Spectral Brand Theory — Framework & Toolkit

Brands are stellar objects. You are the observer.

graph LR
    subgraph Brand["Brand Signal Source"]
        direction TB
        SEM((Semiotic))
        NAR((Narrative))
        IDE((Ideological))
        EXP((Experiential))
        SOC((Social))
        ECO((Economic))
        CUL((Cultural))
        TMP((Temporal))
    end

    subgraph Pipeline["Perception Pipeline"]
        direction TB
        OSP[Observer<br/>Spectral Profile]
        PC[Perception<br/>Cloud]
        CC[Conviction<br/>Collapse]
    end

    Brand -->|"8 dimensions"| OSP
    OSP -->|"filter + weight"| PC
    PC -->|"threshold"| CC

    style SEM fill:#fce4ec,stroke:#c62828
    style NAR fill:#e8eaf6,stroke:#283593
    style IDE fill:#e0f2f1,stroke:#004d40
    style EXP fill:#fff8e1,stroke:#f57f17
    style SOC fill:#f3e5f5,stroke:#6a1b9a
    style ECO fill:#e8f5e9,stroke:#2e7d32
    style CUL fill:#fbe9e7,stroke:#bf360c
    style TMP fill:#e3f2fd,stroke:#0d47a1
    style OSP fill:#e8eaf6,stroke:#333
    style PC fill:#fff3cd,stroke:#333
    style CC fill:#d4edda,stroke:#333

What Is This?

Aaker drew the anatomy chart. SBT built the microscope. Same brands, higher resolution.

Spectral Brand Theory (SBT) models brands as multi-dimensional signal sources perceived differently by every observer. There is no "brand in itself" — only signals and observers. This toolkit provides a seven-module AI-native analytical pipeline that turns any capable LLM into a brand perception X-ray machine, producing structural diagnosis that traditional audits cannot.

SBT's contribution is not the eight dimensions themselves --- it is the measurement infrastructure: the observer-cohort framework, the spectral weight formalism, the metamerism detection mathematics, and the Brand Function specification. This infrastructure enables geometric positioning in perception space regardless of which dimensional decomposition is used.

Quick Start

Analyze your first brand in 10 minutes:

1. Copy the prompt from prompts/01_BRAND_DECOMPOSITION.md
2. Paste into Claude, GPT-4, or any capable LLM with your brand name
3. Get structured YAML output: signal inventory across 8 dimensions
4. Run all 7 modules for a complete Spectral Brand Audit

The 7 Modules

#	Module	What It Does	Input	Output
1	Brand Decomposition	Inventory signals across 8 dimensions	Brand name + materials	Signal map, D/A ratio
2	Observer Mapping	Define audience spectral profiles	Brand context	3-5 cohort profiles
3	Cloud Prediction	Predict per-cohort perception clouds	Modules 1+2	Cloud map per cohort
4	Coherence Audit	Score brand coherence (7 metrics)	Module 3	Grade (A+ to F) + type
5	Emission Strategy	Design dimensionally specific action plan	Modules 1+2+4	Strategy per cohort
6	Re-collapse Simulation	Test disruption resilience	Modules 3+4	Resilience profile
7	Resource Allocation	Optimal investment, alignment gaps, blind spots	Modules 1+2	Allocation plan + gap table

Each module has a prompt + YAML template in templates/.

Module 7 adds four practitioner features not present in Modules 1-6:

• Financial report input: Upload a P&L, 10-K, or departmental budget. The LLM maps line items to 8 dimensions using the Dimension Glossary.

• Code Execution Mode: When the LLM has a Python sandbox (Claude tools, GPT Code Interpreter, any agent), it runs validate_resource_allocation() directly — the math is computed by deterministic code, not LLM inference. Zero hallucination on the hard numbers.

• Data quality gates: Every output is tagged with its data source (survey, financial_report, llm_estimate). Estimated inputs trigger a mandatory warning: results are indicative only until validated with real data. If >30% of budget cannot be mapped to dimensions, the tool refuses to produce results rather than guess.

• Clarification protocol: When budget items are ambiguous (e.g., "marketing" spans Narrative, Semiotic, Social), the LLM asks the user to clarify the split rather than estimating silently.

