From 2b1ee2af1ad2aa93d3eb516056e265c8e92f71ef Mon Sep 17 00:00:00 2001
From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com>
Date: Tue, 23 Jun 2026 06:01:22 -0500
Subject: [PATCH] =?UTF-8?q?docs(traceability):=20V1=20updated=20=E2=80=94?=
 =?UTF-8?q?=20Chentsov=20invariant=20(not=20unique),=20S1-S3=20resolved?=
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---
 TRACEABILITY_GRAPH.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/TRACEABILITY_GRAPH.md b/TRACEABILITY_GRAPH.md
index ac2cec5a..96623c04 100644
--- a/TRACEABILITY_GRAPH.md
+++ b/TRACEABILITY_GRAPH.md
@@ -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** |