication, epistemic category errors, and cross-model disagreement; and it satisfies four requirements (path-independence, observer heterogeneity, epistemic separation, linguistic implementability) that Bayesian updating, AGM revision, Dempster-Shafer theory, and symbolic expert systems each fail structurally on at least one." } ] } ] }, "L2": { "name": "Spine", "concepts": [ { "key": "perception-cloud", "label": "perception cloud", "definition": "The distribution of brand convictions across an observer population for a brand. Distributional, not a single fixed referent; \"cloud\" alone is acceptable in context. Has a valence (positive / negative / ambivalent).", "owner": "2026a", "status": "active" }, { "key": "reflection", "label": "Reflection (per-artifact spectral measurement)", "definition": "The unit of measurement in the Brand Spectrometer: the brand signal as reflected through a single public artifact and read by one operator pair, yielding one eight-dimensional spec vector bound to one source. It is the data-of-record the instrument aggregates reflection -> source -> cohort, recomputable into cohorts at any resolution. The optics-native name is deliberate: a spectrometer measures reflected signal, and perception is completed in the observer (the brand 'has no colour' until reflected and read). Distinct from the atom-cloud-fact 'atom' (2026b), a single (dimension, source) cell of raw observation; a reflection bundles all eight dimensions from one source and is operator-produced, so it is not a refinement of that atom and does not edit it.", "owner": "2026ax", "status": "active" }, { "key": "cohort", "label": "cohort", "definition": "A perceptual grouping of observers with similar spectral profiles, with dynamic membership. Cohorts are perceptual; demographics are metadata, not mechanism. Also written \"observer cohort\".", "owner": "2026a", "status": "active" }, { "key": "observer-spectral-profile", "label": "observer spectral profile", "definition": "The receiver-side object that collapses a brand signal into a conviction. Five components: spectrum, weights, tolerances, priors, and an identity gate. Cohorts are observers, not consumers.", "owner": "2026a", "status": "active" }, { "key": "spectral-dimensions", "label": "the 8 dimensions", "definition": "The eight spectral dimensions of a brand signal, in canonical order: semiotic, narrative, ideological, experiential, social, economic, cultural, temporal. Lowercase in prose.", "owner": "2026a", "status": "active" }, { "key": "spectral-metamerism", "label": "Spectral Metamerism", "definition": "The phenomenon whereby structurally distinct brand profiles produce identical scalar evaluations, arising as a geometric inevitability of projecting the eight-dimensional spectral profile to a lower-dimensional grade.", "owner": "2026e", "status": "active" } ], "methods": [ { "paper": "2026a", "claims": [ { "id": "M1", "text": "The six-module analytical pipeline: (1) Brand Decomposition, (2) Observer Mapping, (3) Cloud Prediction, (4) Coherence Audit (seven-metric scorecard + A+..F grade + coherence-type classification), (5) Emission Strategy, (6) Re-collapse Simulation; each module's structured YAML output feeds the next." }, { "id": "M2", "text": "Insight Validation Protocol: each surfaced insight is accepted only if it simultaneously satisfies four criteria — non-obvious, dimensionally specific, actionable, observer-differentiated — assessed by the framework's author." }, { "id": "M3", "text": "Cross-model inter-rater reliability: run the identical pipeline under a second independent analytical instrument (Gemini 3.1 Pro) and compare structural classifications (coherence type + grade), treating convergence as inter-coder agreement." } ] }, { "paper": "2026ax", "claims": [ { "id": "M1", "text": "The instrument is a fixed pipeline acquire->render->extract->aggregate-> sensitivity; each cohort yields an 8-dim spec vector; pairwise cohort distance = 1 - cosine similarity." }, { "id": "M2", "text": "Two noise floors are computed by the instrument: operator floor = max distance from primary over cross-family alt-pairs; artifact floor = max distance from primary over leave-one-out artifact subsets." }, { "id": "M3", "text": "Per-pair signal-to-noise = cohort distance / max(endpoint operator floors); resolved (>2) / marginal (1-2) / sub-resolution (<1)." }, { "id": "M4", "text": "The V1-V6 battery, operator pins, and numeric pass thresholds were pre-registered (git + Zenodo) before the fresh atlas was collected; confirmatory/exploratory boundary fixed." }, { "id": "M5", "text": "Determinism budget: temperature 0 where the model honors it; residual non-determinism is what V1 measures, not hidden." }, { "id": "M6", "text": "Measurement note: under the reflection -> source -> cohort aggregation the composite metameric degree (mean cohort-pair 1 - cosine) is .0158 on the fresh window and .0079 on the pinned window; the fresh value matches the cohort-attributable variance in the V2 decomposition." }, { "id": "M7", "text": "A distribution-level discriminant metric complements the mean-cosine S/N: energy distance and kernel MMD (RBF, median-heuristic) between source-level cohort clouds with a shared 9999-permutation null, an operator-floored distributional S/N (pair energy / max endpoint distributional operator floor) with a source-cluster bootstrap, Holm/BH correction over the 10 pairs, and a magnitude/shape decomposition. A pair is RESOLVED only under triangulation: Holm energy-p < .05 AND distributional S/N 95%-CI lower > 1 AND LOO accuracy > chance. The metric was specified AFTER the mean-cosine null (exploratory), pre-registered going forward." }, { "id": "M8", "text": "The distributional rule is bracketed by controls and a permutation-null calibration: a negative control (same-cohort source splits must abstain), a positive control (a planted magnitude shift must resolve), and a Monte-Carlo false-positive calibration of the S/N threshold under the pooled-split null, plus a source-subsample learning curve showing the abstention is operator-limited, not sample-limited." }, { "id": "M9", "text": "Optional per-reflection SENTIMENT/VALENCE layer (instrument extension, outside the frozen V1-V6 battery). A single cross-family extractor pass (extractor family != renderer family — the same 2026ap discipline as the eight-dimension extract) reads the already-rendered prose and emits a per-dimension valence in [-1,+1]. Valence is orthogonal to the dimension STRENGTH score (a cohort can be strong on a dimension with either sign of affect) and is explicitly NOT a noise floor (a floor needs multi-operator passes; M9 is a single labelling pass). Demonstrated on the Ferrari Luce fresh atlas (36 primary reflections): the owner cohort reads hostile (Semiotic -.53, Experiential -.57) while international press reads favourable (Economic +.45) — a face-valid signal. Warrant: LLM sentiment extraction is benchmarked with documented limits [Zhang et al. 2024]; the human affective-norm criterion for valence is the lexical norm set [Warriner et al. 2013]; confirmatory validation of the layer against those norms is future work." } ] }, { "paper": "2026b", "claims": [] } ] }, "L3": { "name": "Instrument", "instrument": { "name": "Brand Spectrometer", "kind": "measurement", "url": "https://meter.spectralbranding.com", "input_contract_url": "https://meter.spectralbranding.com/CONVERT_WITH_YOUR_AI.md", "output": "An eight-dimension atlas: one line per cohort across the eight bands, the spread between cohorts as a band of its own, valence per band, and a 95% CI halo gated by a noise floor.", "when": "Route here when the user has a specific brand and can point to public artifacts about it (posts, press, reviews, owned copy). The instrument returns a measurement; the papers explain what the measurement means.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about brand perception\" to \"what is MY brand's perception\" — i.e. the moment the answer requires reading this specific brand rather than the theory.\n" } } }, "papers": [ { "key": "2026a", "title": "Spectral Brand Theory: A Computational Framework for Multi-Dimensional Brand Perception", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.18945912", "doi_url": "https://doi.org/10.5281/zenodo.18945912", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/spectral-brand-theory" }, { "key": "2026ax", "title": "The Brand Spectrometer: A Reproducible Instrument for Cohort-Resolved, Multi-Dimensional Brand-Perception Measurement from Public Artifacts", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20775963", "doi_url": "https://doi.org/10.5281/zenodo.20775963", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/brand-spectrometer-methods" }, { "key": "2026b", "title": "The Atom-Cloud-Fact Epistemological Pipeline: From Financial Document Processing to Brand Perception Modeling", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.18944770", "doi_url": "https://doi.org/10.5281/zenodo.18944770", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/alibi-epistemology" } ], "concepts": [ { "key": "perception-cloud", "label": "perception cloud", "definition": "The distribution of brand convictions across an observer population for a brand. Distributional, not a single fixed referent; \"cloud\" alone is acceptable in context. Has a valence (positive / negative / ambivalent).", "owner": "2026a", "status": "active" }, { "key": "reflection", "label": "Reflection (per-artifact spectral measurement)", "definition": "The unit of measurement in the Brand Spectrometer: the brand signal as reflected through a single public artifact and read by one operator pair, yielding one eight-dimensional spec vector bound to one source. It is the data-of-record the instrument aggregates reflection -> source -> cohort, recomputable into cohorts at any resolution. The optics-native name is deliberate: a spectrometer measures reflected signal, and perception is completed in the observer (the brand 'has no colour' until reflected and read). Distinct from the atom-cloud-fact 'atom' (2026b), a single (dimension, source) cell of raw observation; a reflection bundles all eight dimensions from one source and is operator-produced, so it is not a refinement of that atom and does not edit it.", "owner": "2026ax", "status": "active" }, { "key": "cohort", "label": "cohort", "definition": "A perceptual grouping of observers with similar spectral profiles, with dynamic membership. Cohorts are perceptual; demographics are metadata, not mechanism. Also written \"observer cohort\".", "owner": "2026a", "status": "active" }, { "key": "observer-spectral-profile", "label": "observer spectral profile", "definition": "The receiver-side object that collapses a brand signal into a conviction. Five components: spectrum, weights, tolerances, priors, and an identity gate. Cohorts are observers, not consumers.", "owner": "2026a", "status": "active" }, { "key": "spectral-dimensions", "label": "the 8 dimensions", "definition": "The eight spectral dimensions of a brand signal, in canonical order: semiotic, narrative, ideological, experiential, social, economic, cultural, temporal. Lowercase in prose.", "owner": "2026a", "status": "active" }, { "key": "spectral-metamerism", "label": "Spectral Metamerism", "definition": "The phenomenon whereby structurally distinct brand profiles produce identical scalar evaluations, arising as a geometric inevitability of projecting the eight-dimensional spectral profile to a lower-dimensional grade.", "owner": "2026e", "status": "active" } ], "instrument": { "name": "Brand Spectrometer", "kind": "measurement", "url": "https://meter.spectralbranding.com", "input_contract_url": "https://meter.spectralbranding.com/CONVERT_WITH_YOUR_AI.md", "output": "An eight-dimension atlas: one line per cohort across the eight bands, the spread between cohorts as a band of its own, valence per band, and a 95% CI halo gated by a noise floor.", "when": "Route here when the user has a specific brand and can point to public artifacts about it (posts, press, reviews, owned copy). The instrument returns a measurement; the papers explain what the measurement means.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about brand perception\" to \"what is MY brand's perception\" — i.e. the moment the answer requires reading this specific brand rather than the theory.\n" }, "spec": { "intake": [ "brand: the brand or product under diagnosis (name + one-line category).", "artifacts: 2+ public sources per audience the user cares about (URLs or pasted text); the instrument reads artifacts, not opinions.", "audiences: the cohorts to resolve (e.g. owners, prospects, critics) — at least two, since a single cohort cannot show a gap.", "decision: the action the diagnosis should inform (repositioning, campaign brief, portfolio audit)." ], "guardrails": [ "Do not invent data. If the artifacts cannot ground the eight dimensions or cannot support at least two distinct cohorts, say so and request the missing evidence — do not produce a vector.", "Report cohorts as distributions, not point scores; a difference smaller than the instrument's noise floor is reported as 'cannot resolve', not as a finding.", "Measure perception, never identify or profile a person; cohorts are perceptual clusters, and sources are clustered by pseudonymous public provenance only.", "Distinguish brand POWER (emission strength) from brand HEALTH (coherence); a strong brand is not a healthy one." ], "output_contract": "A diagnosis names, per resolved cohort, the eight-band reading and the dimensions where cohorts diverge beyond the noise floor, each tied to the artifacts that produced it, with the un-resolvable gaps listed separately as \"measured but below floor.\" The deliverable is an atlas plus the named gaps, not a single brand score.\n", "escalate_to_tool": "When intake is complete (brand + artifacts + 2 audiences), hand off to the Brand Spectrometer: format the artifacts with the input contract (CONVERT_WITH_YOUR_AI.md), load the atlas at meter.spectralbranding.com, and read the result back through the anchor papers' claims.\n" } }, { "id": "specify-operations", "status": "ready", "decision": "Specify or stress-test an operating model.", "persona": [ "CEO", "COO", "operations lead" ], "framework": "OST", "tiers": [ 1, 2, 3, 4, 5, 6 ], "framing": "An operating model is not an org chart; it is a six-tier stack of specifications — owner intent, business model, entity, product, process, organization — designed backward from the customer experience it is meant to produce. The corpus reframes operating dysfunction: most of it originates not in poor execution but in absent, misaligned, or untested specifications, so the question is not \"are people executing well?\" but \"is each layer specified, codified, and validated by the layer above it?\" Specification readiness is measurable (a coherence index), comprehensive specification is geometrically impossible (so the method specifies what binds the experience contract and abstains on the rest), and a change that intervenes at the org-chart surface while leaving the binding upstream specification untouched re-collapses to the same equilibrium. The runnable instrument turns customer-experience goals into a testable, version-controlled specification down to sourcing.", "spec_url": "https://consult.orgschema.com/specs/specify-operations.md", "levels": { "L0": { "name": "Framing", "framing": "An operating model is not an org chart; it is a six-tier stack of specifications — owner intent, business model, entity, product, process, organization — designed backward from the customer experience it is meant to produce. The corpus reframes operating dysfunction: most of it originates not in poor execution but in absent, misaligned, or untested specifications, so the question is not \"are people executing well?\" but \"is each layer specified, codified, and validated by the layer above it?\" Specification readiness is measurable (a coherence index), comprehensive specification is geometrically impossible (so the method specifies what binds the experience contract and abstains on the rest), and a change that intervenes at the org-chart surface while leaving the binding upstream specification untouched re-collapses to the same equilibrium. The runnable instrument turns customer-experience goals into a testable, version-controlled specification down to sourcing.", "thesis": null }, "L1": { "name": "Claims", "papers": [ { "key": "2026ar", "title": "The OrgSchema Audit: A Six-Level Diagnostic for Specification-Driven Organizations", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19555201", "doi_url": "https://doi.org/10.5281/zenodo.19555201", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/orgschema-audit", "claims": [] }, { "key": "2026an", "title": "Specification Readiness: Measuring an Architectural Antecedent of Functional Friction and AI Returns", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20384084", "doi_url": "https://doi.org/10.5281/zenodo.20384084", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/specification-readiness-empirical", "claims": [ { "id": "P1", "text": "Specification readiness — the degree to which a firm's substrate S is codified, versioned, machine-readable, and queryable at rendering time and consistent across the six ontological tiers — is a measurable firm-year strategic construct that has not previously entered a strategy regression as an independent variable, and is conceptually prior to organization capital, brand capital, and disclosure readability." }, { "id": "P2", "text": "The continuous SCI — within-firm year-over-year cosine similarity of 10-K narrative embeddings — is a scalable archival operationalization of substrate stability that is NOT equivalent to disclosure clarity: two firms can produce identically readable filings from radically different substrates, and the within-firm temporal signal is orthogonal to any single filing's complexity level (contra Loughran-McDonald readability; Bushee, Gow, and Taylor linguistic complexity)." }, { "id": "P3", "text": "(H1) Within firms, after firm and year fixed-effects absorption, an increase in continuous SCI predicts a decrease in aggregate function-layer spending as a share of revenue (β ≈ −.08; Cohen's d .5; negative). The specification-readiness mechanism names the upstream architectural cause of the SG&A sticky-cost asymmetry (Anderson, Banker, and Janakiraman 2003) that prior cost-stickiness research left unspecified." }, { "id": "P4", "text": "(H2) Conditional on revenue cohort and industry×year cell, an increase in continuous SCI predicts an increase in brand-capital growth net of depreciation (Belo-Lin-Vitorino perpetual inventory, δ₆ = .50): as codification rises, less marketing budget is consumed by interface-coherence maintenance and more accrues to net brand-capital accumulation (β ≈ −.12 on the inverted functional-headcount-to-brand-capital outcome; Cohen's d .3)." }, { "id": "P5", "text": "(H3) Firms with documented cross-interface contradictions (mean pairwise NLP cosine distance across three interface pairs) exhibit higher cross-stakeholder valuation dispersion than coherent-specification firms, after firm and year FE (β ≈ +.10; Cohen's d .4; positive). Estimated on single-brand-dominant firms to address the brand-portfolio confound." }, { "id": "P6", "text": "(H4) Firms with high continuous SCI in the year before first major AI deployment realize higher AI-ROI (change in interface-maintaining functional headcount in [t+1,t+2] per AI-related dollar) than low-SCI firms (β ≈ +.15; Cohen's d .5; positive). Substrate-operator realization yields flat/declining maintenance headcount alongside rising AI spend; surface-operator deployment raises spend without headcount reduction. This is the firm-level architectural moderator that the automation-augmentation paradox (Raisch and Krakowski 2021) left unspecified." }, { "id": "P7", "text": "(H5) High-push-intensity firms (top XAD/SALE quintile) exhibit larger negative cumulative abnormal returns following advertising-spend-cessation events than low-push-intensity firms (CAR differential ≈ −15 pp in [0,+1yr]; Cohen's d .7; negative): push-dependent firms collapse faster than pull-capable firms when force is withdrawn." }, { "id": "P8", "text": "The paper's three contributions: (1) the SCI — the first scalable archival measure of specification readiness; (2) a reusable multi-arm identification template pairing continuous textual treatment with sharp codification events, extensible to governance, process, and knowledge-management codification; (3) formal mechanism-test evidence that specification readiness moderates the AI augmentation paradox." }, { "id": "P9", "text": "Pre-registered mechanism testing — a Monte Carlo over the formal