CORE Preprint
Spectral Brand Theory
SBT (2026a)
8-dimensional decomposition with observer cohorts, coherence types, and conviction dynamics
Research Atlas
A structured map of the Spectral Brand Theory and Organizational Schema Theory research programs. Seven layers, from mathematical foundations to empirical validation. Find your entry point, follow the reading path, identify where contribution is possible.
How to Use This Map
Each paper occupies a block in a layered architecture with a primary layer (where its core contribution lives) and optional secondary layers (where it provides supporting context). Papers marked CORE carry the essential ideas for that layer — read them to get 80% of the layer's content. Supplementary papers deepen, extend, or formalize.
A potential collaborator uses this page to identify their expertise — geometry, empirical methods, org theory, practice — and immediately sees which papers matter and where their contribution could fit.
What Is Your Entry Point?
Select your background. The layers below reorder to prioritize what matters most to you. All layers remain visible.
L0 What is SBT?
Foundations
The foundational architecture — eight dimensions, observer cohorts, coherence types, and conviction dynamics. Start here for orientation regardless of background.
Core — read first
CORE Under Review
Under review
Spec-gap is universal: biology, brands, organizations, code
Supplementary
supp Preprint
Why Eight?
Minimal completeness proof + empirical robustness test (22 LLMs, drop-one/drop-pair/10D)
supp Preprint
Alibi
Domain-agnostic observation-to-knowledge architecture from financial NLP
supp Preprint
Literature Survey
What existed before SBT; why it was not enough; six open problems
supp
primary: L3 Under Review
Under review
Bridge from Aaker's 4 perspectives to SBT's 8 dimensions
L1 What is the mathematical structure?
Geometry
The formal machinery — Fisher-Rao metric, projection bounds, concentration of measure, sphere packing, and multi-observer triangulation.
Core — read first
CORE Preprint
Brand Space Geometry: Formal Metric
R1 (2026d)
Fisher-Rao metric, warped product, 36 independent components; the mathematical foundation
Supplementary
supp Preprint
Metamerism
JL lemma: >152% distortion projecting 8D to 1D; 31-39% brand pairs are metameric
supp Preprint
Cohort Boundaries
57% of simplex volume is boundary at delta=0.10; discrete segmentation is geometrically lossy
supp Preprint
Sphere Packing
E8 kissing number (240) bounds nearest competitors; dimensional correlation collapses capacity
supp Preprint
Triangulation
v1.2.1 · Multi-observer disagreement is signal; Perception DOP predicts estimation error (R^2=.926)
supp
primary: L0 Preprint
Why Eight?
Minimal completeness proof + empirical robustness test (22 LLMs, drop-one/drop-pair/10D)
supp
primary: L0 Preprint
Literature Survey
What existed before SBT; why it was not enough; six open problems
supp
primary: L4 Preprint
Spec Impossibility
48D org space; exhaustive specification is geometrically impossible
supp
primary: L2 Preprint
Spectral Dynamics
v1.1 · Phase space resolves Bonnet ambiguity; trajectory clustering detects competitive convergence
supp
primary: L5 Preprint
Rate-Distortion
J-shaped R(D); intermediate formats beat high-rate formats; 17 architectures converge
L2 How does perception change over time?
Dynamics
Non-ergodic tracking bias, Fokker-Planck diffusion, coherence-resilience under crisis, velocity and acceleration in phase space.
Core — read first
CORE Preprint
Non-Ergodic Brand Perception
R9 (2026o)
Cross-sectional tracking violates ergodicity; three structural sources of bias
CORE Preprint
Dove Case Study: Dimensional Activation
R10 (2026p)
20-year longitudinal decomposition across 4 cohorts; the worked example
Supplementary
supp Preprint
Diffusion
Fokker-Planck SDEs; absorbing boundaries; non-ergodicity proved formally
supp Preprint
Coherence-Resilience
Coherence type (not score) predicts crisis survival via drift geometry
supp Preprint
Spectral Dynamics
v1.1 · Phase space resolves Bonnet ambiguity; trajectory clustering detects competitive convergence
L3 What does SBT predict for real problems?