• Balanced dimension ordering (dimension_order): PRISM-B elicitation experiments found a primacy effect in JSON-based prompts (eta-sq=.217 — dimensions listed first receive ~15.4% weight vs ~8.0% for last). The generate_prism_b_prompt() function supports three modes to counterbalance this bias:

  Mode	Behavior
  "canonical" (default)	Fixed S-N-I-E-So-Ec-C-T order. Backward-compatible.
  "latin_square"	Cycles through 8 orderings from a cyclic Latin square. Each dimension appears in every position exactly once across the 8-row cycle.
  "random"	Random permutation per call. Pass seed= for reproducibility.

  from spectral_branding import generate_prism_b_prompt
  
  # Standard call (canonical order, backward-compatible)
  prompt = generate_prism_b_prompt("Hermes")
  
  # Counterbalanced: cycles through 8 balanced orderings automatically
  prompt = generate_prism_b_prompt("Hermes", "latin_square")
  
  # Reproducible random order
  prompt = generate_prism_b_prompt("Hermes", "random", seed=42)
  

Demonstrated on 5 Brands

Brand	Coherence Type	Grade	Key Finding
Hermès	Ecosystem	A+	Structural absence (dark signals) creates more value than emission
IKEA	Signal	A-	Consistent designed signals produce uniform resilience
Patagonia	Identity	B+	Productive contradiction — ideological core filters cohort compatibility
Erewhon	Experiential asymmetry	B-	Local and mediated audiences perceive structurally different brands
Tesla	Incoherent	C-	Maximum emission power, minimum architectural health

25+ non-obvious insights. 9 candidate mechanisms not found in existing branding literature.

Demand-side analysis: Observer cohort weights decompose market demand into eight dimensions. The validators double as investment guides — metamerism detection reveals the cheapest signal portfolio achieving a target perception, capacity analysis identifies profitable unoccupied positions, and trajectory risk flags cohorts where further investment has zero expected return and tracks per-dimension velocity (signed rate of change, direction, acceleration, and time-to-absorption estimates from sequential snapshots).

All five brand profiles have been retroactively validated against the mathematical bounds from R1-R7. Every profile passes metric axioms (R1), no metameric pairs exist among the five (R2), positioning capacity is unconstrained (R4), and trajectory risk is low across all brands (R6).

Key Concepts

Concept	Definition
Dark signal	Structural absence — designed restriction that functions as a signal
Spectral profile	Observer's sensitivity, weights, and tolerances across 8 dimensions
Perception cloud	Probabilistic cluster of signals forming in an observer's mind
Conviction collapse	Threshold event where a cloud crystallizes into a stable brand conviction
Re-collapse	Full rebuild of brand conviction from scratch when contradicting evidence arrives
D/A ratio	Designed vs. ambient signal balance (optimal zone: 55-65% designed)
Coherence type	Structural category of brand architecture (5 types, each with different resilience)

Mathematical Validation

Every pipeline output is validated against proven mathematical bounds from eight companion research papers (R0-R7):

Validator	Paper	What It Checks
Metric	R1 (Formal Metric)	Signal positivity, simplex constraints, triangle inequality
Metamerism	R2 (Spectral Metamerism)	Brands with similar scores but different 8D structure
Cohort	R3 (Cohort Boundaries)	Over-segmentation, false sharp boundaries
Capacity	R4 (Sphere Packing)	Positioning overcrowding, indistinguishable pairs
Trajectory	R6 (Diffusion Dynamics)	Absorption risk, irreversible perception decline
Specification	R5 (Impossibility)	Organizational spec coverage, cascade consistency
Resource Allocation	R7 (Spectral Resource Allocation)	Optimal dimensional investment, alignment gap, multi-cohort efficiency

The validation module (src/spectral_branding/validators/) is Python + numpy/scipy with 131 unit tests. It runs automatically on pipeline output, flagging geometric violations that no amount of prompt engineering can prevent.

Repository Structure

sbt-framework/
├── prompts/                  7 prompt modules (copy-paste into any LLM)
│   ├── 01_BRAND_DECOMPOSITION.md
│   ├── 02_OBSERVER_MAPPING.md
│   ├── 03_CLOUD_PREDICTION.md
│   ├── 04_COHERENCE_AUDIT.md
│   ├── 05_EMISSION_STRATEGY.md
│   ├── 06_RECOLLAPSE_SIMULATION.md
│   ├── 07_RESOURCE_ALLOCATION.md
│   └── README.md
├── templates/                YAML output schemas for structured results
│   ├── 01-07_*.yaml
│   ├── DIMENSION_GLOSSARY.yaml  Dual-purpose dimension reference (human + LLM)
│   └── FRAMEWORKS.md
├── data/
│   └── ATOM_TAXONOMY.yaml    Signal classification reference
├── docs/
│   ├── FRAMEWORK.md          Full theoretical framework (v2.3.1)
│   ├── GLOSSARY.md           Term definitions and relationships
│   └── architecture/         Mermaid architecture diagrams
│       ├── BRAND_PIPELINE.mmd    Full signal pipeline: emission → cloud → collapse
│       ├── OBSERVER_MODEL.mmd    Observer cohort spectral profiles
│       └── ALIBI_ANALOGY.mmd     Structural analogy: alibi finance ↔ SBT
├── src/spectral_branding/       Python validation module
│   └── validators/              7 math-hardened validators (numpy/scipy)
├── tests/                       131 unit tests for validators and prompt generator
├── pyproject.toml               Package config (hatchling + numpy + scipy)
├── CITATION.cff
├── LICENSE
└── README.md