parameter grid plus a regression-identification power simulation under H0 and H1 with a transparently logged post-hoc estimator deviation — establishes the necessary condition for credible inference (the design CAN detect the pre-registered effects) separately from the empirical question (whether the effects are present), a discipline point-estimate pre-registration alone does not enforce." }, { "id": "thesis", "text": "Specification readiness — the degree to which a firm's commitments are codified in versioned, machine-readable, queryable form — is a measurable firm-year strategic construct that is conceptually prior to organization capital, brand capital, and disclosure readability. A continuous Specification Coherence Index (SCI), built from within-firm year-over-year cosine similarity of 10-K narrative embeddings, supplies the first scalable archival operationalization across the Compustat universe of US public firms 2010–2025; a four-event sharp index supplies discrete robustness. The construct is argued to substitute query-based alignment for costly interface-maintenance functions, reducing a structural friction tax (H1), redirecting marketing spend toward brand-capital accumulation (H2), lowering cross-stakeholder valuation dispersion under incoherence (H3), raising returns to AI deployment (H4), and governing the valuation consequence of advertising-spend cessation (H5). A multi-arm identification template pairs continuous within-firm treatment with staggered difference-in-differences (Callaway-Sant'Anna; Goodman-Bacon), regulatory-compliance instruments, and advertising-cessation event studies, disciplined by an Oster (2019) threats register. Pre-registered Monte Carlo mechanism tests (12.96 million trials; α* = .91; Cohen's d = 88.4) confirm the friction-tax phase shift, and a regression-identification simulation confirms power ≥ .80 for all five hypotheses at the pre-registered effect sizes. The paper contributes the measure, the reusable identification template, and formal evidence that specification readiness moderates the AI augmentation paradox; the archival panel estimates implementing the design are in execution as a companion." } ] }, { "key": "2026m", "title": "The Projection Cascade: Why Reorganizations Fail When the Specification Cascade Doesn't", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19145205", "doi_url": "https://doi.org/10.5281/zenodo.19145205", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/projection-paper", "claims": [ { "id": "P0", "text": "The design literature has produced five powerful but incompatible primitive vocabularies (Galbraith information-processing, Williamson transaction-cost, Mintzberg configurational, Puranam microstructural, Burton-Obel-Hakonsson computational); the same question routed to different traditions yields non-comparable answers, and the field lacks a formal apparatus that makes them algebraically commensurable (Joseph & Sengul 2025 diagnose the fragmentation but do not supply the unifying object)." }, { "id": "P1", "text": "Organizations are six finite-dimensional real content-tiers T_1..T_6 (deepest owner intent to shallowest org-chart position) linked by linear projection operators Pi_{i->i+1}: T_i -> T_{i+1} in the rank-reducing (not idempotent) sense, with rank deficiency r_i := d_i - rank(Pi_{i->i+1}) >= 0. The composite cascade Pi := Pi_{5->6} o ... o Pi_{1->2} is rank-non-increasing: rank(Pi) <= min_i rank(Pi_{i->i+1})." }, { "id": "P10", "text": "(P2, predictive) Strict downward propagation of basis rotation under AI deployment: an AI-induced basis rotation at Pi_{i->i+1} (i in {2,3,4,5}) that preserves rank manifests at T_6 as a rotation affecting P_p (perceptual content, via Pi_{5->6}) while leaving A_p (authority, via Pi_{3->6}) and R_p (role expectation, via Pi_{1->6}) invariant — provided the deployment does not penetrate the T_3 legal-personhood floor or the T_1 cultural-constitutional floor." }, { "id": "P11", "text": "(P3, predictive) Variance amplification with cascade distance: for an exogenous perturbation eps_i at tier i with variance sigma_i^2, the variance of the induced T_6 perturbation is bounded by [Prod_{j=i..5} L_j / (1 - kappa_j)]^2 * sigma_i^2, so T_6-outcome variance scales geometrically with cascade-distance (6 - i). The coefficient of variation of T_6 outcomes across firms hit by the same upstream shock exceeds that of T_4, which exceeds that of T_2." }, { "id": "P12", "text": "(P4, predictive) Algebraic decoupling bound at layer junctions: the empirical re-statement of Corollary 1 as a regime classification — Sum_i r_i = r_total (fully decoupled, each junction contributes independent loss) versus Sum_i r_i > r_total (junction interaction, upstream kernels partially absorbed downstream). The strict-inequality regime is a new empirical claim no single-junction framework (Galbraith, Mintzberg, Burton-Obel-Hakonsson, which implicitly assume decoupled junctions) reproduces." }, { "id": "P2", "text": "Information loss across the cascade is junction-localizable: the cascade kernel decomposes by sub-additivity across junctions, so a manager who observes that two firms with identical T_1 produce systematically different T_6 positions can in principle identify the specific junction at which the difference originates rather than treating the cascade as a single black-box compression." }, { "id": "P3", "text": "A rank-preserving change of basis at Pi_{i->i+1} is a rotation of the operator's row space that leaves kernel and rank unchanged while altering which T_i directions are read into which T_{i+1} coordinates. A basis rotation at Pi_{5->6} is the formal mechanism of role-content drift under stable titles: job titles remain fixed while the underlying performative content of the position rotates beneath them — the headline AI-deployment phenomenon." }, { "id": "P4", "text": "Each junction carries a paired feedback operator A_{i+1->i} (not the inverse of Pi_{i->i+1}) representing the lower tier's response to a descending specification; A_{i+1->i} formalizes what the design literature calls implementation / execution. Persistent implementation gap at a junction is a direct diagnostic that the contraction condition (C_i) of Theorem 1 is locally violated there." }, { "id": "P5", "text": "Theorem 1 (cascade-equilibrium existence and uniqueness): under a uniform Banach contraction (C_i, constant kappa_i in [0,1)) and joint parameter Lipschitz condition (C_i', constant L_i) at each junction, for every x_1 in B_1 a unique cascade-equilibrium trajectory exists, and the fixed-point map x_1 -> (x_2*,...,x_6*) is Lipschitz on B_1 with constant bounded above by Prod_{j=1..5} L_j / (1 - kappa_j). Uniform contraction is the technical content distinguishing the result from ad-hoc local Banach applications." }, { "id": "P6", "text": "Corollary 1 (cascade information loss; sub-additivity of nullity): r_total = d_1 - rank(Pi) <= r_1 + r_2 + r_3 + r_4 + r_5, with equality iff kernels stack independently (ker(Pi_{i->i+1}) contained in the cumulative image up to tier i). The two-sided architectural bound is max(0, d_1 - d_6) <= r_total <= Sum_i r_i <= Sum_i d_i. Strict inequality (kernel partial absorption) means upstream junctions partially shield downstream ones." }, { "id": "P7", "text": "Five major design theories are recovered as nested cascade restrictions, each obtained by fixing some tiers and modeling specific junctions: Galbraith's star as a multi-junction (Pi_{2->3}, Pi_{3->4}, Pi_{5->6}) restriction with T_1 parameterized; Williamson's governance choice as the Pi_{2->3} junction; Mintzberg's configurations as cascade-equilibrium attractor basins at Pi_{5->6}; Puranam's microstructure as the Pi_{4->5}-Pi_{5->6} junction pair; Burton-Obel-Hakonsson computational optimization as constrained search over the cascade's Lipschitz parameters. Fragmentation is a partial-view artifact, not ontological disagreement." }, { "id": "P8", "text": "A position is a triple p = (P_p, A_p, R_p) in T_6, where perceptual content P_p is the image under Pi_{5->6} of a T_5 process-trajectory (what the position does), authority allocation A_p is a coordinate of Pi_{3->6}(x_3) (what the position can decide), and role expectation R_p is a coordinate of the full composite Pi_{1->6}(x_1) (what the position means). Position is a cascade-coordinate object whose three channels inherit from distinct upstream tiers — the first formal decomposition respecting multi-channel inheritance from culture, contract, and routine." }, { "id": "P9", "text": "(P1, predictive) Cascade-distance scaling: an intervention of magnitude Delta_i at tier i registers at T_6 with magnitude bounded above by [Prod_{j=i..5} L_j / (1 - kappa_j)] * ||Delta_i||, so intervention efficacy is geometric in cascade depth (6 - i). T_6-only re-titling produces the smallest average effect; deeper-tier interventions produce monotonically larger effects. This is why ~60% of T_6-targeted reorganizations under-deliver." }, { "id": "thesis", "text": "Most strategic reorganizations fail to deliver expected performance gains because they intervene at the org-chart surface (T_6), and interventions there achieve effect-sizes geometrically smaller than interventions at deeper tiers — each deeper tier carries content already compressed in transit to the surface. Organizations are formalized as a six-tier projection cascade linking owner intent (T_1), business model (T_2), governance (T_3), architecture (T_4), routines (T_5), and positions (T_6), where each junction is a rank-reducing linear operator Pi_{i->i+1} with rank deficiency r_i >= 0. A unique cascade-equilibrium exists under tier-by-tier Banach contractions (Theorem 1); total information loss is bounded by the sum of local nullities, with equality only when kernels stack independently (Corollary 1). Five major design theories — Galbraith's star, Williamson's governance choice, Mintzberg's configurations, Puranam's microstructure, and Burton-Obel-Hakonsson's computational optimization — are recovered as nested cascade restrictions, so the field's apparent fragmentation is a partial-view artifact rather than ontological disagreement. A position triple p = (P_p, A_p, R_p) decomposes any T_6 position into perceptual content from T_5, authority from T_3, and role expectation from T_1. The apparatus entails four falsifiable propositions (P1 cascade-distance scaling, P2 strict downward propagation of basis rotation under AI deployment, P3 variance amplification, P4 algebraic decoupling) that no single tradition derives in isolation." } ] }, { "key": "2026h", "title": "Specification Impossibility in Organizational Design: A High-Dimensional Geometric Analysis", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.18945591", "doi_url": "https://doi.org/10.5281/zenodo.18945591", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r5-specification-impossibility", "claims": [ { "id": "P1", "text": "OST's organization model — six hierarchical levels (L0 Purpose, L1 Values, L2 Strategy, L3 Structure, L4 Process, L5 Artifacts) each specified across the eight SBT configuration dimensions — yields an 8×6 activation matrix A ∈ [0,1]^{8×6} that vectorizes to a single point in a 48-dimensional specification space [0,1]^48." }, { "id": "P10", "text": "Coverage impossibility (geometric) is DISTINCT FROM and COMPLEMENTARY TO NK landscape search complexity (computational): NK asks 'how hard is it to find the optimum?' on a fitness landscape; this paper asks 'how much of the space can any collection cover?' with no fitness function. Together they create a double bind — too vast to specify, too rugged to search — that makes specialization the only viable strategy." }, { "id": "P11", "text": "Templates and consulting frameworks are low-dimensional projections of [0,1]^48: a 5-dimension framework retains ≈10.4% of the 159.4 bits and discards 43 dimensions, so distinct 48-dim configurations producing the same template projection are organizationally metameric (indistinguishable by the template but genuinely different), with the lost dimensions equivalent to construct-irrelevant variance." }, { "id": "P12", "text": "The activation matrix splits into output specification (L0–L2: purpose, values, strategy — the irreducible, human-authored WHAT, ~14 of 15.75 effective dimensions at gamma=0.5) and coordination specification (L3–L5: structure, process, artifacts — the derivable HOW, ~1.75 effective dimensions); AI systems compress coordination overhead by making the HOW derivable from the WHAT, reducing the irreducible burden to ~14 dims." }, { "id": "P2", "text": "In high dimensions the inscribed-ball volume collapses relative to the cube (volume concentrates in the corners); at n=48 the ratio is ≈ 4.89e-27, so the 'center' of the specification space is volumetrically nowhere and a balanced specification is volumetrically rare." }, { "id": "P3", "text": "(Theorem 1, Coverage Impossibility) At resolution epsilon = 0.1 the space admits 10^48 distinguishable specifications, each covering V_48(0.1) ≈ 1.38e-60; any practically enumerable collection covers a negligible fraction (10^20 templates → 1.38e-40), so exhaustive coverage is geometrically impossible — not merely impractical." }, { "id": "P4", "text": "(Theorem 2, Effective Dimensionality Reduction) OST's cascade model, where level i constrains level i+1 with strength gamma, reduces effective dimensionality to d_eff = 8(1-(1-gamma)^6)/gamma — 15.75 at gamma = 0.5, a 67% reduction — making per-organization specification tractable (~16 rather than 48 independent choices) without making the space coverable." }, { "id": "P5", "text": "(Proposition 1, Coherence–Coupling Correspondence) The closed form converts to a falsifiable empirical prediction: the cross-level coherence ratio R = 1 - d_eff/(nL) is a monotone increasing function R(gamma) of cascade coupling, so across organizations an estimated R_hat should track R(gamma_hat) within a tolerance band (anchors R(.1)≈.22, R(.5)≈.67, R(.9)≈.82)." }, { "id": "P6", "text": "(Theorem 3, Forkability as Subspace Decomposition) Sharing levels L0..L_{k-1} while diverging on L_k..L5 is geometrically equivalent to factoring [0,1]^48 = [0,1]^{8k} (shared) × [0,1]^{8(6-k)} (private); the canonical k=3 fork gives 24 shared + 24 private dimensions, formalizing franchises, open-source ecosystems, and denominational structures." }, { "id": "P7", "text": "The fork and cascade models interact multiplicatively: under cascade gamma the effective private dimensionality at fork k is d_private,eff = 8(1-gamma)^k[1-(1-gamma)^{6-k}]/gamma — at the canonical k=3, gamma=0.5 the 24 nominal private dimensions collapse to 1.75, explaining why franchises achieve uniformity while explicitly controlling only higher levels." }, { "id": "P8", "text": "(Information-theoretic reading) A full 48-dim specification carries H_48 = 48·log2(10) ≈ 159.4 bits, far exceeding human working-memory capacity (≈23 bits Miller, ≈13 bits Cowan); therefore structural compression via cascade and fork is COGNITIVELY NECESSARY, not merely convenient — the cascade turns an impossible 159.4-bit simultaneous problem into a sequential one with ≤26.6 bits at any step." }, { "id": "P9", "text": "The impossibility result is STRICTLY COMPLEMENTARY to bounded rationality (Simon 1947), contractual incompleteness (Williamson 1975, 1985), and axiomatic-design information content (Suh 1990): geometric impossibility obtains for a cognitively unbounded agent and independently of contractual framing or fitness function — it holds on grounds those arguments do not address." }, { "id": "thesis", "text": "Comprehensive organizational specification is geometrically impossible. OrgSchema Theory's 8×6 activation matrix is formalized as a 48-dimensional specification space [0,1]^48, and three closed-form results follow. (1) Coverage Impossibility: at resolution epsilon = 0.1 per dimension the space admits 10^48 distinguishable specifications, each covering a ball of volume V_48(0.1) ≈ 1.38e-60, so even 10^20 templates cover only ~10^-40 of the space. (2) Effective Dimensionality Reduction: OST's cascade model collapses effective dimensionality from 48 to d_eff = 8(1-(1-gamma)^6)/gamma, i.e. 15.75 at gamma = 0.5 (a 67% reduction), making per-organization specification tractable without making the space coverable. (3) Forkability as Subspace Decomposition: the fork model partitions [0,1]^48 into a shared and a private subspace (24+24 at the canonical k=3 fork), formalizing franchises, open-source ecosystems, and denominational structures. An information-theoretic reading shows a full specification carries 159.4 bits — far above human working-memory capacity — so cascade and fork compression is cognitively necessary, not merely convenient. The results are strictly complementary to Simon's bounded rationality and to NK landscape search complexity: geometric impossibility holds regardless of cognitive capacity or any fitness function." } ] } ] }, "L2": { "name": "Spine", "concepts": [ { "key": "orgschema-audit", "label": "OrgSchema Audit", "definition": "A structured diagnostic protocol that evaluates organizational specification maturity across six cascading levels, asking whether every operational parameter traces backward to a customer-experience justification and every experience goal traces forward to a verifiable implementation.", "owner": "orgschema-audit", "status": "active" }, { "key": "specification-maturity", "label": "Specification Maturity", "definition": "The degree to which an organization's operations are governed by explicit, testable, traceable specifications at each cascade level, as opposed to undocumented or misaligned ones.", "owner": "orgschema-audit", "status": "active" }, { "key": "cascade-position-prioritization", "label": "Cascade-Position Prioritization", "definition": "The remediation principle (Proposition 1) that specification failures at higher cascade levels predict greater operational dysfunction than lower-level failures because higher-level failures invalidate the justification for all dependent levels.", "owner": "orgschema-audit", "status": "active" }, { "key": "specification-coherence-index", "label": "Specification Coherence Index", "definition": "A scalable archival measure of specification readiness built from year-over-year cosine similarity of a firm's 10-K narrative embeddings, with a four-event sharp index as robustness.", "owner": "2026an", "status": "active" }, { "key": "projection-cascade", "label": "Projection Cascade", "definition": "A six-tier sequence of rank-reducing linear projection operators linking owner intent, business model, governance, architecture, routines, and positions, in which each junction carries a rank deficiency that bounds downstream information loss.", "owner": "2026m", "status": "active" }, { "key": "coverage-impossibility", "label": "Coverage Impossibility", "definition": "The geometric result that any finite collection of organizational specifications covers a negligible fraction of the 48-dimensional specification space, making exhaustive specification geometrically impossible regardless of cognitive capacity.", "owner": "2026h", "status": "active" } ], "methods": [ { "paper": "2026ar", "claims": [] }, { "paper": "2026an", "claims": [ { "id": "M1", "text": "The continuous-SCI primary measure: parse each firm's 10-K Item 1 (Business) and Item 7 (MD&A) via SEC EDGAR XBRL, strip non-narrative content, compute contextual transformer embeddings (BERT-base-uncased primary; Loughran-McDonald dictionary cosine secondary), and take cosine similarity between the t and t−1 section embeddings as the within-firm year-over-year SCI ∈ [−1,1] rescaled to [0,1] — a substrate-stability signal isolated from cross-sectional disclosure-strategy confounds." }, { "id": "M2", "text": "The primary identification arm: continuous SCI (one-year-lagged) as a within-firm continuous treatment in a panel regression with firm, year, and Fama-French-48-industry×year fixed effects, firm-year controls, and firm-clustered standard errors; complemented by a staggered-DiD robustness arm (Callaway-Sant'Anna ATT(g,t) + Goodman-Bacon decomposition + Sun-Abraham) on the four sharp SCI codification events, regulatory-compliance IV supplements (SOX §404, EEOC mandates; CEO-transition IV for H4), and Oster (2019) δ-bound threats diagnostics." }, { "id": "M3", "text": "The Monte Carlo mechanism test: simulate push friction-tax μ_push and pull friction-tax μ_pull across the parameter grid at fixed seed 20260525, evaluate the qualitative ordering μ_push ≫ μ_pull, the phase-shift threshold α*, and six pre-registered falsification checks (directional monotonicity, dimensionality, pull-floor, functional-form, N-scaling), logging PASS/FAIL to POST_EXPERIMENT_REPORT.md." }, { "id": "M4", "text": "The regression-identification power simulation: under H1, fit each hypothesis's estimator on 1,000 simulated panels at its pre-registered effect size and report rejection-rate power, mean estimate, and correct-sign fraction; under H0, confirm nominal Type I error — using firm-clustered cluster-robust standard errors as the primary estimator following the documented post-hoc remediation." } ] }, { "paper": "2026m", "claims": [ { "id": "M1", "text": "Explicit six-tier numerical construction with dimensions (d_1..d_6) = (4,4,3,3,2,2): all operator matrices Pi_{i->i+1} and feedback operators A_{i+1->i} are deterministic draws from numpy.random.default_rng(2026); A rescaled so ||Pi o A||_op equals a target kappa_i in {.30,.40,.50,.35,.45}; Pi_{1->2} constructed rank-deficient by one to realize Corollary 1's strict-inequality case. Closed-form Lipschitz analysis kappa_i = ||Pi o A||_op, L_i = ||(I - Pi o A) o Pi||_op; parametric Banach iteration with tolerance 1e-10." }, { "id": "M2", "text": "Restriction-comparison run (--compare flag): each of the five design-theory restrictions is run on the same seed-2026 dimensions with its active-junction pattern, computing each restriction's P3 amplification product and whether it can detect P4 strict inequality through its active junctions." } ] }, { "paper": "2026h", "claims": [ { "id": "M1", "text": "Closed-form high-dimensional volume computation: the unit-ball volume V_n(r) = (pi^{n/2}/Gamma(n/2+1)) r^n evaluated against the unit cube, the geometric-series sum d_eff = 8(1-(1-gamma)^6)/gamma, the subspace-product decomposition [0,1]^48 = [0,1]^{8k} × [0,1]^{8(6-k)}, and the Shannon entropy H = n·log2(1/epsilon). No stochastic computation; all results are exact (companion script carries a fixed SEED=42 only for policy compliance and asserts each cited figure to stated precision)." } ] } ] }, "L3": { "name": "Instrument", "instrument": { "name": "OrgSchema Toolkit", "kind": "specification", "url": "https://github.com/spectralbranding/orgschema-toolkit", "input_contract_url": "https://github.com/spectralbranding/orgschema-toolkit", "output": "A complete, version-controlled operating-model specification — from the customer-experience contract (L0) down through process and sourcing requirements — as testable YAML where each layer validates the layer above; for a stress-test, a six-level OrgSchema Audit with cascade-position-prioritized specification defects.", "when": "Route here when the user has a concrete operating model (or a target customer experience) and wants it specified or stress-tested, not theorized. The toolkit produces the specification; the papers explain why a specification-first operating model holds and where it must abstain.