Applications
Practitioner tools — the Spectral Audit, the Dove longitudinal case study, resource allocation, portfolio interference, and AI-native identity.
Core — read first
CORE Under Review
Under review
Six-step diagnostic: run it on any brand today for ~$0.80
CORE Preprint
Dove Case Study: Dimensional Activation
R10 (2026p)
20-year longitudinal decomposition across 4 cohorts; the worked example
CORE Preprint
Non-Ergodic Brand Perception
R9 (2026o)
Cross-sectional tracking violates ergodicity; three structural sources of bias
CORE Preprint
Dimensional Collapse in AI-Mediated Brand Perception: LLMs as Metameric Observers
R15 (2026v)
v3.0 · 21,350 calls, 24 models, 9 cultural traditions; dimensional collapse is universal (cosine .977); specification paradox (1,440 calls)
Supplementary
supp Preprint
Resource Allocation
Optimal investment proportional to cohort weights; alignment gap bounds loss
supp Working Paper
Portfolio Theory
Multi-brand interference: LVMH constructive vs Unilever destructive
supp Preprint
AI-Native Identity
v1.8.1 · Behavioral signatures replace logos for AI observers; Brand Function verification
supp Under Review
Under review
Bridge from Aaker's 4 perspectives to SBT's 8 dimensions
supp
primary: L2 Preprint
Coherence-Resilience
Coherence type (not score) predicts crisis survival via drift geometry
supp Working Paper
OrgSchema Audit
OST equivalent of the Spectral Audit; Spectra Coffee worked example; 2 propositions
L4 Where else does this structure appear?
Cross-Domain
The rendering problem is universal — organizations, biology, code, canon. OST, specification impossibility, and coordinate-free positioning.
Core — read first
CORE Under Review
Under review
Spec-gap is universal: biology, brands, organizations, code
Supplementary
supp Under Review
Under review
6-level cascade; acceptance testing as the missing construct
supp Preprint
Spec Impossibility
48D org space; exhaustive specification is geometrically impossible
supp Under Review
Under review
Org positions project process space onto personnel dimension
supp Under Review
Under review
Version-controlled IP specification; Shakespeare fork demo
supp Under Review
Under review
Temporal stability: value > process > org form
L5 Does it hold against data?
Empirical
21,350 API calls across 24 LLMs and 7 training traditions confirm dimensional collapse. Rate-distortion curve maps 17 encoder architectures.
Core — read first
CORE Preprint
Dimensional Collapse in AI-Mediated Brand Perception: LLMs as Metameric Observers
R15 (2026v)
v3.0 · 21,350 calls, 24 models, 9 cultural traditions; dimensional collapse is universal (cosine .977); specification paradox (1,440 calls)
Supplementary
supp Preprint
Rate-Distortion
J-shaped R(D); intermediate formats beat high-rate formats; 17 architectures converge
supp
primary: L1 Preprint
Metamerism
JL lemma: >152% distortion projecting 8D to 1D; 31-39% brand pairs are metameric
supp
primary: L3 Preprint
AI-Native Identity
v1.8.1 · Behavioral signatures replace logos for AI observers; Brand Function verification
supp
primary: L1 Preprint
Triangulation
v1.2.1 · Multi-observer disagreement is signal; Perception DOP predicts estimation error (R^2=.926)
supp Preprint
Spectral Immunity
9,925 obs (v2.0 + v3.0), 40 brands, 13 models, 7 traditions; 0/20 FDR-significant = spectral immunity; Geely Auto multi-turn d = -1.11
supp Working Paper
PRISM Instrument
v1.0.2 · Five-layer scaffold; PRISM-B items, 1-5 ordinal, DCI scoring; 4 propositions
L6 How should research itself be structured?