Research

Resource	Description
Research Papers	Working papers on SBT and the underlying epistemological architecture
Brand Code	Executable brand identity specification — spectral palette, particle system source, AI-readable prompt
Preprint (DOI)	Formal academic paper — Spectral Brand Theory: A Computational Framework for Multi-Dimensional Brand Perception
R0: Literature Survey	Critical survey of geometric approaches to brand perception
R1: Formal Metric	Aitchison + Fisher-Rao metric for brand/observer spaces
R2: Spectral Metamerism	Information loss bounds under dimensional projection (JL lemma)
R3: Cohort Boundaries	Concentration of measure on the probability simplex
R4: Sphere Packing	E8 lattice bounds on brand positioning capacity
R5: Specification Impossibility	Geometric impossibility bounds for organizational design
R6: Diffusion Dynamics	Non-ergodic perception dynamics on manifolds
R7: Spectral Resource Allocation

Citation

@article{zharnikov2026sbt,
  title={Spectral Brand Theory: A Computational Framework for
         Multi-Dimensional Brand Perception},
  author={Zharnikov, Dmitry},
  year={2026},
  url={https://github.com/spectralbranding/sbt-framework}
}

See CITATION.cff for machine-readable citation.

Author

Dmitry Zharnikov — [email protected]

License

MIT — use freely with attribution.

Trademarks

"Spectral Brand Theory" and "Brand Code" are trademarks of Dmitry Zharnikov. The MIT license applies to the source code only and does not grant permission to use the project trademarks. You may fork and modify the code freely, but derivative works should not use these names in ways that imply endorsement or official affiliation.

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1 | Getting Started

Clone the repository and synchronise the Python environment:

git clone https://github.com/spectralbranding/sbt-framework.git
cd sbt-framework
uv sync --extra dev

The project anchor is pyproject.toml at the repository root (name = "sbt-framework", requires-python = ">=3.14,<3.15"). The full unit-test suite (131 tests) verifies the validator math:

uv run pytest -q

Or run the orchestrator for a single-command verification:

./reproduce.sh

2 | Project Layout

sbt-framework/
├── prompts/                 7 prompt modules (copy-paste into any LLM)
├── templates/               YAML output schemas + DIMENSION_GLOSSARY.yaml
├── data/                    ATOM_TAXONOMY.yaml and other reference data
├── docs/                    FRAMEWORK.md, GLOSSARY.md, architecture diagrams
├── src/spectral_branding/   Python validation module (7 validators)
├── tests/                   131 unit tests
├── output/
│   ├── figures/             generated PNG / SVG / PDF
│   ├── tables/              generated CSV / TeX / HTML
│   └── logs/                run logs (master_run.log per orchestrator run)
├── pyproject.toml           Package config (hatchling + numpy + scipy)
├── reproduce.sh             Single-command verification orchestrator
├── CITATION.cff             Machine-readable citation
├── LICENSE                  MIT (code)
├── LICENSE-data             CC BY 4.0 (data, figures, tables)
└── README.md

4 | Dependencies

Runtime (pyproject.toml [project.dependencies]):

• Python >=3.14,<3.15
• numpy>=1.26.0
• scipy>=1.12.0

Development extras (pyproject.toml [project.optional-dependencies.dev]):

• pytest>=8.0.0
• black>=24.0.0
• flake8>=7.0.0
• mypy>=1.8.0

Install everything with uv sync --extra dev. The lockfile (uv.lock) is committed for reproducibility.

6 | Citation

@software{zharnikov2026sbtframework,
  title  = {Spectral Brand Theory: AI-Native Brand Analysis Toolkit},
  author = {Zharnikov, Dmitry},
  year   = {2026},
  url    = {https://github.com/spectralbranding/sbt-framework}
}

Machine-readable metadata in CITATION.cff. The underlying paper (concept DOI 10.5281/zenodo.18945912) is referenced under preferred-citation and exposed by GitHub / Zenodo "Cite this repository" widgets.

7 | Licence

Dual-licensed in line with PUBLIC_MIRROR_STANDARD.md:

• Code (Python module, scripts, configs, reproduce.sh): MIT — see LICENSE.
• Data, figures, tables, generated artifacts under output/ and data/: Creative Commons Attribution 4.0 International (CC BY 4.0) — see LICENSE-data.

Trademark notice above applies to the project names; the dual licence does not transfer trademark rights.

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Last updated: 2026-05-29