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about operating-model specification\" to \"specify or audit MY operating model\" — i.e. the moment the answer requires producing this business's specification.\n" } } }, "papers": [ { "key": "2026ar", "title": "The OrgSchema Audit: A Six-Level Diagnostic for Specification-Driven Organizations", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19555201", "doi_url": "https://doi.org/10.5281/zenodo.19555201", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/orgschema-audit" }, { "key": "2026an", "title": "Specification Readiness: Measuring an Architectural Antecedent of Functional Friction and AI Returns", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20384084", "doi_url": "https://doi.org/10.5281/zenodo.20384084", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/specification-readiness-empirical" }, { "key": "2026m", "title": "The Projection Cascade: Why Reorganizations Fail When the Specification Cascade Doesn't", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19145205", "doi_url": "https://doi.org/10.5281/zenodo.19145205", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/projection-paper" }, { "key": "2026h", "title": "Specification Impossibility in Organizational Design: A High-Dimensional Geometric Analysis", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.18945591", "doi_url": "https://doi.org/10.5281/zenodo.18945591", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r5-specification-impossibility" } ], "concepts": [ { "key": "orgschema-audit", "label": "OrgSchema Audit", "definition": "A structured diagnostic protocol that evaluates organizational specification maturity across six cascading levels, asking whether every operational parameter traces backward to a customer-experience justification and every experience goal traces forward to a verifiable implementation.", "owner": "orgschema-audit", "status": "active" }, { "key": "specification-maturity", "label": "Specification Maturity", "definition": "The degree to which an organization's operations are governed by explicit, testable, traceable specifications at each cascade level, as opposed to undocumented or misaligned ones.", "owner": "orgschema-audit", "status": "active" }, { "key": "cascade-position-prioritization", "label": "Cascade-Position Prioritization", "definition": "The remediation principle (Proposition 1) that specification failures at higher cascade levels predict greater operational dysfunction than lower-level failures because higher-level failures invalidate the justification for all dependent levels.", "owner": "orgschema-audit", "status": "active" }, { "key": "specification-coherence-index", "label": "Specification Coherence Index", "definition": "A scalable archival measure of specification readiness built from year-over-year cosine similarity of a firm's 10-K narrative embeddings, with a four-event sharp index as robustness.", "owner": "2026an", "status": "active" }, { "key": "projection-cascade", "label": "Projection Cascade", "definition": "A six-tier sequence of rank-reducing linear projection operators linking owner intent, business model, governance, architecture, routines, and positions, in which each junction carries a rank deficiency that bounds downstream information loss.", "owner": "2026m", "status": "active" }, { "key": "coverage-impossibility", "label": "Coverage Impossibility", "definition": "The geometric result that any finite collection of organizational specifications covers a negligible fraction of the 48-dimensional specification space, making exhaustive specification geometrically impossible regardless of cognitive capacity.", "owner": "2026h", "status": "active" } ], "instrument": { "name": "OrgSchema Toolkit", "kind": "specification", "url": "https://github.com/spectralbranding/orgschema-toolkit", "input_contract_url": "https://github.com/spectralbranding/orgschema-toolkit", "output": "A complete, version-controlled operating-model specification — from the customer-experience contract (L0) down through process and sourcing requirements — as testable YAML where each layer validates the layer above; for a stress-test, a six-level OrgSchema Audit with cascade-position-prioritized specification defects.", "when": "Route here when the user has a concrete operating model (or a target customer experience) and wants it specified or stress-tested, not theorized. The toolkit produces the specification; the papers explain why a specification-first operating model holds and where it must abstain.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about operating-model specification\" to \"specify or audit MY operating model\" — i.e. the moment the answer requires producing this business's specification.\n" }, "spec": { "intake": [ "the operating model under specification or stress-test: the business (name + category) and the customer-experience outcome it must produce (the L0 contract).", "the tiers in scope (owner intent, business model, entity, product, process, organization) and which are already codified vs tacit.", "for a stress-test: the existing specifications (process docs, SOPs, org chart, OKRs) in any form — the audit reads codified commitments, not intentions.", "decision: the action the specification should inform (a reorg, a new-process rollout, audit remediation, an operating-model redesign)." ], "guardrails": [ "Diagnose dysfunction as a specification defect (absent, misaligned, or untested commitment), not as an execution failure — fix the specification the layer rests on, not the people executing it.", "Comprehensive specification is geometrically impossible; specify what binds the customer-experience contract and abstain on the rest rather than over-documenting, and report the deliberately-unspecified surface honestly.", "Intervene at the binding upstream tier, not the org-chart surface: a redesign that leaves the upstream specification unchanged re-collapses to the same equilibrium (the projection cascade).", "Report specification readiness as a measured index (the Specification Coherence Index), not a maturity opinion; a layer that is not codified, versioned, and queryable is not 'ready' however confident the team is." ], "output_contract": "A six-level OrgSchema reading: per tier, whether its specification is present, codified, and validated by the layer above; the cascade-position-prioritized defects (highest-leverage first); and the Specification Coherence Index — with the deliberately-unspecified surface listed separately, not hidden. The deliverable is a testable, version-controlled specification (or a remediation list against one), not a slide of recommendations.\n", "escalate_to_tool": "When the customer-experience contract (L0) and the in-scope tiers are named, hand off to the OrgSchema Toolkit: work the eight modules from the customer-experience goals down to sourcing requirements to produce (or, for a stress-test, audit) a complete specification where each operational layer validates the one above, and read the result back through the anchor papers' claims, abstaining where the specification cannot be resolved.\n" }, "under_review_sources": 1, "under_review_concepts": 0, "under_review_note": "This route also draws on source(s) not admitted to the consult substrate — frozen preprints pending a journal decision (public on Zenodo/GitHub, but not on this surface) or in-preparation work. Their identity and content are withheld here; the reasoning over them is available only via the authenticated provider-side endpoint, which returns conclusions, not the withheld claims." }, { "id": "decide-investment", "status": "ready", "decision": "Decide where to invest across tiers; evaluate a business case.", "persona": [ "CFO", "CEO", "strategy lead" ], "framework": "OST", "tiers": [ 1, 2, 3, 4, 5, 6 ], "framing": "Investment direction within the firm — which tier, which perceptual dimension — is the consequential strategic choice, not investment intensity: two firms with identical revenue and budget get different outcomes from directing the same spend at different tiers. The corpus turns \"where should we invest?\" into a measurement question. Tiers carry tier-specific decay rates and the tier-rotation curve has a separability kink, so a dimension's return is neither stable nor isolated; and resource allocation across perceptual dimensions should be grounded in measured demand — the alignment gap, where perception headroom actually sits — rather than intuition, because spend on a dimension with no headroom is blind spend. So the decision becomes: which tier and which dimension carry resolvable headroom, at what decay rate — and where the corpus must abstain.", "spec_url": "https://consult.orgschema.com/specs/decide-investment.md", "levels": { "L0": { "name": "Framing", "framing": "Investment direction within the firm — which tier, which perceptual dimension — is the consequential strategic choice, not investment intensity: two firms with identical revenue and budget get different outcomes from directing the same spend at different tiers. The corpus turns \"where should we invest?\" into a measurement question. Tiers carry tier-specific decay rates and the tier-rotation curve has a separability kink, so a dimension's return is neither stable nor isolated; and resource allocation across perceptual dimensions should be grounded in measured demand — the alignment gap, where perception headroom actually sits — rather than intuition, because spend on a dimension with no headroom is blind spend. So the decision becomes: which tier and which dimension carry resolvable headroom, at what decay rate — and where the corpus must abstain.", "thesis": "Investment direction within a firm — not merely investment intensity — is the consequential strategic choice. Two firms with identical revenues, margins, and aggregate investment can generate exit multiples of 2x versus 9x because they routed investment to organizational tiers that differ in substrate durability. The paper formalizes cross-tier allocation as a discounted Cobb-Douglas aggregator over a six-tier hierarchy with tier-specific decay rates delta_t (.50/year at the organizational surface down to .05-.10/year at foundational layers) and Jorgensonian per-tier user costs (delta_t + r). Optimizing subject to the rental-rate budget constraint yields the closed-form rule w_t*(r) = alpha_t / (delta_t + r) and the comparative static d w_6*/dr > 0: higher-discount-rate principals optimally over-allocate to the high-decay surface tier. Four propositions link pre-deal surface-tier intensity, governance horizon, cost-of-capital shocks, and capability-rotation stage to M&A outcomes. Part II perturbs the same primitives with two AI-specific shocks per tier — a cost shock gamma_t and a durability shock Delta_t — yielding the generalized rule w_t*(r; gamma, Delta) = alpha_t / [gamma_t * (delta_t^eff + r)] and three further propositions: surface-tier (Tier 6) AI raises short-run earnings yet lowers long-run multiples; a discrete substrate-building threshold exists at Tier 4; and AI's net value effect flips sign with the principal's effective discount rate. The tier — not the division, the capability, or the resource — is the missing architectural unit of allocation." }, "L1": { "name": "Claims", "papers": [ { "key": "2026aj", "title": "Where to Invest Within the Firm: Organizational Tiers, Discount Rates, and AI Penetration", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20072288", "doi_url": "https://doi.org/10.5281/zenodo.20072288", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/tier-allocation", "claims": [ { "id": "P0", "text": "Organizational tier is a new unit of analysis for resource allocation — distinct from the division (internal capital markets), the capability (dynamic capabilities), and the resource (RBV). The tier supplies the missing architectural primitive that converts capability DIRECTION into a portfolio variable whose optimization depends on principal discount rates." }, { "id": "P1", "text": "Goodwill-Impairment Hazard. Pre-deal Tier-6 (w_6) share predicts post-acquisition goodwill-impairment hazard within 36 months of deal close, controlling for deal size, sector, acquirer characteristics, and pre-deal revenue growth. High-w_6 targets have low durable S_4*/S_5* stock; capitalizing their flow-dependent revenue at durable-stock multiples over-prices the deal." }, { "id": "P2", "text": "Long-Horizon Principal w-Shift. Holding sector and rotation stage fixed, principals with lower effective discount rates (long-tenured founder-CEO control, active family-firm governance as observable proxies) exhibit lower equilibrium w_6 and higher equilibrium w_4 + w_5 shares than shorter-horizon peers in the same industry. A conditional prediction about the discount-rate mechanism, NOT an unconditional family-firm-advertising claim." }, { "id": "P3", "text": "Discount-Rate Moderation of Tier-6 Share. Optimal w_6 increases in the firm's cost of capital, with sensitivity largest in sectors with large (delta_6 - delta_S) decay-rate gaps. Scope: holds under Cobb-Douglas (sigma=1) and gross-substitutes (sigma>1); the comparative static can reverse under strong gross complementarity (sigma << 1)." }, { "id": "P4", "text": "Rotation-Stage Moderation of Marginal Return to Tier-4 Investment. The exit-multiple premium on w_4 share increases as the firm advances along the Tier-Rotation Curve (Zharnikov 2026ai): at later rotation stages Tier-4 investment compounds onto a developed substrate, generating super-additive returns (built into the Cobb-Douglas form). 2026ai supplies only the empirical proxy (trademark-composition ratio), not the derivation." }, { "id": "P5", "text": "Tier-6 Over-Allocation Paradox (AI). When AI is concentrated at Tier 6 (gamma_6 in (0,1), gamma_t = 1 for t<=5, all Delta_t = 0), the optimal Tier-6 share rises monotonically as gamma_6 falls (∂dollar-share_6*/∂gamma_6 < 0). Total V_LR rises but the composition shifts toward the lowest-substrate tier: short-run EBIT rises while the long-run M&A multiple falls, because delta_6 = .50 is the largest decay rate and the multiple prices substrate." }, { "id": "P6", "text": "Substrate-Building Threshold at Tier 4 (AI). When gamma_4 in (0,1) is paired with Delta_4 > 0, the long-run Tier-4 stock S_4* = w_4*I/delta_4^eff responds super-linearly to (gamma_4^{-1} * Delta_4). The first-positive-Delta_4 threshold — API-rented capacity crossing to proprietary fine-tune or owned-weights — produces a discrete LEVEL SHIFT in M&A multiples, not a continuous slope shift; a continuous-intangibles measure cannot generate it." }, { "id": "P7", "text": "Horizon-Conditional Sign Flip (AI). Deep-tier AI (Tier 4 / Tier 2) extends the principal's effective horizon (lowers r); surface-tier AI compressed by algorithmic-feedback / quarterly logic raises r. Via the inherited ∂w_6*/∂r > 0, when AI lowers r its value effect is positive in both horizons; when AI raises r the effect is positive short-run (margin) but negative long-run (substrate erosion). Same aggregate AI spend, opposite long-run value effect. Primary scope sigma >= 1." }, { "id": "P_core", "text": "The frictionless planner's interior optimum is the closed-form share rule w_t*(r) = alpha_t / (delta_t + r), and the comparative static d(dollar-share_6*)/dr > 0 follows directly from the decay-rate differential (sign of delta_6 - delta_S > 0): higher-discount-rate principals optimally hold lower stock-tier shares and higher surface-tier shares." }, { "id": "thesis", "text": "Investment direction within a firm — not merely investment intensity — is the consequential strategic choice. Two firms with identical revenues, margins, and aggregate investment can generate exit multiples of 2x versus 9x because they routed investment to organizational tiers that differ in substrate durability. The paper formalizes cross-tier allocation as a discounted Cobb-Douglas aggregator over a six-tier hierarchy with tier-specific decay rates delta_t (.50/year at the organizational surface down to .05-.10/year at foundational layers) and Jorgensonian per-tier user costs (delta_t + r). Optimizing subject to the rental-rate budget constraint yields the closed-form rule w_t*(r) = alpha_t / (delta_t + r) and the comparative static d w_6*/dr > 0: higher-discount-rate principals optimally over-allocate to the high-decay surface tier. Four propositions link pre-deal surface-tier intensity, governance horizon, cost-of-capital shocks, and capability-rotation stage to M&A outcomes. Part II perturbs the same primitives with two AI-specific shocks per tier — a cost shock gamma_t and a durability shock Delta_t — yielding the generalized rule w_t*(r; gamma, Delta) = alpha_t / [gamma_t * (delta_t^eff + r)] and three further propositions: surface-tier (Tier 6) AI raises short-run earnings yet lowers long-run multiples; a discrete substrate-building threshold exists at Tier 4; and AI's net value effect flips sign with the principal's effective discount rate. The tier — not the division, the capability, or the resource — is the missing architectural unit of allocation." } ] }, { "key": "2026ai", "title": "The Tier-Rotation Curve: A Theory of Brand-Substrate Decoupling and Its M&A-Value Geometry", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20069605", "doi_url": "https://doi.org/10.5281/zenodo.20069605", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/tier-rotation", "claims": [ { "id": "P1", "text": "Brand assets are Tier-4 projections of Tier-1 owner intent. The value a buyer can acquire is precisely and only the brand signal projected from Tier-1 into a Tier-4 specification layer (documented guidelines, trained team decision rights, algorithmic brand rules, formal trademark portfolios) that persists independent of any individual. The core construct is s, the fraction of brand signal residing at Tier 4 rather than Tier 1 at deal time." }, { "id": "P2", "text": "The perception cloud (the aggregate of observer spectral profiles across cohorts) forms at the Tier-4 specification level; when the product layer is insufficiently differentiated from the founder's