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docs(traceability): V1 updated — Chentsov invariant (not unique), S1-S3 resolved

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Allaun Silverfox 2026-06-23 06:01:22 -05:00
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TRACEABILITY_GRAPH.md
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@ -26,7 +26,7 @@ If any GIVEN is ever falsified, the entire graph collapses.
[F0] √a·√b = √(ab)
│
▼
[F1] Chentsov ──→ [V1] g_p(u,v) = Σ uᵢvᵢ/pᵢ
[F1] Chentsov (invariant, not unique) ──→ [V1] g_p(u,v) = Σ uᵢvᵢ/pᵢ
│
▼
[V2] φ(p) = (√p₁,...,√p₈) ∈ S⁷
@ -53,7 +53,7 @@ If any GIVEN is ever falsified, the entire graph collapses.
| Node | Formula | Depends On | Verified By | Consensus Value | Status |
|------|---------|-----------|-------------|-----------------|--------|
| V1 | g_p(u,v) = Σ uᵢvᵢ/pᵢ | F1 (Chentsov) | Given theorem | N/A | ✅ GIVEN |
| V1 | g_p(u,v) = Σ uᵢvᵢ/pᵢ | F1 (Chentsov invariant) | Proven: invariance under coarse-graining (Verification 005) | N/A | ✅ INVARIANT (uniqueness open) |
| V2 | φ(p) = (√p₁,...,√p₈) | V1 (metric def) | Direct calc | ‖φ(p)‖₂ = 1.0 | ✅ VERIFIED |
| V3 | d_{S⁷}(a,b) = arccos(⟨a,b⟩) | F2 (round metric) | Given theorem | N/A | ✅ GIVEN |
| **V4** | **⟨φ(p),φ(q)⟩ = Σ√(pᵢqᵢ)** | **V2 + F0** | **Alpha,Beta,Gamma** | **0.97586930** | **✅ 3-AGENT** |