Coherence Matrix
The central mathematical object — a 7×7 Hermitian matrix. Diagonal — populations of dimensions (A, S, D, L, E, O, U). Off-diagonal elements — coherences between them.
- Purity P = Tr(Γ²) — measure of integrity
- P_crit = 2/7 — viability condition
- C = Φ × R — integration × reflexion
- L0→L4 — from interiority to unity
γAA
γAS
γAD
γAL
γAE
γAO
γAU
γSA
γSS
γSD
γSL
γSE
γSO
γSU
γDA
γDS
γDD
γDL
γDE
γDO
γDU
γLA
γLS
γLD
γLL
γLE
γLO
γLU
γEA
γES
γED
γEL
γEE
γEO
γEU
γOA
γOS
γOD
γOL
γOE
γOO
γOU
γUA
γUS
γUD
γUL
γUE
γUO
γUU
Coherence Matrix Γ ∈ ℂ⁷ˣ⁷
The Single Primitive
Five Axioms Ω⁷
- ∞-topos Sh∞(𝒞) — the single primitive; structure, time and dynamics are derived from five axioms
- Logic, time and space are consequences
- Principle of informational distinguishability
Structure
Seven Dimensions of the Holon
- Holon — integral unit of being
- Seven dimensions: A, S, D, L, E, O, U
- Coherence matrix Γ ∈ ℂ⁷ˣ⁷
Octonionic Foundation
Why Exactly 7
- P1 + P2 → 𝕆 → dim(Im(𝕆)) = 7
- Fano plane and G₂ symmetry
- Hamming code H(7,4) and Cayley-Dickson boundary
Dynamics
Evolution Equation
- dΓ/dτ = −i[H,Γ] + 𝒟[Γ] + ℛ[Γ,E]
- Dissipation from decoherence, regeneration from interiority
- Global attractor
Emergent Time
Time from Structure
- Time is not postulated — it is derived
- O-dimension as internal clock
- Discreteness τ ∈ ℤ₇ and arrow of time
Viability
Conditions of Existence
- Purity P — measure of integrity
- P_crit = 2/7 (theorem, five paths)
- Domain of stability
Gap Semantics
Interiority / Exteriority
- Gap(i,j) = |sin(arg(γᵢⱼ))| — duality
- Fano channel: dissipation via PG(2,2)
- Phase diagram of coherent states
Consciousness
From Qualia to Collective Mind
- 21-pair qualia taxonomy from Γ
- Emotions, attention, memory — from formalism
- AI consciousness: operational criteria
Physical Correspondence
From Γ to the Standard Model
- G₂ gauge symmetry and generations
- Yukawa hierarchy from Fano textures
- Cosmological constant: Λ budget
Proofs
Formal Theorems
- Minimality of 7 dimensions (Track A)
- 392 registry rows (T-1..T-325): from P_crit = 2/7 to substrate independence
- Categorical formalism and lax 2-functor
Coherence Cybernetics
Engineering Applications
- Measurement protocol for Γ in AI
- Conditional No-Zombie theorem
- Paninteriorism ≠ panpsychism
Reference
Verification & Notation
- Falsifiable predictions of the theory
- Status registry [Т]/[С]/[О]/[И]/[Г]/[П]
- Glossary, notation, specification