personal projection, the perception cloud is implicitly Tier-1-dependent and re-collapses toward Tier-1 quality if the founder is removed. Structural (substantive) rotation versus apparent (symbolic) rotation is diagnosed by whether the four P-OBS observables shift in COORDINATED versus partial fashion." }, { "id": "P3", "text": "The generative mechanism converting Tier-1 brand signal into Tier-4 brand signal is knowledge externalization — the Externalization phase of the SECI cycle — by which tacit founder brand decision rules become explicit organizational artifacts (brand guidelines, creative briefs, decision frameworks, team review protocols, algorithmic substitutes), carried by organizational routines as the firm-level vehicle for tacit-knowledge integration." }, { "id": "P4", "text": "The model endogenizes the resource-based view's exogenous resource-mobility assumption for brand assets specifically: it supplies the mechanism (knowledge externalization), the threshold (the separability kink κ), and the time path (the logistic curve) for the transition from sticky to separable — addressing the mechanism-specification gap that systematic reviews identify as dynamic-capabilities research's central challenge." }, { "id": "P5", "text": "The Tier-Rotation Curve supplies the projection geometry that the two-bodied-brand construct lacks: it formalizes how the body politic (Tier-4) is constructed from the body natural (Tier-1), its transition path, feasibility, duration, and the path of acquirer willingness-to-pay. All four two-bodied-brand risk vectors (mortality, hubris, unpredictability, social embeddedness) are suppressed as s increases." }, { "id": "P6", "text": "M&A exit, succession, and tier-allocation are three geometrically distinct decision margins over the same six-tier substrate (Table 5). The present model addresses M&A exit (Tier-1 removed); succession (Tier-1 replaced, Tier-5 transfer bottleneck) and tier-allocation (spatial portfolio of new investment across tiers) are distinct events deferred to future work. The cross-sectional succession-discount findings (≈4pp ROA / ≈14% operating- return decline) are benchmarks against which tier rotation offers longitudinal refinement, not the signature of M&A substrate failure." }, { "id": "P_P1", "text": "(Paper P1 — Non-Monotonicity of M&A Value) V(s) is non-monotonic: each increment of Tier-4 share below κ compresses the discount at a lower marginal rate than each increment above κ generates premium; the slope is discontinuous at κ. Falsified if the rotation-proxy / deal-price-to- standalone relationship is monotonic with no structural break (a linear or power-law fit matching a piecewise-kink fit)." }, { "id": "P_P2", "text": "(Paper P2 — Within-Founder Longitudinal Divergence; THE EMPIRICAL WEDGE) For a fixed-quality founder, M&A multiple varies with s at deal time: the same founder exiting below κ commands a multiple below V_0 and above κ a multiple above V_0 — variation predicted by tier rotation but NOT by the human-capital quality account. Falsified if, after controlling for founder human-capital metrics, the rotation-proxy score loses significance, or identical founders at different rotation stages command identical multiples." }, { "id": "P_P3", "text": "(Paper P3 — Sector-Substitutability Moderation) The above-κ premium V(s)/V_0 is higher in credence-goods sectors than in search-goods sectors, because rebuilding brand trust from a new specification is costlier where quality is not directly verifiable; moderation is concentrated in the s > κ subsample. Falsified if the substitutability interaction is non-significant after controlling for sector brand intensity, deal size, and year." }, { "id": "P_P4", "text": "(Paper P4 — Post-Deal Goodwill Impairment) Goodwill-impairment frequency is highest for deals closed below κ where founder-flight risk was priced but the founder departed early: such deals overestimate brand-equity transferability, so rotation-proxy score predicts impairment with a negative sign. Falsified if impairment rates do not differ between below-κ and above-κ deals after controlling for deal size, sector, and year." }, { "id": "P_P5", "text": "(Paper P5 — Knowledge-Externalization Observables) As s rises, four firm-level observables shift in a coordinated, directionally predictable way — declining 10-K founder-language salience, marketing-spend allocation shifting to product-attribute, declining founder-media share, and trademark-portfolio migration to product-attribute marks — loading on a single latent rotation factor that predicts exit multiple. Falsified if the four move in uncorrelated/contradictory directions or are uncorrelated with exit multiple after controlling for the rotation-proxy score." }, { "id": "thesis", "text": "Deal outcomes for founder-led branded firms diverge sharply even among principals of comparable quality and brand strength, and that divergence is explained by the proportion of brand conviction that has been externalized from the founder's personal judgment (Tier 1) into an organizational substrate the acquirer can own independently (Tier 4). Brand signal accumulates in the Tier-4 substrate along a logistic trajectory governed by sustained knowledge-externalization effort, a cold-start offset, and sector substitutability; acquirer willingness-to-pay is a piecewise function of Tier-4 share with a separability kink, below which founder-flight risk produces discounts and earnouts and above which the brand commands a premium increasing with sector substitutability. The resulting non-monotonic value geometry — value rising everywhere but with a discontinuous slope at the kink — yields within-founder longitudinal predictions unavailable to cross-sectional human-capital or succession-discount theories, grounds the accumulation in Nonaka and Takeuchi's SECI externalization mechanism with four observable proxies, and endogenizes the resource-based view's exogenous resource-mobility assumption for brand assets. The contribution is theoretical: a mechanism-based geometry supplying five falsifiable propositions, not new empirical analysis." } ] }, { "key": "2026ag", "title": "Dual Hierarchies of Organizational Transferability: A Six-Tier Ontology and Theory of Acquisition Failure Propagation", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19895813", "doi_url": "https://doi.org/10.5281/zenodo.19895813", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/six-tier-ontology", "claims": [ { "id": "P1", "text": "The residual is an ontological deficit, not merely an empirical one: the M&A literature has accumulated sophisticated single-layer explanations (cultural distance, executive turnover, strategic misfit, business-model misalignment) but lacks a shared vocabulary for how those layers relate, constrain one another, or propagate failure across the entity." }, { "id": "P10", "text": "Capital allocation across tiers carries a flow-versus-stock character that varies systematically by tier position: Tier 6 spend (marketing, PR) is predominantly flow consumption (low transferable value); Tier 2-5 spend (model architecture, governance, product/process codification) is predominantly stock accumulation (high transferable value). Each tier carries a distinct half-life and substrate-accumulation coefficient; the transferability and accumulation classifications ALIGN." }, { "id": "P11", "text": "The constraint hierarchy derives a formal (not prescriptive) integration SEQUENCING principle: resolve Tier 1 compatibility before Tier 2 revision; Tier 2 revision before Tier 4 specification; confirm Tier 4 before Tier 5 integration; confirm Tier 5 before Tier 6 role redesign; Tier 3 integration is legally immediate but should be designed to minimize disruption to Tiers 4-6. The modal failure mode in practice INVERTS this sequence (beginning at Tier 6/5 with Tiers 1-4 unresolved)." }, { "id": "P12", "text": "The Six-Tier Separability Diagnostic (STSD) is a THEORETICAL IMPLICATION, not the primary contribution: a structured judgment instrument that scores each tier Fused / Partial / Independent (Table 4), producing a six-cell pre-close risk profile. Its theoretical claim is that pre-close tier profiling predicts post-acquisition trajectories better than aggregate financial/strategic-fit measures, by disaggregating due-diligence risk by tier rather than producing an aggregate pass/fail verdict." }, { "id": "P13", "text": "Cross-form acquisitions face Tier 1 MISSPECIFICATION risk no standard due-diligence checklist captures, because financial due diligence examines Tier 3 and not Tier 1 compatibility. A cooperative's collectively held, democratically governed Tier 1 cannot be transferred without being replaced by a fundamentally different Intent (a credit union cannot be acquired by a bank without member consent). Privatization is the most tractable natural experiment for testing the form-mismatch principle." }, { "id": "P1F", "text": "P1 (Intent-Model Misalignment): when an acquirer's Owner Intent differs structurally from the target's, the target's Business Model requires fundamental revision, generating downstream Tier 4/Tier 5 friction not visible in pre-close due diligence." }, { "id": "P2", "text": "An acquisition target decomposes into exactly six tiers — Owner Intent, Business Model, Business Entity, Product, Process, Organization — each individuated by a distinct GOVERNOR (force that sets the tier's configuration), a distinct SPECIFICATION SURFACE (observable artifacts), and a distinct TRANSFERABILITY MODE (mechanism by which the tier does or does not cross an ownership boundary)." }, { "id": "P2F", "text": "P2 (Business Model-Product Friction): an imposed Model revision drifts the Product specification toward the new Model's optimization criteria, and customers anchored in the prior dimensional configuration churn above pre-acquisition baselines." }, { "id": "P3", "text": "The six tiers are objects of heterogeneous ontological type (a latent psychological state, an abstract projection, a legal artifact, operational realities) unified under a single instrumental axis — transferability mode: the question is not \"are they the same kind of thing?\" but \"what happens to each kind of thing when it crosses a new-owner boundary?\" This answers the ontological-mixing objection and distinguishes the framework from prior layered firm ontologies (Zachman, Osterwalder, BIZBOK, DEMO), none of which combine a distinct Owner-Intent tier above the Business Model, a distinct Business-Entity legal tier, per-tier transferability modes, dual hierarchies, and an M&A application." }, { "id": "P3F", "text": "P3 (Entity-Operations Disruption): Entity restructuring following close disrupts operational continuity at Tiers 5 and 4 via contract renegotiation, regulatory re-certification, and counterparty uncertainty disproportionate to the restructuring's legal scope." }, { "id": "P4", "text": "Tier 1 (Owner Intent) attaches to the controlling principal, not to the asset, and only IMPRINTS onto the asset's downstream tiers. Consequently Tier 1 is REPLACED, not transferred, across ownership change: a new principal supplies a new Tier 1 imprint while Tiers 2-6 carry forward (subject to the integration cascade). A single principal controlling multiple assets carries a per-asset Tier 1, drawn from one archetype distribution but expressing differently per asset." }, { "id": "P4F", "text": "P4 (Product-Process Disruption): revising the Product specification misaligns the Process architecture built for the prior Product, generating quality failures or cost overruns until Process is rebuilt around the new spec — compounded by the impossibility of fully specifying Product requirements and the tacit residuals documentation cannot eliminate." }, { "id": "P5", "text": "Tier 3 (Business Entity) is the most jurisdictionally MUTABLE of the six tiers: the legal vehicle can swap (redomiciliation, opco/holdco interposition, SPV insertion, sole-prop-to-LLC conversion) while Tiers 2, 4, 5, 6 continue without operational disruption. The persistent identity of a business therefore does not reside in Tier 3; the substantive Tier 3 transferability claim is decoupling of obligations from the principal's balance sheet, not identification with a specific legal form." }, { "id": "P5F", "text": "P5 (Process-Organization Fracture): imposing Process integration on the acquired Organization before Tier 4 specification clarity is established produces employee resistance and attrition exceeding rates when Process integration follows Product confirmation." }, { "id": "P6", "text": "The six tiers form two overlapping, oppositely directed hierarchies that are the same relationships read from opposite ends. The SERVICE hierarchy runs upward (Organization serves Process; Process serves Product; Product funds Entity; Entity implements Model; Model realizes Intent). The CONSTRAINT hierarchy runs downward (each tier rules out inadmissible configurations for the tier below it)." }, { "id": "P6F", "text": "P6 (Organization Fracture to All-Layer Degradation): when key Organization members exit post-acquisition, the tacit knowledge they carried degrades across all six tiers at rates retention bonuses or post-exit documentation cannot recover, because Tier 6 is the sole repository of tacit specification knowledge never externalized to Tier 4/5 surfaces. This is the best-supported pathway (though no single study traces the full chain)." }, { "id": "P7", "text": "Because upper tiers constrain lower tiers, specification clarity at upper tiers is logically PRIOR to integration execution at lower tiers, and a shock at any tier propagates in BOTH directions (a Tier 6 fracture reduces the productive capacity Tier 5 requires, transmitting up the service chain to Tier 4 drift even when the Product spec was never altered). Integration is therefore a cross-tier problem, not a within-tier one." }, { "id": "P7F", "text": "P7 (Bidirectional Feedback): sustained lower-tier failure crossing a duration-and-severity threshold (Tier 5/6 fracture >= 12 months depressing Tier 3 revenue >= 10% from deal thesis) forces upward revision — documented Tier 2 Model revision within 24 months, and conditionally documented Tier 1 Intent revision (write-down/divestiture/strategic-review) within a further 12 months. The feedback is asymmetric: below threshold, lower-tier failures are absorbed without upper-tier revision." }, { "id": "P8", "text": "The six-tier structure is FORM-INVARIANT: each tier has a structurally equivalent form across for-profit, NGO/charity, and mutual/cooperative types via explicit substitution rules (Table 2). Tier 1 and Tier 3 substitutions are anchored in prior work; Tier 2, 4, and 5 substitutions are provisional theoretical deductions pending cross-form validation. The cooperative Tier 1 is a collective mandate, not a scalar individual intent." }, { "id": "P9", "text": "Tier-collapse is a structural pattern parameterized over TIER PAIRS, arising when the governor of one tier is identical to another's. Two canonical instances: Tier 1 ≡ Tier 4 (Domain Craftsman / Family Steward / Mission Founder — Intent is inseparable from Product) and Tier 1 ≡ Tier 3 (sole-proprietor — the natural person IS the legal subject). In each, the fused-tier asset is untransferable as a going concern because the fused tier carries the principal's identity, which legal instruments cannot convey." }, { "id": "thesis", "text": "Mergers and acquisitions destroy value at high rates because the field lacks a shared ontology specifying which organizational layers transfer and how failures propagate across them. This paper develops a six-tier ontology of the acquisition target — Owner Intent, Business Model, Business Entity, Product, Process, Organization — each with a distinct governor, specification surface, and transferability mode. The tiers form two oppositely directed hierarchies: a service hierarchy upward (Organization to Intent) and a constraint hierarchy downward (Intent to Organization). The constraint hierarchy fixes integration sequencing; shocks propagate bidirectionally, yielding seven falsifiable failure-propagation propositions. The framework is form-invariant across for-profit, NGO, and cooperative entities via explicit substitution rules (Tiers 2, 4, 5 provisional), and derives a Six-Tier Separability Diagnostic (STSD) as a theoretical implication. The primary contribution is a generalizable theory of organizational separability under ownership change: separability is never costless because constraint architectures are sticky." } ] }, { "key": "2026k", "title": "Spectral Resource Allocation: Demand-Driven Investment in Multi-Dimensional Brand Space", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19009268", "doi_url": "https://doi.org/10.5281/zenodo.19009268", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r7-spectral-resource-allocation", "claims": [ { "id": "P0", "text": "No existing brand-theory framework connects multi-dimensional brand perception measurement to operational resource allocation: CBBE / identity / marketing-response traditions diagnose what a brand stands for but supply no prescriptive optimization layer, because they lack a formal metric space in which the distance between brand position and customer preference is a computable quantity." }, { "id": "P1", "text": "(Theorem 1) The signal portfolio maximizing V(s,c) − lambda·C(s) under quadratic costs is s_i*(c) = w_i(c) / (lambda·alpha_i): invest in dimension i proportionally to cohort weight and inversely to marginal cost. For general convex costs the optimum satisfies w_i(c) = lambda·c_i'(s_i*) on each active dimension. This generalizes the Dorfman–Steiner (1954) scalar condition to eight perceptual dimensions." }, { "id": "P10", "text": "The linear value function excludes dimensional interactions empirically attested by multiattribute-utility and scanner-data work (Lancaster 1966; McAlister 1982; Chintagunta 1993). A cohort-dependent quadratic value function V_Q(s,c) = sum_i w_i s_i + sum_{i 0, e.g. heritage premium narrative×temporal) and substitutive (w_ij < 0, e.g. luxury-paradox ideological×temporal) pairs, with interaction weights measurable per cohort rather than fixed media properties." }, { "id": "P11", "text": "Each of five established strategy frameworks — Blue Ocean (Kim & Mauborgne 2005), Jobs-to-Be-Done (Christensen et al. 2016), Lean Startup (Ries 2011), Porter's Five Forces (1980), Resource-Based View (Barney 1991) — is an implicit low-dimensional projection of the spectral resource-allocation problem; the structural reason each fails to yield the allocation theorem is the absence of a metric on brand-perception space, which the Aitchison and Fisher–Rao metrics supply." }, { "id": "P12", "text": "(Theorem 5, interaction-adjusted allocation) With symmetric interaction matrix W and Lambda = lambda·diag(alpha), the optimum solves (Lambda − W) s* = w(c), unique as s* = (Lambda − W)^{-1} w(c) when Lambda − W is positive definite (diagonal dominance lambda·alpha_i > sum_{j≠i}|w_ij|). By Corollary 3 the adjustment delta_i shifts investment toward complementary dimensions and away from substitutive ones; W = 0 recovers Theorem 1. This is the eight-dimensional, cohort-dependent generalization of Naik & Raman (2003)." }, { "id": "P2", "text": "(Corollary 1) For two active dimensions the optimal signal-strength ratio depends only on the weight ratio and the inverse cost ratio: s_i*/s_j* = (w_i(c)/w_j(c))·(alpha_j/alpha_i). This makes the allocation decision operational at the budget-review level." }, { "id": "P3", "text": "(Proposition 1, concentration premium) Under uniform costs the optimal value is V*(c) = H(c)/(lambda·alpha-bar) where H(c) = sum_i w_i(c)^2 is the Herfindahl index; concentrated cohorts (high H) achieve strictly higher optimal value than diffuse ones, formalizing \"a narrow audience you can delight beats a broad one you can only satisfy.