Where the theory stands
Every statement of the corpus carries one of the registry's statuses. Here is the short account.
[T] Proved as mathematics
- Time as the reading of an internal clock: the depth register gives the time line ℝT-53b, T-118
- Viability window 2/7 < P ≤ 3/7; inside it no single resource optimumP_crit, T-222
- Standard Model group (kernel ℤ₆) and one complete generation with ν_R, anomaly-free, in ℂ⊗𝕆T-326, T-329
- Lorentzian 3+1 whose rotations commute with colour48c
- A tower of holons closes to the hyperfinite II₁ factor — given the split property, the algebra of a de Sitter observer, trace to traceT-348
[C] [I] Conditional or interpretive
- The physical reading of the above rests on two bridge premises, (Cl₀) and (P); neither follows from the axiomsT-347
- The axioms follow from the properties of a viable holon under three named conditionsT-190
- That the inner aspect of Γ is experience is an interpretation; its structure is tested empirically[I]
Coherence Matrix
The central object is the state of a holon: a 7×7 density matrix — Hermitian, positive, of trace one. The diagonal holds the populations of the seven dimensions; the 21 off-diagonal entries are the coherences between them. Hover over or tap a cell to read its meaning.
- P = Tr Γ² — purity, from 1/7 (maximally mixed) to 1 (pure)
- 2/7 < P ≤ 3/7 — the viability window
- C = Φ · R — consciousness measure: integration × reflection, threshold 1/3
- L0 → L4 — levels of interiority, separated by an A₄ (swallowtail) bifurcation
Coherence Matrix Γ ∈ ℂ⁷ˣ⁷
The corpus
The Single Primitive
Five Axioms Ω⁷
- The ∞-topos Sh∞(𝒞) over the states Γ — the single primitive
- Five axioms; every further input named on the premises page
- Distinguishability as the Bures metric
Structure
Seven Dimensions of the Holon
- Holon — the unit that models itself
- Seven dimensions: A, S, D, L, E, O, U
- All seven are necessary and functionally distinct (theorem 7/7)
Octonionic Foundation
Why Seven
- Hurwitz: dim Im 𝕆 = 7; N ≥ 7 is a theorem, no decomposition below 7 — premise (Σ₆), T-349
- Fano plane, the canonical orientation and G₂
- Hamming code H(7,4) and the Cayley–Dickson boundary
Dynamics
Evolution Equation
- dΓ/dτ = −i[H,Γ] + 𝒟[Γ] + ℛ[Γ,E]
- Dissipation by decoherence, regeneration by the self-model
- Living attractors in the window; the regeneration rate is free (T-346)
Emergent Time
Time from Structure
- Time is not postulated: the clock register of A5 (T-87)
- The time line ℝ from the depth register (T-53b, T-118)
- The arrow of time is indexed by stratal depth
Viability
Conditions of Existence
- Purity P — a measure of integrity
- Critical purity P_crit = 2/7 — theorem
- The window 2/7 < P ≤ 3/7 and its resource geometry (T-222)
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
- Qualia structure from the geometry of Γ (enriched Yoneda)
- Empirical programme: calibration, structure, engineering
- AI consciousness: operational criteria
Physical Correspondence
From Γ to the Standard Model
- The Standard Model group and one generation in ℂ⊗𝕆 — under (Cl₀)
- Flavour: what the clock can and cannot fix (T-345)
- Strong CP and Λ: honest no-go results
Proofs
Formal Theorems
- Minimality of the seven dimensions
- Critical purity, the viability window, the No-Zombie core
- Categorical formalism: the Grothendieck construction (T-211)
Coherence Cybernetics
Engineering Applications
- Measurement protocol for Γ in AI
- No-Zombie: mathematical core [T], reading [I]
- Paninteriorism ≠ panpsychism
Reference
Verification & Notation
- Falsification criteria and their current verdicts
- Status registry: [T] [C] [H] [D] [I] [P] [Pr] [✗]
- Premises, glossary, notation