A rigorous mathematical framework for representing, analyzing, and transforming business configurations within a 64-state semantic space.
Economic Geometry is a formal theory that treats economic agents, capital, and business models as geometric objects in a multidimensional state space. It provides the mathematical foundation for the SUBIT-64 ontology and enables structural analysis of business configurations.
Every economic entity can be uniquely represented as a vector ω in the product space:
Ω = A × V × T
where:
- A (WHO — Agency) = {ME, WE, YOU, THEY}
- V (WHERE — Vector) = {EAST, SOUTH, WEST, NORTH}
- T (WHEN — Phase) = {SPRING, SUMMER, AUTUMN, WINTER}
This yields |Ω| = 64 canonical states, isomorphic to the 6-bit cube {0,1}⁶.
economic-geometry/
│
├── README.md # This file
├── LICENSE # MIT License
├── CITATION.cff # Citation metadata for academic use
│
├── axioms/ # Foundational principles
│ ├── space-definition.md # Ω = A × V × T: proof of completeness
│ ├── orthogonality-proof.md # Independence of WHO, WHERE, WHEN
│ └── binary-isomorphism.md # {0,1}⁶ mapping and Anima/Animus duality
│
├── geometry/ # Mathematical structure
│ ├── metric-space.md # Hamming distance, structural friction SF(ω)
│ ├── geodesics.md # Optimal transformation paths
│ ├── observables.md # CES, risk, monetization as functionals
│ └── symmetry-group.md # Transformation operators T: Ω → Ω
│
├── dynamics/ # Evolution and change
│ ├── transformation-operators.md # Scale, Pivot, Harvest, etc.
│ ├── phase-transitions.md # First and second-order transitions
│ ├── bifurcation-theory.md # Critical points and instability
│ └── trajectory-prediction.md # Forecasting business paths
│
├── atlas/ # Complete mapping of Ω
│ ├── subit-64-catalog.md # All 64 states with descriptions
│ ├── capital-efficiency-heatmap.md # CES values across Ω
│ ├── structural-friction-tensor.md # SF(ω) for all configurations
│ └── risk-profiles/ # Detailed risk analysis per region
│ ├── quadrant-1.md
│ ├── quadrant-2.md
│ └── ...
│
├── applications/ # Practical implementations
│ ├── business-diagnostics/ # How to identify ω for real companies
│ │ ├── methodology.md
│ │ └── case-studies/
│ │ ├── amazon-trajectory.md
│ │ ├── tesla-evolution.md
│ │ └── startup-failures.md
│ ├── portfolio-theory.md # Diversification as dispersion in Ω
│ ├── investment-criteria.md # Geometric due diligence
│ └── policy-framework.md # National economic cartography
│
├── extensions/ # Advanced topics
│ ├── n-dimensional-generalization.md # Ωₙ beyond 3 dimensions
│ ├── quantum-analogies.md # Superposition of business states
│ ├── fractal-hierarchy.md # Self-similarity across scales
│ └── category-theory-foundations.md # Functorial approaches
│
└── implementations/ # Computational tools
├── python/
└── README.md
├── omega_space.py
├── metrics.py
├── transformers.py
└── visualization/
├── lattice-3d.py
└── trajectory-plotter.py
| Concept | Symbol | Definition |
|---|---|---|
| State Space | Ω | A × V × T, the complete economic configuration space |
| State Vector | ω | (a, v, t), a point representing a business configuration |
| Structural Distance | d(ω₁, ω₂) | Hamming distance between states |
| Structural Friction | SF(ω) | Internal inconsistency measure |
| Capital Efficiency | CES(ω) | (Fₗ × M_v × Pₜ) - SF, the principal observable |
| Transformation | T: Ω → Ω | Operators representing business evolution |
This repository provides the mathematical foundation for the SUBIT-Omega-Analyzer tool:
| Repository | Purpose |
|---|---|
| economic-geometry | Formal theory, axioms, proofs, mathematical structure |
| subit-omega-analyzer | Practical implementation, prompts, business diagnostics |
- Begin with the axioms/space-definition.md
- Explore the atlas/subit-64-catalog.md to understand all 64 states
- Study geometry/metric-space.md for the mathematical core
- See applications/business-diagnostics/methodology.md for practical use
We welcome contributions from mathematicians, economists, entrepreneurs, and philosophers. See community/contributing.md for guidelines.
Current priorities:
- Formal proofs of completeness theorems
- Empirical validation studies
- Python implementation of core calculus
- Case study documentation
MIT License
v1.0 — Geometric Foundation (March 2026)
- Axiomatic definition of Ω-space
- Complete metric structure
- Transformation group specification
- Full atlas of 64 states