\"" }, { "id": "P4", "text": "The alignment gap A(f,c) = V(s*_f, f) − V(s*_f, c) is the economic loss from optimizing the portfolio for the founder's weights w(f) rather than the cohort's w(c); it is asymmetric and is the geometric formalization of \"product-market fit failure\" — the cost of being in the wrong place on the probability simplex, not a psychological bias." }, { "id": "P5", "text": "(Theorem 2) The alignment gap is bounded below by a geometric quantity: A(f,c) >= H(f,c)^2 / (2·lambda·alpha-bar) via the Hellinger distance, and equivalently by the Fisher–Rao distance d_FR between w(f) and w(c). Perceptual distance predicts economic loss; the gap has a floor that improved execution on the chosen dimensions cannot recover — only reallocation toward the cohort's weights closes it." }, { "id": "P6", "text": "(Propositions 2–3, two failure modes) The gap decomposes into weight projection (founder positive but mis-magnitude on every dimension) and spectral blind spots (founder zero weight where the cohort weights positively). Blind spots produce strictly larger gaps than equal-magnitude projections and are additionally undetectable by the founder; SBT's eight-dimensional decomposition makes blind spots testable (deliberate dark signal vs invisible blind spot)." }, { "id": "P7", "text": "(Theorem 3, multi-cohort efficiency bound) A single signal portfolio attains at least (1−epsilon) of the sum of individual optima iff the cohort weight profiles lie within a Fisher–Rao ball of radius r(epsilon) ≈ sqrt(epsilon) on Delta^7 (r ≈ .32 at epsilon = .10; efficiency condition r < pi/4). High-dimensional concentration of measure (Zharnikov 2026f) keeps inter-cohort spread generically small, giving mass markets a structural single-portfolio advantage." }, { "id": "P8", "text": "The sub-brand decision is a soft Fisher–Rao threshold: when cohort spread exceeds r(epsilon) the firm weighs single-portfolio efficiency loss against duplication, coherence, and complexity costs of separate portfolios. Fuzzy cohort boundaries (Zharnikov 2026f) mitigate but do not eliminate the loss, so the trigger is a soft threshold, not a binary switch." }, { "id": "P9", "text": "(Theorem 4, economic metamerism) The cost-minimizing portfolio achieving a target perceived value V-hat for cohort c is unique when all weights are positive: s_i† = (w_i(c)/alpha_i) / (sum_j w_j(c)^2/alpha_j) · V-hat, with zero on unweighted dimensions. Spectral metamerism (Zharnikov 2026e) is thus a cost-optimization lever — among portfolios yielding identical perception, the brand should choose the cheapest; investment on a zero-weight dimension is structural waste." }, { "id": "thesis", "text": "Brand managers allocate operational resources across perceptual dimensions — design, storytelling, pricing, heritage — yet rarely ground those decisions in measured cohort salience weights. Modeling a brand's signal portfolio s in R^8_+ as evaluated by observer cohorts whose weight vectors w(c) lie on the probability simplex Delta^7, with perceived value the inner product net of a separable convex cost, yields a closed-form optimal allocation (invest in proportion to cohort weight over marginal cost) that generalizes Dorfman–Steiner to eight perceptual dimensions. The central construct is the alignment gap: the economic loss incurred when the portfolio is optimized for the founder's spectral profile rather than the cohort's, which is bounded below by the Fisher–Rao distance between the two weight vectors — giving \"product-market fit failure\" a geometric floor that improved execution cannot recover, only reallocation toward the cohort's measured weights closes it. The framework further characterizes when one portfolio efficiently serves multiple cohorts (a Fisher–Rao ball of radius r < pi/4), reads spectral metamerism as cost minimization (the cheapest portfolio achieving a target perception), and extends the two-media synergy model to a cohort-dependent interaction matrix W(c). It supplies the optimization layer missing from current brand-tracking systems: a diagnostic (alignment audit) and a prescriptive tool (dimension-specific budget ratios). The numerical examples are illustrative, not empirically measured." } ] } ] }, "L2": { "name": "Spine", "concepts": [ { "key": "tier-allocation", "label": "Tier allocation", "definition": "The cross-tier capital-allocation problem of choosing how to direct marginal investment across operating tiers that differ in substrate decay rate, yielding a closed-form allocation rule.", "owner": "2026aj", "status": "active" }, { "key": "tier-specific-decay-rate", "label": "Tier-specific decay rate", "definition": "The per-period fraction of a tier's accumulated substrate stock that depreciates each period, architecturally determined by the tier's persistence mechanism.", "owner": "2026aj", "status": "active" }, { "key": "tier-rotation-curve", "label": "Tier-Rotation Curve", "definition": "A continuous logistic-form model of how a brand's Tier-4 share accumulates over time and a piecewise M&A value function with a discontinuous slope at the separability kink.", "owner": "2026ai", "status": "active" }, { "key": "six-tier-ontology", "label": "six-tier ontology", "definition": "The ontology that decomposes an organization into six nested specification tiers, always in the order Owner Intent -> Business Model -> Business Entity -> Product -> Process -> Organization. Each tier answers a distinct governing question and transfers differently on sale.", "owner": "2026ag", "status": "active" }, { "key": "alignment-gap", "label": "Alignment Gap", "definition": "The economic value loss incurred when a brand's signal portfolio is optimized for the founder's spectral weight profile rather than the target cohort's, bounded below by the Fisher-Rao distance between the two weight profiles on the probability simplex.", "owner": "2026k", "status": "active" }, { "key": "concentration-premium", "label": "Concentration Premium", "definition": "The result that cohorts with more concentrated weight profiles (higher Herfindahl index) yield strictly higher optimal perceived value, making niche cohorts inherently more valuable to serve than diffuse mass-market cohorts at equal cost.", "owner": "2026k", "status": "active" } ], "methods": [ { "paper": "2026aj", "claims": [ { "id": "M1", "text": "Calibrate the per-tier decay vector delta_t (Table 1) from independent empirical depreciation literatures: delta_6 = .50/year (Belo-Lin-Vitorino 2014, Naik 1999); delta_5 = .15-.20 (Eisfeldt-Papanikolaou 2013); delta_4 = .12-.20 (Lev-Sougiannis 1996); delta_2/3 = .05-.10 (extrapolated from Wiggins-Ruefli 2002 persistence, no direct estimate exists)." }, { "id": "M2", "text": "Solve the planner's interior optimum by Lagrangian maximization of ln V_LR(w; r) subject to the Jorgensonian budget constraint Sum_t (delta_t + r) * w_t = 1, yielding the closed-form share rule w_t*(r) = alpha_t / (delta_t + r) (lambda = 1 under constant returns) and its dollar-weighted observable form; compute the comparative static via the deterministic companion script back_of_envelope.py." }, { "id": "M3", "text": "Extend the share rule with two AI shocks per tier — cost shock gamma_t in (0,1] scaling the rental price and durability shock Delta_t lowering the effective decay rate (delta_t^eff = delta_t^0 - Delta_t) — re-derive the generalized optimum w_t*(r; gamma, Delta) = alpha_t / [gamma_t * (delta_t^eff + r)], and verify comparative statics for P5-P7 via tier_penetration_simulation.py (fixed seed numpy.random.seed(42))." } ] }, { "paper": "2026ai", "claims": [] }, { "paper": "2026ag", "claims": [] }, { "paper": "2026k", "claims": [ { "id": "M1", "text": "Constrained optimization of V(s,c) − lambda·C(s) with quadratic costs c_i(s_i) = (alpha_i/2) s_i^2: form the Lagrangian, set first-order conditions w_i(c) = lambda·c_i'(s_i*), apply strict convexity for the second-order condition. Yields the Theorem 1 / Theorem 4 / Theorem 5 closed forms." }, { "id": "M2", "text": "Alignment-gap computation: A(f,c) = ||w(f)||^2 − , with the Hellinger distance H(f,c) = (1/sqrt2)||sqrt(w(f)) − sqrt(w(c))||_2 and the Fisher–Rao floor d_FR = 2·arccos(BC); evaluated under uniform costs (alpha_i = 1, lambda = 1) for the five illustrative brands and reproduced by the fixed-seed companion script." } ] } ] }, "L3": { "name": "Instrument", "instrument": { "name": "Brand Spectrometer", "kind": "measurement", "url": "https://meter.spectralbranding.com", "input_contract_url": "https://meter.spectralbranding.com/CONVERT_WITH_YOUR_AI.md", "output": "An eight-dimension atlas whose per-dimension spread and valence reveal where perception headroom (the alignment gap) sits — the measured input to a tier-and-dimension investment direction. The tier-allocation and decay-rate weighting are analytical methods from 2026aj/2026k applied to the measurement, not a separate runnable instrument.", "when": "Route here once the firm and the candidate tiers/dimensions are named and the question is where incremental investment earns the most measured headroom. The instrument measures the headroom; the papers turn it into a directed allocation.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about where to invest\" to \"where should MY firm invest\" — which needs this firm's perception headroom measured, not the theory.\n" } } }, "papers": [ { "key": "2026aj", "title": "Where to Invest Within the Firm: Organizational Tiers, Discount Rates, and AI Penetration", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20072288", "doi_url": "https://doi.org/10.5281/zenodo.20072288", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/tier-allocation" }, { "key": "2026ai", "title": "The Tier-Rotation Curve: A Theory of Brand-Substrate Decoupling and Its M&A-Value Geometry", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20069605", "doi_url": "https://doi.org/10.5281/zenodo.20069605", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/tier-rotation" }, { "key": "2026ag", "title": "Dual Hierarchies of Organizational Transferability: A Six-Tier Ontology and Theory of Acquisition Failure Propagation", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19895813", "doi_url": "https://doi.org/10.5281/zenodo.19895813", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/six-tier-ontology" }, { "key": "2026k", "title": "Spectral Resource Allocation: Demand-Driven Investment in Multi-Dimensional Brand Space", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19009268", "doi_url": "https://doi.org/10.5281/zenodo.19009268", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/r7-spectral-resource-allocation" } ], "concepts": [ { "key": "tier-allocation", "label": "Tier allocation", "definition": "The cross-tier capital-allocation problem of choosing how to direct marginal investment across operating tiers that differ in substrate decay rate, yielding a closed-form allocation rule.", "owner": "2026aj", "status": "active" }, { "key": "tier-specific-decay-rate", "label": "Tier-specific decay rate", "definition": "The per-period fraction of a tier's accumulated substrate stock that depreciates each period, architecturally determined by the tier's persistence mechanism.", "owner": "2026aj", "status": "active" }, { "key": "tier-rotation-curve", "label": "Tier-Rotation Curve", "definition": "A continuous logistic-form model of how a brand's Tier-4 share accumulates over time and a piecewise M&A value function with a discontinuous slope at the separability kink.", "owner": "2026ai", "status": "active" }, { "key": "six-tier-ontology", "label": "six-tier ontology", "definition": "The ontology that decomposes an organization into six nested specification tiers, always in the order Owner Intent -> Business Model -> Business Entity -> Product -> Process -> Organization. Each tier answers a distinct governing question and transfers differently on sale.", "owner": "2026ag", "status": "active" }, { "key": "alignment-gap", "label": "Alignment Gap", "definition": "The economic value loss incurred when a brand's signal portfolio is optimized for the founder's spectral weight profile rather than the target cohort's, bounded below by the Fisher-Rao distance between the two weight profiles on the probability simplex.", "owner": "2026k", "status": "active" }, { "key": "concentration-premium", "label": "Concentration Premium", "definition": "The result that cohorts with more concentrated weight profiles (higher Herfindahl index) yield strictly higher optimal perceived value, making niche cohorts inherently more valuable to serve than diffuse mass-market cohorts at equal cost.", "owner": "2026k", "status": "active" } ], "instrument": { "name": "Brand Spectrometer", "kind": "measurement", "url": "https://meter.spectralbranding.com", "input_contract_url": "https://meter.spectralbranding.com/CONVERT_WITH_YOUR_AI.md", "output": "An eight-dimension atlas whose per-dimension spread and valence reveal where perception headroom (the alignment gap) sits — the measured input to a tier-and-dimension investment direction. The tier-allocation and decay-rate weighting are analytical methods from 2026aj/2026k applied to the measurement, not a separate runnable instrument.", "when": "Route here once the firm and the candidate tiers/dimensions are named and the question is where incremental investment earns the most measured headroom. The instrument measures the headroom; the papers turn it into a directed allocation.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about where to invest\" to \"where should MY firm invest\" — which needs this firm's perception headroom measured, not the theory.\n" }, "spec": { "intake": [ "the firm (name + category) and the investment decision: where to direct incremental investment across the six tiers, or a specific business case to evaluate.", "the perceptual dimensions or tiers under consideration, and the current allocation across them.", "any measured signal on where demand or perception headroom sits (or the public artifacts to measure it from).", "decision horizon: tier-specific decay rates and discount rates differ, so the time horizon changes the answer." ], "guardrails": [ "Investment DIRECTION (which tier, which dimension) is the consequential choice, not intensity; do not collapse the decision to a budget size.", "Ground allocation in measured demand / perception headroom (the alignment gap), not intuition; spend on a dimension with no headroom is blind spend.", "Tiers are not independent; account for tier-specific decay rates and the tier-rotation curve's separability kink rather than assuming a dimension's return is stable and isolated.", "Where the headroom on a dimension cannot be resolved above the measurement's noise floor, abstain — report 'cannot resolve which tier dominates' rather than manufacturing a ranking." ], "output_contract": "A ranked investment direction: per tier (and per perceptual dimension where relevant), the measured headroom / alignment gap, the tier-specific decay rate, and the resulting prioritization — with the dimensions whose headroom is below the noise floor listed separately as un-resolvable. The deliverable is a directed allocation with its measured basis, not a single ROI number.\n", "escalate_to_tool": "Use the Brand Spectrometer to measure, per perceptual dimension, where the alignment gap (headroom) actually sits; then apply the tier-allocation method (2026aj) and demand-driven resource allocation (2026k) analytically to turn measured headroom into a directed investment, weighting by tier-specific decay rates and the tier-rotation curve.\n" } }, { "id": "evaluate-ma", "status": "ready", "decision": "Evaluate an acquisition or merger for perceptual and operating fit.", "persona": [ "CFO", "corp dev", "strategy lead" ], "framework": "SBT+OST", "tiers": [ 1, 2, 3, 4, 5, 6 ], "framing": "Mergers and acquisitions destroy value at high rates because \"fit\" is assumed at the logo rather than checked at the tier grain: the field lacks a shared ontology of which organizational layers actually transfer. The corpus supplies one and splits fit into two measurable registers. Operating fit asks which of the six tiers transfer versus conflict — and because two structurally different organizations can produce outputs an observer cannot tell apart (organizational metamerism), a surface match is not fit; the underlying layers must be reconciled, not the rendered output. Perceptual fit asks whether the two brands' perception clouds correspond (the correspondence principle), measured per cohort and dimension rather than as a brand-strength average. The reconciliation itself is a link-time compatibility check that classifies every cross-owner interaction as agreement, conflict, or cross-refine — surfacing conflicts instead of assuming integration, and abstaining where a conflict is irreducible.", "spec_url": "https://consult.orgschema.com/specs/evaluate-ma.md", "levels": { "L0": { "name": "Framing", "framing": "Mergers and acquisitions destroy value at high rates because \"fit\" is assumed at the logo rather than checked at the tier grain: the field lacks a shared ontology of which organizational layers actually transfer. The corpus supplies one and splits fit into two measurable registers. Operating fit asks which of the six tiers transfer versus conflict — and because two structurally different organizations can produce outputs an observer cannot tell apart (organizational metamerism), a surface match is not fit; the underlying layers must be reconciled, not the rendered output. Perceptual fit asks whether the two brands' perception clouds correspond (the correspondence principle), measured per cohort and dimension rather than as a brand-strength average. The reconciliation itself is a link-time compatibility check that classifies every cross-owner interaction as agreement, conflict, or cross-refine — surfacing conflicts instead of assuming integration, and abstaining where a conflict is irreducible.", "thesis": "The incumbent brand-equity frameworks — Aaker's brand equity, Keller's customer-based brand equity, Kapferer's identity prism, the Ehrenberg-Bass distinctiveness school, and single-figure brand valuation — are not rivals to Spectral Brand Theory (SBT) but its limiting cases. Modeling a brand as an observer-completed probability measure mu on an eight-dimensional perception manifold, each incumbent is represented as a measurable projection-and-aggregation operator T_k that induces a Blackwell garbling of the full perception measurement (the representation lemma). Two theorems follow. The CORRESPONDENCE THEOREM: the aggregate brand-health score is a sufficient statistic for the managerial decision problem if and only if four regime conditions hold jointly (a tight unimodal cloud; slow temporal dynamics; a human-only observer set; a firm-dominated signal); in that corner SBT reduces to the incumbent, which is why the incumbent worked, and the Ehrenberg-Bass \"brands differ little in image\" finding is relocated as an empirical diagnosis of which regime a category occupies, not a universal law. The DECISION-EFFICIENCY THEOREMS: outside that corner the score is a garbling of the cloud, so the full measurement weakly dominates the score for every decision-maker (directed-gradient dominance), and the realized decision loss is bounded below by a quantity monotone in four regime-departure parameters (metameric arbitrage). The theorems entail a manager-runnable decision procedure — regime test, blind-spot diagnostic, directed-intervention rule, metameric-substitution rule — realized in an atomic-perception measurement architecture. SBT is brand metrology (the astronomer), not brand management (the astronaut); Blackwell's theorem is the bridge by which finer measurement provably helps every mission without SBT being a theory of any mission." }, "L1": { "name": "Claims", "papers": [ { "key": "2026au", "title": "The Correspondence Principle of Brand Management", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20757596", "doi_url": "https://doi.org/10.5281/zenodo.20757596", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/brand-correspondence-principle", "claims": [ { "id": "P1", "text": "Representation lemma. Every incumbent brand-equity framework is a measurable projection-and-aggregation operator T_k = A_k o Pi_k on mu, and the experiment 'observe T_k(mu)' is a Blackwell garbling of the experiment 'observe mu': there is a stochastic (Markov) kernel carrying the full perception measurement into the incumbent summary." }, { "id": "P2", "text": "Correspondence theorem. The aggregate brand-health score T_k(mu) is a sufficient statistic for the managerial decision problem (a, g) — SBT and the incumbent prescribe the same optimal action for every payoff g — if and only if the four regime conditions hold jointly: (i) mu is tight and unimodal (low sigma); (ii) dynamics are slow relative to the measurement cadence (low v); (iii) the observer set is human-only (alpha = 0); (iv) the signal is firm-dominated (low epsilon)." }, { "id": "P3", "text": "Directed-gradient dominance. Outside the classical regime the score is a strict garbling of the cloud, so the full perception measurement weakly Blackwell-dominates the score for every decision-maker and every bounded payoff; equivalently, the cloud-optimizing manager moves the signal only along (dimension, cohort) directions with observable payoff, whereas the score-optimizing manager allocates part of its effort along unobserved directions ('blind spend') whose sign it cannot determine." }, { "id": "P4", "text": "Metameric arbitrage. Signal-metamerism (distinct signals inducing equal perception) yields a cheaper-signal