Meta-Science
Verification crisis as specification crisis. Paper as YAML spec. Git-native publishing protocol. The epistemological pipeline that made SBT verifiable.
Core — read first
CORE Under Review
Under review
Verification crisis = specification crisis; Paper Spec (YAML) with 5 layers
Supplementary
supp Preprint
Research Repo
v2.0 · Git-native protocol; papers are renders, repos are the artifact
supp
primary: L0 Preprint
Alibi
Domain-agnostic observation-to-knowledge architecture from financial NLP
supp
primary: L4 Under Review
Under review
Version-controlled IP specification; Shakespeare fork demo
Reading Paths by Audience
Ten structured paths through the program. Each starts where your expertise intersects, then expands outward.
Brand practitioner L3 → L0 → L3
You run brand strategy, communications, or marketing. Start with the diagnostic, then understand why it works.
Brand equity / Aaker tradition L3 → L0
You work in or cite the Aaker brand equity framework and want to see the relationship.
- Engage Aaker L3
- SBT L0
- Why Eight? L0
Empirical researcher L5 → L0 → L5
You evaluate this as a contribution to quantitative marketing science.
- PRISM-B L5
- SBT L0
- Rate-Distortion L5
AI / ML researcher L5 → L3 → L1
You study how language models represent concepts. The empirical and geometry layers are most relevant.
- PRISM-B L5
- AI-Native Identity L3
- Rate-Distortion L5
- Metamerism L1
Mathematician / Geometer L1 straight through
You want to verify the formal machinery before engaging with applications.
- Brand Geometry L1
- Metamerism L1
- Cohort Boundaries L1
- Sphere Packing L1
Information theorist L5 → L1 → L5
You think in bits, rate-distortion, and channel capacity.
- Rate-Distortion L5
- Metamerism L1
- PRISM-B L5
Psychometrician / Survey designer L1 → L5 → L1
You design measurement instruments. The triangulation and PRISM papers are most directly relevant.
- Triangulation L1
- PRISM-B L5
- Brand Geometry L1
Strategy / management scholar L2 → L3
You study competitive dynamics and long-run brand trajectories.
- Non-Ergodic L2
- Dove Case L3
- Coherence-Resilience L2
Organizational theorist L4
You study how structure relates to performance. The rendering problem is your entry point.
- Rendering Problem L4
- OST L4
- Projection L4
Philosopher of science L6 → L0
You care about how knowledge is structured and verified. Start with the meta-science layer.
- Paper Spec L6
- Research Repo L6
- Alibi L0
Open Problems
Identified gaps in the current program. A collaborator who fills any of these makes a direct contribution to the architecture.
| # | Gap | Layers | Priority | Potential paper |
|---|---|---|---|---|
| 1 | Human-subject empirical validation | L5 | HIGH | MaxDiff or conjoint study validating cohort divergence on the 8 dimensions with human respondents. Synthetic cohort pre-pilot (Run 15, eta-sq .091-.394) demonstrates PRISM-B sensitivity; primacy effect identified + Latin-square mitigation. Human study is next. |
| 2 | Temporal dynamics validation | L2 L5 | HIGH | Longitudinal LLM brand perception tracking across model updates. Exp 3 (300 calls) confirms LLMs detect trajectory direction; Bonnet pair resolution confirmed empirically. Longitudinal tracking across model versions is the remaining gap. |
| 3 | Agentic commerce integration | L3 L4 | MEDIUM | How brands survive multi-step AI shopping agent workflows where dimensional collapse compounds across retrieval, comparison, and recommendation stages. Initial 3-step pipeline test (425 calls, 6 models) confirms compounding (eta-sq = .029). Specification Paradox discovered (1,440 calls, 8 models): information framing amplifies collapse (d = .820); constraint framing reduces it 42% (d = -.983). "Tell the model what to DO, not what to KNOW." Realistic multi-turn agents with memory are the remaining gap. |
| 4 | Capstone synthesis (premature) | L6 | PREMATURE | Unified review of the full theory architecture; needs human data first |