lever; perception-metamerism (one signal inducing divergent perception across cohorts) yields a mis-targeting loss; both are invisible to the aggregate model. The realized decision loss of score-based versus cloud-based management is bounded below by a quantity monotone non-decreasing in each of the four regime-departure parameters (sigma, v, alpha, epsilon) and equal to zero at the classical corner." }, { "id": "P5", "text": "Falsifiability. The framework is falsifiable through three observable signatures and the decision/payoff patterns that reject each theorem: (a) regime-parameter estimates (reject P2 if the score-vs-cloud action agreement does not track the four-parameter regime test); (b) blind-spend share (reject P3 if cloud access does not weakly improve realized payoff net of measurement cost outside the regime); (c) metameric-substitution opportunities and the loss surface (reject P4 if the realized loss is non-monotone in the regime parameters or non-zero at the classical corner)." }, { "id": "P6", "text": "Derived managerial procedure. The two theorems entail a manager-runnable decision procedure: (a) regime test — estimate (sigma, v, alpha, epsilon) to decide whether the cheap aggregate score is sufficient for the category (do not over-prescribe SBT where the incumbent suffices); (b) blind-spot diagnostic — identify which of the eight dimensions the current framework projects away; (c) directed-intervention rule — act on the single (dimension, cohort) with the largest observable payoff-per-cost; (d) metameric-substitution rule — choose the cheapest signal in a perceptual equivalence class. An atomic-perception measurement architecture is the realized instrument: it reads the cloud, including AI cohorts, from existing artifacts, proving the prescribed measurement is feasible today." }, { "id": "thesis", "text": "The incumbent brand-equity frameworks — Aaker's brand equity, Keller's customer-based brand equity, Kapferer's identity prism, the Ehrenberg-Bass distinctiveness school, and single-figure brand valuation — are not rivals to Spectral Brand Theory (SBT) but its limiting cases. Modeling a brand as an observer-completed probability measure mu on an eight-dimensional perception manifold, each incumbent is represented as a measurable projection-and-aggregation operator T_k that induces a Blackwell garbling of the full perception measurement (the representation lemma). Two theorems follow. The CORRESPONDENCE THEOREM: the aggregate brand-health score is a sufficient statistic for the managerial decision problem if and only if four regime conditions hold jointly (a tight unimodal cloud; slow temporal dynamics; a human-only observer set; a firm-dominated signal); in that corner SBT reduces to the incumbent, which is why the incumbent worked, and the Ehrenberg-Bass \"brands differ little in image\" finding is relocated as an empirical diagnosis of which regime a category occupies, not a universal law. The DECISION-EFFICIENCY THEOREMS: outside that corner the score is a garbling of the cloud, so the full measurement weakly dominates the score for every decision-maker (directed-gradient dominance), and the realized decision loss is bounded below by a quantity monotone in four regime-departure parameters (metameric arbitrage). The theorems entail a manager-runnable decision procedure — regime test, blind-spot diagnostic, directed-intervention rule, metameric-substitution rule — realized in an atomic-perception measurement architecture. SBT is brand metrology (the astronomer), not brand management (the astronaut); Blackwell's theorem is the bridge by which finer measurement provably helps every mission without SBT being a theory of any mission." } ] }, { "key": "2026ag", "title": "Dual Hierarchies of Organizational Transferability: A Six-Tier Ontology and Theory of Acquisition Failure Propagation", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19895813", "doi_url": "https://doi.org/10.5281/zenodo.19895813", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/six-tier-ontology", "claims": [ { "id": "P1", "text": "The residual is an ontological deficit, not merely an empirical one: the M&A literature has accumulated sophisticated single-layer explanations (cultural distance, executive turnover, strategic misfit, business-model misalignment) but lacks a shared vocabulary for how those layers relate, constrain one another, or propagate failure across the entity." }, { "id": "P10", "text": "Capital allocation across tiers carries a flow-versus-stock character that varies systematically by tier position: Tier 6 spend (marketing, PR) is predominantly flow consumption (low transferable value); Tier 2-5 spend (model architecture, governance, product/process codification) is predominantly stock accumulation (high transferable value). Each tier carries a distinct half-life and substrate-accumulation coefficient; the transferability and accumulation classifications ALIGN." }, { "id": "P11", "text": "The constraint hierarchy derives a formal (not prescriptive) integration SEQUENCING principle: resolve Tier 1 compatibility before Tier 2 revision; Tier 2 revision before Tier 4 specification; confirm Tier 4 before Tier 5 integration; confirm Tier 5 before Tier 6 role redesign; Tier 3 integration is legally immediate but should be designed to minimize disruption to Tiers 4-6. The modal failure mode in practice INVERTS this sequence (beginning at Tier 6/5 with Tiers 1-4 unresolved)." }, { "id": "P12", "text": "The Six-Tier Separability Diagnostic (STSD) is a THEORETICAL IMPLICATION, not the primary contribution: a structured judgment instrument that scores each tier Fused / Partial / Independent (Table 4), producing a six-cell pre-close risk profile. Its theoretical claim is that pre-close tier profiling predicts post-acquisition trajectories better than aggregate financial/strategic-fit measures, by disaggregating due-diligence risk by tier rather than producing an aggregate pass/fail verdict." }, { "id": "P13", "text": "Cross-form acquisitions face Tier 1 MISSPECIFICATION risk no standard due-diligence checklist captures, because financial due diligence examines Tier 3 and not Tier 1 compatibility. A cooperative's collectively held, democratically governed Tier 1 cannot be transferred without being replaced by a fundamentally different Intent (a credit union cannot be acquired by a bank without member consent). Privatization is the most tractable natural experiment for testing the form-mismatch principle." }, { "id": "P1F", "text": "P1 (Intent-Model Misalignment): when an acquirer's Owner Intent differs structurally from the target's, the target's Business Model requires fundamental revision, generating downstream Tier 4/Tier 5 friction not visible in pre-close due diligence." }, { "id": "P2", "text": "An acquisition target decomposes into exactly six tiers — Owner Intent, Business Model, Business Entity, Product, Process, Organization — each individuated by a distinct GOVERNOR (force that sets the tier's configuration), a distinct SPECIFICATION SURFACE (observable artifacts), and a distinct TRANSFERABILITY MODE (mechanism by which the tier does or does not cross an ownership boundary)." }, { "id": "P2F", "text": "P2 (Business Model-Product Friction): an imposed Model revision drifts the Product specification toward the new Model's optimization criteria, and customers anchored in the prior dimensional configuration churn above pre-acquisition baselines." }, { "id": "P3", "text": "The six tiers are objects of heterogeneous ontological type (a latent psychological state, an abstract projection, a legal artifact, operational realities) unified under a single instrumental axis — transferability mode: the question is not \"are they the same kind of thing?\" but \"what happens to each kind of thing when it crosses a new-owner boundary?\" This answers the ontological-mixing objection and distinguishes the framework from prior layered firm ontologies (Zachman, Osterwalder, BIZBOK, DEMO), none of which combine a distinct Owner-Intent tier above the Business Model, a distinct Business-Entity legal tier, per-tier transferability modes, dual hierarchies, and an M&A application." }, { "id": "P3F", "text": "P3 (Entity-Operations Disruption): Entity restructuring following close disrupts operational continuity at Tiers 5 and 4 via contract renegotiation, regulatory re-certification, and counterparty uncertainty disproportionate to the restructuring's legal scope." }, { "id": "P4", "text": "Tier 1 (Owner Intent) attaches to the controlling principal, not to the asset, and only IMPRINTS onto the asset's downstream tiers. Consequently Tier 1 is REPLACED, not transferred, across ownership change: a new principal supplies a new Tier 1 imprint while Tiers 2-6 carry forward (subject to the integration cascade). A single principal controlling multiple assets carries a per-asset Tier 1, drawn from one archetype distribution but expressing differently per asset." }, { "id": "P4F", "text": "P4 (Product-Process Disruption): revising the Product specification misaligns the Process architecture built for the prior Product, generating quality failures or cost overruns until Process is rebuilt around the new spec — compounded by the impossibility of fully specifying Product requirements and the tacit residuals documentation cannot eliminate." }, { "id": "P5", "text": "Tier 3 (Business Entity) is the most jurisdictionally MUTABLE of the six tiers: the legal vehicle can swap (redomiciliation, opco/holdco interposition, SPV insertion, sole-prop-to-LLC conversion) while Tiers 2, 4, 5, 6 continue without operational disruption. The persistent identity of a business therefore does not reside in Tier 3; the substantive Tier 3 transferability claim is decoupling of obligations from the principal's balance sheet, not identification with a specific legal form." }, { "id": "P5F", "text": "P5 (Process-Organization Fracture): imposing Process integration on the acquired Organization before Tier 4 specification clarity is established produces employee resistance and attrition exceeding rates when Process integration follows Product confirmation." }, { "id": "P6", "text": "The six tiers form two overlapping, oppositely directed hierarchies that are the same relationships read from opposite ends. The SERVICE hierarchy runs upward (Organization serves Process; Process serves Product; Product funds Entity; Entity implements Model; Model realizes Intent). The CONSTRAINT hierarchy runs downward (each tier rules out inadmissible configurations for the tier below it)." }, { "id": "P6F", "text": "P6 (Organization Fracture to All-Layer Degradation): when key Organization members exit post-acquisition, the tacit knowledge they carried degrades across all six tiers at rates retention bonuses or post-exit documentation cannot recover, because Tier 6 is the sole repository of tacit specification knowledge never externalized to Tier 4/5 surfaces. This is the best-supported pathway (though no single study traces the full chain)." }, { "id": "P7", "text": "Because upper tiers constrain lower tiers, specification clarity at upper tiers is logically PRIOR to integration execution at lower tiers, and a shock at any tier propagates in BOTH directions (a Tier 6 fracture reduces the productive capacity Tier 5 requires, transmitting up the service chain to Tier 4 drift even when the Product spec was never altered). Integration is therefore a cross-tier problem, not a within-tier one." }, { "id": "P7F", "text": "P7 (Bidirectional Feedback): sustained lower-tier failure crossing a duration-and-severity threshold (Tier 5/6 fracture >= 12 months depressing Tier 3 revenue >= 10% from deal thesis) forces upward revision — documented Tier 2 Model revision within 24 months, and conditionally documented Tier 1 Intent revision (write-down/divestiture/strategic-review) within a further 12 months. The feedback is asymmetric: below threshold, lower-tier failures are absorbed without upper-tier revision." }, { "id": "P8", "text": "The six-tier structure is FORM-INVARIANT: each tier has a structurally equivalent form across for-profit, NGO/charity, and mutual/cooperative types via explicit substitution rules (Table 2). Tier 1 and Tier 3 substitutions are anchored in prior work; Tier 2, 4, and 5 substitutions are provisional theoretical deductions pending cross-form validation. The cooperative Tier 1 is a collective mandate, not a scalar individual intent." }, { "id": "P9", "text": "Tier-collapse is a structural pattern parameterized over TIER PAIRS, arising when the governor of one tier is identical to another's. Two canonical instances: Tier 1 ≡ Tier 4 (Domain Craftsman / Family Steward / Mission Founder — Intent is inseparable from Product) and Tier 1 ≡ Tier 3 (sole-proprietor — the natural person IS the legal subject). In each, the fused-tier asset is untransferable as a going concern because the fused tier carries the principal's identity, which legal instruments cannot convey." }, { "id": "thesis", "text": "Mergers and acquisitions destroy value at high rates because the field lacks a shared ontology specifying which organizational layers transfer and how failures propagate across them. This paper develops a six-tier ontology of the acquisition target — Owner Intent, Business Model, Business Entity, Product, Process, Organization — each with a distinct governor, specification surface, and transferability mode. The tiers form two oppositely directed hierarchies: a service hierarchy upward (Organization to Intent) and a constraint hierarchy downward (Intent to Organization). The constraint hierarchy fixes integration sequencing; shocks propagate bidirectionally, yielding seven falsifiable failure-propagation propositions. The framework is form-invariant across for-profit, NGO, and cooperative entities via explicit substitution rules (Tiers 2, 4, 5 provisional), and derives a Six-Tier Separability Diagnostic (STSD) as a theoretical implication. The primary contribution is a generalizable theory of organizational separability under ownership change: separability is never costless because constraint architectures are sticky." } ] }, { "key": "2026af", "title": "Organizational Metamerism: Observer-Relative State Equivalence in Organizational Configurations", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19869871", "doi_url": "https://doi.org/10.5281/zenodo.19869871", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/org-as-metadata", "claims": [] }, { "key": "2026at", "title": "Negotiating Vocabularies at Link Time: A Deterministic Six-Class Compatibility Check for Federated Ontology Modules", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20751395", "doi_url": "https://doi.org/10.5281/zenodo.20751395", "github_url": "https://github.com/spectralbranding/federated-negotiation/tree/main", "claims": [] } ] }, "L2": { "name": "Spine", "concepts": [ { "key": "brand-management-correspondence-theorem", "label": "Brand-management correspondence theorem", "definition": "The result that an incumbent aggregate brand-health score is a sufficient statistic for the managerial decision problem — so the incumbent framework and Spectral Brand Theory prescribe the same optimal action for every payoff — if and only if four regime conditions hold jointly (a tight unimodal perception cloud, slow temporal dynamics, a human-only observer set, and a firm-dominated signal); in that limit Spectral Brand Theory reduces to the incumbent, which is why the incumbent worked.", "owner": "2026au", "status": "active" }, { "key": "six-tier-ontology", "label": "six-tier ontology", "definition": "The ontology that decomposes an organization into six nested specification tiers, always in the order Owner Intent -> Business Model -> Business Entity -> Product -> Process -> Organization. Each tier answers a distinct governing question and transfers differently on sale.", "owner": "2026ag", "status": "active" }, { "key": "organizational-metamerism", "label": "Organizational Metamerism", "definition": "An observer-relative condition in which two structurally distinct organizational configurations executing the same process map to identical value outputs for a specific evaluator.", "owner": "org-as-metadata", "status": "active" }, { "key": "federated-ontology-negotiation", "label": "Federated ontology negotiation", "definition": "The cross-author generalization of single-author ontology linking: given two namespaced module sets from distinct authorities, mechanically classify every cross-owner term interaction and propose a typed, justified reconciliation, before either author reads the other's prose.", "owner": "federated-negotiation", "status": "active" }, { "key": "conflict-class", "label": "CONFLICT", "definition": "The interaction class where both authors own the same term_key with different def_hash; UNRESOLVED (fails the gate); SKOS closeMatch (same concept, divergent definition) or relatedMatch (key collides on distinct concepts); reconciliation operation NAMESPACE the colliding keys + curate the mapping, FORK the loser's key if the concepts truly differ.", "owner": "federated-negotiation", "status": "active" }, { "key": "reconciliation-operation", "label": "Reconciliation operation", "definition": "One of lock / fork / rebase / merge — the single-author spine operation vocabulary lifted to operate across distinct owners, proposed per interaction class as the typed action that would reconcile it (MERGE for AGREEMENT, REBASE for CROSS_REFINE, NAMESPACE+FORK for CONFLICT, BLOCK for the dangling/incompatible cases).", "owner": "federated-negotiation", "status": "active" } ], "methods": [ { "paper": "2026au", "claims": [ { "id": "M1", "text": "Monte Carlo computation of expected decision loss of score-based versus cloud-based management as a function of the four regime-departure parameters, with mu a von Mises-Fisher mixture on the perception manifold calibrated to a real high-frequency dataset; fixed seed, >= 5000 draws per parameter combination." } ] }, { "paper": "2026ag", "claims": [] }, { "paper": "2026af", "claims": [] }, { "paper": "2026at", "claims": [] } ] }, "L3": { "name": "Instrument", "instrument": { "name": "Brand Spectrometer", "kind": "measurement", "url": "https://meter.spectralbranding.com", "input_contract_url": "https://meter.spectralbranding.com/CONVERT_WITH_YOUR_AI.md", "output": "Two cohort atlases (acquirer + target) whose per-dimension correspondence measures perceptual fit. Operating fit is then specified with the OrgSchema Toolkit and reconciled by the six-class link-time compatibility check (2026at) — a federated-negotiation method applied analytically — to classify which tiers transfer and which conflict.", "when": "Route here once both firms are named and the question is whether they fit — perceptually, operationally, or both. The instrument measures perceptual correspondence; the toolkit and the negotiation method handle operating fit.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about M&A fit\" to \"do THESE two firms fit\" — which needs both firms' cohorts measured and both operating models specified, not the theory.\n" } } }, "papers": [ { "key": "2026au", "title": "The Correspondence Principle of Brand Management", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20757596", "doi_url": "https://doi.org/10.5281/zenodo.20757596", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/brand-correspondence-principle" }, { "key": "2026ag", "title": "Dual Hierarchies of Organizational Transferability: A Six-Tier Ontology and Theory of Acquisition Failure Propagation", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19895813", "doi_url": "https://doi.org/10.5281/zenodo.19895813", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/six-tier-ontology" }, { "key": "2026af", "title": "Organizational Metamerism: Observer-Relative State Equivalence in Organizational Configurations", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.19869871", "doi_url": "https://doi.org/10.5281/zenodo.19869871", "github_url": "https://github.com/spectralbranding/orgschema-papers/tree/main/org-as-metadata" }, { "key": "2026at", "title": "Negotiating Vocabularies at Link Time: A Deterministic Six-Class Compatibility Check for Federated Ontology Modules", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20751395", "doi_url": "https://doi.org/10.5281/zenodo.20751395", "github_url": "https://github.com/spectralbranding/federated-negotiation/tree/main" } ], "concepts": [ { "key": "brand-management-correspondence-theorem", "label": "Brand-management correspondence theorem", "definition": "The result that an incumbent aggregate brand-health score is a sufficient statistic for the managerial decision problem — so the incumbent framework and Spectral Brand Theory prescribe the same optimal action for every payoff — if and only if four regime conditions hold jointly (a tight unimodal perception cloud, slow temporal dynamics, a human-only observer set, and a firm-dominated signal); in that limit Spectral Brand Theory reduces to the incumbent, which is why the incumbent worked.", "owner": "2026au", "status": "active" }, { "key": "six-tier-ontology", "label": "six-tier ontology", "definition": "The ontology that decomposes an organization into six nested specification tiers, always in the order Owner Intent -> Business Model -> Business Entity -> Product -> Process -> Organization. Each tier answers a distinct governing question and transfers differently on sale.", "owner": "2026ag", "status": "active" }, { "key": "organizational-metamerism", "label": "Organizational Metamerism", "definition": "An observer-relative condition in which two structurally distinct organizational configurations executing the same process map to identical value outputs for a specific evaluator.", "owner": "org-as-metadata", "status": "active" }, { "key": "federated-ontology-negotiation", "label": "Federated ontology negotiation", "definition": "The cross-author generalization of single-author ontology linking: given two namespaced module sets from distinct authorities, mechanically classify every cross-owner term interaction and propose a typed, justified reconciliation, before either author reads the other's prose.", "owner": "federated-negotiation", "status": "active" }, { "key": "conflict-class", "label": "CONFLICT", "definition": "The interaction class where both authors own the same term_key with different def_hash; UNRESOLVED (fails the gate); SKOS closeMatch (same concept, divergent definition) or relatedMatch (key collides on distinct concepts); reconciliation operation NAMESPACE the colliding keys + curate the mapping, FORK the loser's key if the concepts truly differ.", "owner": "federated-negotiation", "status": "active" }, { "key": "reconciliation-operation", "label": "Reconciliation operation", "definition": "One of lock / fork / rebase / merge — the single-author spine operation vocabulary lifted to operate across distinct owners, proposed per interaction class as the typed action that would reconcile it (MERGE for AGREEMENT, REBASE for CROSS_REFINE, NAMESPACE+FORK for CONFLICT, BLOCK for the dangling/incompatible cases).", "owner": "federated-negotiation", "status": "active" } ], "instrument": { "name": "Brand Spectrometer", "kind": "measurement", "url": "https://meter.spectralbranding.com", "input_contract_url": "https://meter.spectralbranding.com/CONVERT_WITH_YOUR_AI.md", "output": "Two cohort atlases (acquirer + target) whose per-dimension correspondence measures perceptual fit. Operating fit is then specified with the OrgSchema Toolkit and reconciled by the six-class link-time compatibility check (2026at) — a federated-negotiation method applied analytically — to classify which tiers transfer and which conflict.", "when": "Route here once both firms are named and the question is whether they fit — perceptually, operationally, or both. The instrument measures perceptual correspondence; the toolkit and the negotiation method handle operating fit.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about M&A fit\" to \"do THESE two firms fit\" — which needs both firms' cohorts measured and both operating models specified, not the theory.\n" }, "spec": { "intake": [ "acquirer and target (names + categories) and the M&A thesis: what fit is assumed (brand/perceptual, operating, or both).", "for perceptual fit: public artifacts for each firm's relevant cohorts, so the two perception clouds can be measured and compared.", "for operating fit: each firm's operating-model specification (or the materials to produce one) at the tier grain — which layers the deal assumes will transfer.", "decision: integrate / keep separate / walk away, and which synergies the valuation depends on." ], "guardrails": [ "M&A destroys value when 'fit' is assumed at the logo rather than checked at the tier/layer grain; specify which organizational layers actually transfer before crediting a synergy.", "Two structurally different organizations can look identical to an observer (organizational metamerism); a surface match is not operating fit — check the underlying layers, not the rendered output.", "Perceptual fit is whether the two brands' perception clouds correspond (the correspondence principle), measured per cohort and dimension, not a brand-strength average.", "Reconcile the two firms' vocabularies as a link-time compatibility check (agreement / conflict / cross-refine / …); surface every CONFLICT and abstain on irreducible ones rather than forcing a merged reading." ], "output_contract": "A fit report in two registers: perceptual fit (per cohort and dimension, where the two perception clouds correspond vs diverge beyond the noise floor) and operating fit (per tier, which layers transfer, which conflict under the six-class compatibility check), with the irreducible conflicts and un-resolvable comparisons escalated to human judgment rather than averaged away. The deliverable is a typed fit verdict, not a go/no-go score.\n", "escalate_to_tool": "Measure perceptual fit with the Brand Spectrometer (compare the acquirer's and target's cohort readings); specify each firm's operating model with the OrgSchema Toolkit; then reconcile the two specifications as a federated ontology negotiation — the six-class link-time compatibility check (2026at) — to classify which tiers transfer (agreement / cross-refine) and which conflict, abstaining where a conflict is irreducible.\n" } }, { "id": "reach-an-audience", "status": "ready", "decision": "Reach a perceptual cohort that has no mailing address.", "persona": [ "CMO", "growth lead", "media planner" ], "framework": "SBT", "tiers": [ 4 ], "framing": "A perceptual cohort has no native media address and does not need one. Reach is not \"find their list\" but a choice among three measurable bridges from a perception to a delivery: broadcast the dimension that defines the cohort and let self-selection route the signal to it; follow the provenance of the signals the cohort already emits and treats as address; or accept a demographic proxy and pay its quantified join loss. Targeting a cohort through an addressable proxy is a Blackwell garbling of targeting the perception directly — lossy in a way you can measure rather than guess. So the corpus turns \"how do we reach them?\" into \"which bridge costs least, and is the defining dimension even resolvable?\" — a measurement question before it is a media-buying one.", "spec_url": "https://consult.orgschema.com/specs/reach-an-audience.md", "levels": { "L0": { "name": "Framing", "framing": "A perceptual cohort has no native media address and does not need one. Reach is not \"find their list\" but a choice among three measurable bridges from a perception to a delivery: broadcast the dimension that defines the cohort and let self-selection route the signal to it; follow the provenance of the signals the cohort already emits and treats as address; or accept a demographic proxy and pay its quantified join loss. Targeting a cohort through an addressable proxy is a Blackwell garbling of targeting the perception directly — lossy in a way you can measure rather than guess. So the corpus turns \"how do we reach them?\" into \"which bridge costs least, and is the defining dimension even resolvable?\" — a measurement question before it is a media-buying one.", "thesis": "The correspondence principle (2026au) shows that an aggregate brand score is a Blackwell garbling of the eight-dimensional perception cloud and prescribes acting on the highest- payoff (dimension, cohort) — the directed-intervention rule P6. But P6 presumes a cohort is ACTIONABLE without showing it is REACHABLE: a cohort defined by perceptual proximity has no native media address, unlike the addressable audiences (channels, cookies, lookalikes) of traditional activation. This applied companion closes that gap. \"Actionable\" decomposes into three measurable bridge mechanisms from perception space to action, unified by a measurement->activation HANDOFF CONTRACT consistent with SBT's metrology posture (the astronomer supplies coordinates and the bridge cost; the manager flies): (b) BROADCAST-A-DIMENSION — emit on the dimension the cohort is sensitive to and let self-selection route the signal; zero address required. Formally a separating signal on a degraded broadcast channel (Cover 1972): the observer's channel quality is the inner product of the signal vector with the observer's spectral-sensitivity vector, so off-peak observers receive a metamer-to-null. The self-selection sharpness equals the same sin^2(beta) that the parent paper counts as a perception-metamerism LOSS: the targeting BUG becomes a self-selection FILTER. This is the headline. (c) PROVENANCE-AS-ADDRESS — the reflection-based perception architecture's reflections carry the surfaces (and recency) where each perception was found; a cohort of reflections traces back to re-reachable channels. (a) PERCEPTION->PROXY JOIN — map the cohort to addressable proxies and QUANTIFY the Blackwell-garbling decision loss L(P) of doing so; report the minimal-loss proxy P*. The reach answer is a structural TAILWIND, not a patch: the only route needing an address (a) is a measurable, lossy projection, and the address-free route (b) is exactly where post- cookie activation is already heading (the industry's own Topics-API cohort pivot), so SBT does not depend on the identity-addressability the advertising industry is losing. The individual observer spectral profile is the primitive; cohorts are derived clusters in that space." }, "L1": { "name": "Claims", "papers": [ { "key": "2026av", "title": "Reaching a Perception: From Perceptual Cohort to Reachable Audience", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20765556", "doi_url": "https://doi.org/10.5281/zenodo.20765556", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/reaching-a-perception", "claims": [ { "id": "P1", "text": "The handoff-contract rule. For a target (dimension, cohort), the measurement->activation contract emits (i) the recommended bridge mechanism and (ii) its quantified cost: dimension-distinct cohort (sin^2(beta) > threshold) -> broadcast-a-dimension (b), cost = predicted spill; reflections clustered on few live surfaces -> provenance-as-address (c), cost = coverage bias; else -> minimal-loss proxy (a), cost = L(P*). SBT supplies target + bridge cost; media execution is the management layer." }, { "id": "P2", "text": "Resonance over-index (broadcast-a-dimension). A signal emitted strong on dimension d produces salience/response for observer i monotone in ; therefore a dimension-strong creative over-indexes on the dimension-d-sensitive cohort relative to a dimension-neutral control, and the magnitude of over-index is increasing in the cohort's dimensional distinctiveness sin^2(beta) — the SAME quantity that is the perception-metamerism LOSS in 2026au. The mis-targeting bug is, read forward, the self-selection filter; formally a degraded broadcast channel (Cover 1972) with channel quality || and resonance bandwidth = sin^2(beta)." }, { "id": "P3", "text": "Proxy-join loss ordering. Targeting cohort C through an addressable proxy P is a Blackwell garbling of targeting on the perceptual cohort directly; the expected decision loss L(P) is non-negative and ordered by the informativeness of P about cohort membership, with a minimal-loss proxy P* identifiable from the mutual information I(C; P). When even P* leaves L(P*) above the predicted spill of route (b), the contract (P1) routes to (b) instead — making the reach choice a measured comparison, not a default to addressability." }, { "id": "thesis", "text": "The correspondence principle (2026au) shows that an aggregate brand score is a Blackwell garbling of the eight-dimensional perception cloud and prescribes acting on the highest- payoff (dimension, cohort) — the directed-intervention rule P6. But P6 presumes a cohort is ACTIONABLE without showing it is REACHABLE: a cohort defined by perceptual proximity has no native media address, unlike the addressable audiences (channels, cookies, lookalikes) of traditional activation. This applied companion closes that gap. \"Actionable\" decomposes into three measurable bridge mechanisms from perception space to action, unified by a measurement->activation HANDOFF CONTRACT consistent with SBT's metrology posture (the astronomer supplies coordinates and the bridge cost; the manager flies): (b) BROADCAST-A-DIMENSION — emit on the dimension the cohort is sensitive to and let self-selection route the signal; zero address required. Formally a separating signal on a degraded broadcast channel (Cover 1972): the observer's channel quality is the inner product of the signal vector with the observer's spectral-sensitivity vector, so off-peak observers receive a metamer-to-null. The self-selection sharpness equals the same sin^2(beta) that the parent paper counts as a perception-metamerism LOSS: the targeting BUG becomes a self-selection FILTER. This is the headline. (c) PROVENANCE-AS-ADDRESS — the reflection-based perception architecture's reflections carry the surfaces (and recency) where each perception was found; a cohort of reflections traces back to re-reachable channels. (a) PERCEPTION->PROXY JOIN — map the cohort to addressable proxies and QUANTIFY the Blackwell-garbling decision loss L(P) of doing so; report the minimal-loss proxy P*. The reach answer is a structural TAILWIND, not a patch: the only route needing an address (a) is a measurable, lossy projection, and the address-free route (b) is exactly where post- cookie activation is already heading (the industry's own Topics-API cohort pivot), so SBT does not depend on the identity-addressability the advertising industry is losing. The individual observer spectral profile is the primitive; cohorts are derived clusters in that space." } ] }, { "key": "2026au", "title": "The Correspondence Principle of Brand Management", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20757596", "doi_url": "https://doi.org/10.5281/zenodo.20757596", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/brand-correspondence-principle", "claims": [ { "id": "P1", "text": "Representation lemma. Every incumbent brand-equity framework is a measurable projection-and-aggregation operator T_k = A_k o Pi_k on mu, and the experiment 'observe T_k(mu)' is a Blackwell garbling of the experiment 'observe mu': there is a stochastic (Markov) kernel carrying the full perception measurement into the incumbent summary." }, { "id": "P2", "text": "Correspondence theorem. The aggregate brand-health score T_k(mu) is a sufficient statistic for the managerial decision problem (a, g) — SBT and the incumbent prescribe the same optimal action for every payoff g — if and only if the four regime conditions hold jointly: (i) mu is tight and unimodal (low sigma); (ii) dynamics are slow relative to the measurement cadence (low v); (iii) the observer set is human-only (alpha = 0); (iv) the signal is firm-dominated (low epsilon)." }, { "id": "P3", "text": "Directed-gradient dominance. Outside the classical regime the score is a strict garbling of the cloud, so the full perception measurement weakly Blackwell-dominates the score for every decision-maker and every bounded payoff; equivalently, the cloud-optimizing manager moves the signal only along (dimension, cohort) directions with observable payoff, whereas the score-optimizing manager allocates part of its effort along unobserved directions ('blind spend') whose sign it cannot determine." }, { "id": "P4", "text": "Metameric arbitrage. Signal-metamerism (distinct signals inducing equal perception) yields a cheaper-signal lever; perception-metamerism (one signal inducing divergent perception across cohorts) yields a mis-targeting loss; both are invisible to the aggregate model. The realized decision loss of score-based versus cloud-based management is bounded below by a quantity monotone non-decreasing in each of the four regime-departure parameters (sigma, v, alpha, epsilon) and equal to zero at the classical corner." }, { "id": "P5", "text": "Falsifiability. The framework is falsifiable through three observable signatures and the decision/payoff patterns that reject each theorem: (a) regime-parameter estimates (reject P2 if the score-vs-cloud action agreement does not track the four-parameter regime test); (b) blind-spend share (reject P3 if cloud access does not weakly improve realized payoff net of measurement cost outside the regime); (c) metameric-substitution opportunities and the loss surface (reject P4 if the realized loss is non-monotone in the regime parameters or non-zero at the classical corner)." }, { "id": "P6", "text": "Derived managerial procedure. The two theorems entail a manager-runnable decision procedure: (a) regime test — estimate (sigma, v, alpha, epsilon) to decide whether the cheap aggregate score is sufficient for the category (do not over-prescribe SBT where the incumbent suffices); (b) blind-spot diagnostic — identify which of the eight dimensions the current framework projects away; (c) directed-intervention rule — act on the single (dimension, cohort) with the largest observable payoff-per-cost; (d) metameric-substitution rule — choose the cheapest signal in a perceptual equivalence class. An atomic-perception measurement architecture is the realized instrument: it reads the cloud, including AI cohorts, from existing artifacts, proving the prescribed measurement is feasible today." }, { "id": "thesis", "text": "The incumbent brand-equity frameworks — Aaker's brand equity, Keller's customer-based brand equity, Kapferer's identity prism, the Ehrenberg-Bass distinctiveness school, and single-figure brand valuation — are not rivals to Spectral Brand Theory (SBT) but its limiting cases. Modeling a brand as an observer-completed probability measure mu on an eight-dimensional perception manifold, each incumbent is represented as a measurable projection-and-aggregation operator T_k that induces a Blackwell garbling of the full perception measurement (the representation lemma). Two theorems follow. The CORRESPONDENCE THEOREM: the aggregate brand-health score is a sufficient statistic for the managerial decision problem if and only if four regime conditions hold jointly (a tight unimodal cloud; slow temporal dynamics; a human-only observer set; a firm-dominated signal); in that corner SBT reduces to the incumbent, which is why the incumbent worked, and the Ehrenberg-Bass \"brands differ little in image\" finding is relocated as an empirical diagnosis of which regime a category occupies, not a universal law. The DECISION-EFFICIENCY THEOREMS: outside that corner the score is a garbling of the cloud, so the full measurement weakly dominates the score for every decision-maker (directed-gradient dominance), and the realized decision loss is bounded below by a quantity monotone in four regime-departure parameters (metameric arbitrage). The theorems entail a manager-runnable decision procedure — regime test, blind-spot diagnostic, directed-intervention rule, metameric-substitution rule — realized in an atomic-perception measurement architecture. SBT is brand metrology (the astronomer), not brand management (the astronaut); Blackwell's theorem is the bridge by which finer measurement provably helps every mission without SBT being a theory of any mission." } ] }, { "key": "2026a", "title": "Spectral Brand Theory: A Computational Framework for Multi-Dimensional Brand Perception", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.18945912", "doi_url": "https://doi.org/10.5281/zenodo.18945912", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/spectral-brand-theory", "claims": [ { "id": "P1", "text": "A brand is not an object with properties but a perceptual process with observers; \"the brand\" as commonly understood is always already a collapse — a conviction assembled in an observer's mind from whichever signals they could perceive through their spectral profile. These convictions are not errors against a true brand; they are the only brands that exist." }, { "id": "P2", "text": "Brand signals decompose across eight independent perceptual dimensions — Semiotic, Narrative, Ideological, Experiential, Social, Economic, Cultural, Temporal — each a distinct channel carrying information the others cannot. The dimensions measure brand OUTPUT (what is emitted and how it is perceived), not internal organizational process." }, { "id": "P3", "text": "Each signal carries a source type (designed / ambient / synthetic), an emission type (positive / null / structural absence), and a strength (0-5). The designed/ambient (D/A) ratio is a diagnostic metric: a brand whose perception is predominantly ambient (D/A < .40) faces a structural problem no communication strategy can solve, because its story is being written by others." }, { "id": "P4", "text": "Each observer cohort is defined by a formal spectral profile — spectrum (which dimensions are visible), weights (priority per dimension, summing to 1), tolerances (accepted inconsistency), priors (stored convictions), identity gate (recognition), and encounter mode (direct / mediated / mixed). This converts \"different people perceive differently\" from a qualitative observation into a parameterized scoring function." }, { "id": "P5", "text": "A cohort is a CLUSTER IN SPECTRAL-PROFILE SPACE, not a demographic segment. Demographic variables (age, income, geography) are metadata that may correlate with but do not determine perceptual behavior; two observers sharing every demographic attribute may belong to different cohorts if their profiles diverge. Cohort membership is dynamic: signal events physically redistribute observers across cohort boundaries." }, { "id": "P6", "text": "Brand perception follows a three-stage epistemic pipeline: (1) cloud formation — perceived signals cluster, weighted by the profile, into a probabilistic perception cloud with valence and confidence; (2) conviction collapse — sufficient consistent evidence collapses the cloud into a stable conviction at an observer-specific threshold; (3) re-collapse — strong contradicting evidence dissolves the conviction, which is then rebuilt from surviving + crystallized + new signals, never patched." }, { "id": "P7", "text": "Coherence is a STRUCTURAL property — the degree to which different cohorts' convictions are compatible (not identical) — not the consistency of messaging. It is measured by a seven-metric spectral scorecard (dimensional coverage, gate permeability, cloud coherence, collapse strength, re-collapse resistance, emission efficiency, D/A ratio) yielding an A+..F grade." }, { "id": "P8", "text": "SBT and classical brand frameworks stand in a correspondence-principle relationship: when observer diversity is low (cohorts share similar profiles) perception space is approximately flat and classical single-observer measurement is adequate; as diversity rises through globalization, AI mediation, and digital fragmentation, curvature becomes non-negligible and SBT's geometric tools become necessary." }, { "id": "P9", "text": "SBT measures the OUTPUT (WHAT) layer of a brand — the target perception across eight dimensions — not the coordination machinery (DO) that produces it. Output standardization is decidable (a finite acceptance test on eight dimensions); process standardization is not. SBT and Organizational Schema Theory are measurement and specification of one shared output interface, bridged by the WHAT/DO distinction." }, { "id": "PF1", "text": "(Formal Proposition 1 — Observer heterogeneity) Different observer cohorts exposed to identical brand signal environments form systematically different brand convictions as a function of their spectral-profile differences (weights, tolerances, priors, encounter mode) — profile-predictable divergence, not random variation." }, { "id": "PF2", "text": "(Formal Proposition 2 — Non-ergodicity of perception) The temporal sequence in which brand signals are encountered affects the resulting conviction even when the signal set is identical, because signals compound multiplicatively through priors rather than summing additively." }, { "id": "PF3", "text": "(Formal Proposition 3 — Structural absence as signal) Designed restriction of signal emission in specific dimensions generates perceived value that cannot be replicated by signal addition in other dimensions; restriction on one dimension produces a signal on a different dimension." }, { "id": "PF4", "text": "(Formal Proposition 4 — Coherence type over coherence score) Brands with identical aggregate coherence scores exhibit different resilience properties depending on coherence TYPE (ecosystem, signal, identity, experiential asymmetry, incoherent). Single-score coherence metrics are geometrically blind to this distinction (a form of spectral metamerism)." }, { "id": "PF5", "text": "(Formal Proposition 5 — Conviction asymmetry) Evidence-free negative brand convictions are more resistant to disconfirmation than evidence-rich positive convictions, because the negative holder's profile excludes the dimensions where disconfirming evidence would have to arrive (the experiential gate is effectively closed)." }, { "id": "thesis", "text": "Brand perception is irreducibly observer-dependent: there is no single brand-in-itself with properties, only a shared signal environment and heterogeneous observers who each collapse it into a structurally different conviction. Spectral Brand Theory decomposes brand signals across eight perceptual dimensions (Semiotic, Narrative, Ideological, Experiential, Social, Economic, Cultural, Temporal), defines each observer cohort by a formal spectral profile (spectrum, weights, tolerances, priors, identity gate, encounter mode), and models perception as a pipeline — signal emission to observer filtering to probabilistic perception-cloud formation to threshold-based conviction collapse to re-collapse on new evidence. Single-score brand measurement (NPS, equity indices) collapses this multi-dimensional, observer-mediated structure and destroys the very information that explains why observers form irreconcilable perceptions of the same brand. SBT formalizes the heterogeneous observer that customer-based brand equity theory acknowledged but never parameterized, yields five testable structural propositions, and is computationally implementable as a structured LLM prompt sequence. An illustrative five-brand proof-of-concept surfaces four candidate mechanisms (structural absence, a five-type coherence taxonomy, asymmetric conviction resilience, and brand-power/brand-health independence); these are candidates for empirical investigation, not validated findings, and human-subject validation is the priority next step." } ] } ] }, "L2": { "name": "Spine", "concepts": [ { "key": "perception-to-proxy-join", "label": "Perception-to-proxy join", "definition": "The activation bridge that maps a perceptual cohort onto addressable proxy features (platform, geography, register, recency, panel demographics) stored alongside the eight-dimensional vector. The map is a Blackwell garbling of the perceptual experiment, so it is weakly less valuable for the targeting decision; its cost is the proxy-join loss.", "owner": "2026av", "status": "active" }, { "key": "broadcast-a-dimension", "label": "Broadcast a dimension", "definition": "The address-free activation bridge: emit a brand signal strong on the perceptual dimension a target cohort is sensitive to and let self-selection route it, so observers whose spectral-sensitivity profile peaks on that dimension perceive a salient signal (resonate) while off-peak observers receive a metamer-to-null. Formally a separating signal on a degraded broadcast channel whose per-observer channel quality is the projection of the signal onto the observer's sensitivity vector; the cohort is selected, not addressed.", "owner": "2026av", "status": "active" }, { "key": "provenance-as-address", "label": "Provenance as address", "definition": "The activation bridge that traces a perceptual cohort back to re-reachable channels using the source, platform, geography, and content-date provenance each Brand Spectrometer reflection already carries: a cohort of reflections is a recency-aware list of surfaces where the perception is currently expressed. A special case of the perception-to-proxy join in which the proxy features are natively addressable rather than statistically inferred; its cost is the coverage bias of the harvested surfaces (the silent majority may not surface).", "owner": "2026av", "status": "active" }, { "key": "proxy-join-loss", "label": "Proxy-join loss", "definition": "The expected decision loss L(P) of targeting a perceptual cohort C through an addressable proxy P, non-negative and ordered by the informativeness of P about cohort membership (the mutual information between membership and the proxy); the minimal-loss proxy P-star maximizes that information. When L(P-star) exceeds the predicted spill of broadcast-a-dimension the handoff contract routes to broadcast, making the reach choice a measured comparison rather than a default to addressability.", "owner": "2026av", "status": "active" }, { "key": "self-selection-filter", "label": "Self-selection filter", "definition": "The forward reading of perception-metamerism: the same off-axis perceptual distinctiveness (sin-squared-beta) that is a mis-targeting LOSS under push-targeting in the parent paper becomes, under broadcast-a-dimension, the SHARPNESS with which a dimension-strong signal sorts the responsive cohort from the rest — the targeting bug read forward as a filter. A dimension-strong creative therefore over-indexes on the dimension-sensitive cohort with magnitude increasing in that distinctiveness (resonance over-index).", "owner": "2026av", "status": "active" }, { "key": "cohort", "label": "cohort", "definition": "A perceptual grouping of observers with similar spectral profiles, with dynamic membership. Cohorts are perceptual; demographics are metadata, not mechanism. Also written \"observer cohort\".", "owner": "2026a", "status": "active" } ], "methods": [ { "paper": "2026av", "claims": [ { "id": "M1", "text": "Minimal model: 2-D perceptual space, 2 observer types (peak on dim-1 vs dim-2), ternary signal (emit dim-1 / dim-2 / neutral). Extends Cover (1972) degraded broadcast channel; channel quality q_i = ||; capacity region <-> resonance bandwidth; decision loss L(P) = Blackwell garbling on the posterior over cohort membership. Yields Figure 1 (loss surface over sin^2(beta) x spill cost) and, under the ME2 calibration, Figure 2 (resonance over-index vs distinctiveness, with the public anchors marked)." }, { "id": "ME1", "text": "PRIMARY empirical spine: two-cell field experiment — dimension-strong vs dimension-neutral creative delivered via contextual slots, linked to PRE-MEASURED individual perceptual profiles (PRISM-style elicitation), >=1,500 complete profiles per cell, >=4 product categories spanning involvement x sin^2(beta). Tests P2 (resonance over-index) at the individual level." }, { "id": "ME2", "text": "EXECUTED empirical spine (the realized path; no data partnership available, so the JAR-acceptable methods-companion fallback rather than ME1). Calibrated broadcast-channel Monte Carlo: the cohort single-dimension distinctiveness distribution is calibrated to an OBSERVED public proxy — the five canonical SBT brand profiles (the corpus's public anchors), NOT a non-public perception instrument — by the concentration of each centered profile on its dominant dimension; cohorts are drawn from the method-of-moments Beta and run through the M1 two-type model; over-index, effect size, and routing fraction are reported with bootstrap 95% CIs. Two case studies instantiate the P1 contract: a maintenance campaign (established distinctive brand, Hermes) and a category-creation campaign (undifferentiated new entrant, distinctiveness at the 1/8 floor). Supports P1 (contract bridge-selection) and P2 (resonance over-index)." }, { "id": "ME3", "text": "Proxy-join loss estimation: mutual information I(C;P) and decision-loss L(P) between perceptual cohort membership and addressable proxy features in the reflection corpus / panel; identify P* and bound unobservables." } ] }, { "paper": "2026au", "claims": [ { "id": "M1", "text": "Monte Carlo computation of expected decision loss of score-based versus cloud-based management as a function of the four regime-departure parameters, with mu a von Mises-Fisher mixture on the perception manifold calibrated to a real high-frequency dataset; fixed seed, >= 5000 draws per parameter combination." } ] }, { "paper": "2026a", "claims": [ { "id": "M1", "text": "The six-module analytical pipeline: (1) Brand Decomposition, (2) Observer Mapping, (3) Cloud Prediction, (4) Coherence Audit (seven-metric scorecard + A+..F grade + coherence-type classification), (5) Emission Strategy, (6) Re-collapse Simulation; each module's structured YAML output feeds the next." }, { "id": "M2", "text": "Insight Validation Protocol: each surfaced insight is accepted only if it simultaneously satisfies four criteria — non-obvious, dimensionally specific, actionable, observer-differentiated — assessed by the framework's author." }, { "id": "M3", "text": "Cross-model inter-rater reliability: run the identical pipeline under a second independent analytical instrument (Gemini 3.1 Pro) and compare structural classifications (coherence type + grade), treating convergence as inter-coder agreement." } ] } ] }, "L3": { "name": "Instrument", "instrument": { "name": "Brand Spectrometer", "kind": "measurement", "url": "https://meter.spectralbranding.com", "input_contract_url": "https://meter.spectralbranding.com/CONVERT_WITH_YOUR_AI.md", "output": "The dimension(s) on which the target cohort separates from others beyond the noise floor — i.e. the dimension to broadcast — plus confirmation the cohort is resolvable at all. The reach step itself (the three bridges) is an analytical method from 2026av, not yet a separate runnable instrument.", "when": "Route here once a target cohort is named perceptually (by what it believes / how it reads the brand) and the question is delivery. The instrument confirms the cohort is real and finds the dimension that defines it; the bridges then route to it.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about reaching cohorts\" to \"how do I reach MY cohort\" — which needs this brand's cohort measured, not the theory.\n" } } }, "papers": [ { "key": "2026av", "title": "Reaching a Perception: From Perceptual Cohort to Reachable Audience", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20765556", "doi_url": "https://doi.org/10.5281/zenodo.20765556", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/reaching-a-perception" }, { "key": "2026au", "title": "The Correspondence Principle of Brand Management", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.20757596", "doi_url": "https://doi.org/10.5281/zenodo.20757596", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/brand-correspondence-principle" }, { "key": "2026a", "title": "Spectral Brand Theory: A Computational Framework for Multi-Dimensional Brand Perception", "status": "active", "citable": true, "has_knowledge": true, "doi": "10.5281/zenodo.18945912", "doi_url": "https://doi.org/10.5281/zenodo.18945912", "github_url": "https://github.com/spectralbranding/sbt-papers/tree/main/spectral-brand-theory" } ], "concepts": [ { "key": "perception-to-proxy-join", "label": "Perception-to-proxy join", "definition": "The activation bridge that maps a perceptual cohort onto addressable proxy features (platform, geography, register, recency, panel demographics) stored alongside the eight-dimensional vector. The map is a Blackwell garbling of the perceptual experiment, so it is weakly less valuable for the targeting decision; its cost is the proxy-join loss.", "owner": "2026av", "status": "active" }, { "key": "broadcast-a-dimension", "label": "Broadcast a dimension", "definition": "The address-free activation bridge: emit a brand signal strong on the perceptual dimension a target cohort is sensitive to and let self-selection route it, so observers whose spectral-sensitivity profile peaks on that dimension perceive a salient signal (resonate) while off-peak observers receive a metamer-to-null. Formally a separating signal on a degraded broadcast channel whose per-observer channel quality is the projection of the signal onto the observer's sensitivity vector; the cohort is selected, not addressed.", "owner": "2026av", "status": "active" }, { "key": "provenance-as-address", "label": "Provenance as address", "definition": "The activation bridge that traces a perceptual cohort back to re-reachable channels using the source, platform, geography, and content-date provenance each Brand Spectrometer reflection already carries: a cohort of reflections is a recency-aware list of surfaces where the perception is currently expressed. A special case of the perception-to-proxy join in which the proxy features are natively addressable rather than statistically inferred; its cost is the coverage bias of the harvested surfaces (the silent majority may not surface).", "owner": "2026av", "status": "active" }, { "key": "proxy-join-loss", "label": "Proxy-join loss", "definition": "The expected decision loss L(P) of targeting a perceptual cohort C through an addressable proxy P, non-negative and ordered by the informativeness of P about cohort membership (the mutual information between membership and the proxy); the minimal-loss proxy P-star maximizes that information. When L(P-star) exceeds the predicted spill of broadcast-a-dimension the handoff contract routes to broadcast, making the reach choice a measured comparison rather than a default to addressability.", "owner": "2026av", "status": "active" }, { "key": "self-selection-filter", "label": "Self-selection filter", "definition": "The forward reading of perception-metamerism: the same off-axis perceptual distinctiveness (sin-squared-beta) that is a mis-targeting LOSS under push-targeting in the parent paper becomes, under broadcast-a-dimension, the SHARPNESS with which a dimension-strong signal sorts the responsive cohort from the rest — the targeting bug read forward as a filter. A dimension-strong creative therefore over-indexes on the dimension-sensitive cohort with magnitude increasing in that distinctiveness (resonance over-index).", "owner": "2026av", "status": "active" }, { "key": "cohort", "label": "cohort", "definition": "A perceptual grouping of observers with similar spectral profiles, with dynamic membership. Cohorts are perceptual; demographics are metadata, not mechanism. Also written \"observer cohort\".", "owner": "2026a", "status": "active" } ], "instrument": { "name": "Brand Spectrometer", "kind": "measurement", "url": "https://meter.spectralbranding.com", "input_contract_url": "https://meter.spectralbranding.com/CONVERT_WITH_YOUR_AI.md", "output": "The dimension(s) on which the target cohort separates from others beyond the noise floor — i.e. the dimension to broadcast — plus confirmation the cohort is resolvable at all. The reach step itself (the three bridges) is an analytical method from 2026av, not yet a separate runnable instrument.", "when": "Route here once a target cohort is named perceptually (by what it believes / how it reads the brand) and the question is delivery. The instrument confirms the cohort is real and finds the dimension that defines it; the bridges then route to it.\n", "escalate_when": "As soon as the question turns from \"what does the corpus say about reaching cohorts\" to \"how do I reach MY cohort\" — which needs this brand's cohort measured, not the theory.\n" }, "spec": { "intake": [ "brand + the target cohort, defined perceptually (the conviction or dimension that distinguishes it), not as a demographic list.", "the candidate route(s): a dimension to broadcast, a provenance trail to follow, or a demographic proxy under consideration.", "decision: campaign routing / channel choice / whether a proxy's join loss is acceptable." ], "guardrails": [ "A cohort is perceptual, not an address list; do not silently collapse it to a demographic proxy — that substitution has a cost (proxy-join loss) that must be quantified, not ignored.", "Targeting via an addressable proxy is a Blackwell garbling of targeting the perception directly; report the join loss, and prefer the lowest-loss bridge the evidence supports.", "Broadcast-a-dimension works only if that dimension actually separates the cohort above the noise floor; confirm separability before recommending a broadcast.", "Measure perception, never identify or profile a person; provenance-as-address follows pseudonymous public signal, not individuals." ], "output_contract": "For the target cohort, name the three bridges with their measurable costs — (1) broadcast-a-dimension + self-selection routing, (2) provenance-as-address, (3) proxy-join with its quantified loss — and recommend the lowest-loss route the evidence supports, or abstain where the defining dimension is not resolvable above the floor. The deliverable is a routed reach plan with costs, not a lookalike audience.\n", "escalate_to_tool": "Use the Brand Spectrometer to confirm the cohort is resolvable and to find the separating dimension to broadcast; then apply the 2026av bridges analytically, reading the proxy-join loss before committing to any addressable proxy.\n" } } ] }