From 7709520806ed56b93e0dce7a427f193e37705c1a Mon Sep 17 00:00:00 2001
From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com>
Date: Tue, 23 Jun 2026 05:50:42 -0500
Subject: [PATCH] =?UTF-8?q?docs(verification):=20P5=20=CE=A6-corkscrew=20v?=
 =?UTF-8?q?erified=20=E2=80=94=20all=207=20formulas=20now=203-agent=20cons?=
 =?UTF-8?q?ensus?=
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---
 VERIFICATION_LOG.md | 24 +++++++++++++++++++++++-
 1 file changed, 23 insertions(+), 1 deletion(-)

diff --git a/VERIFICATION_LOG.md b/VERIFICATION_LOG.md
index 6853ec50..6f530f83 100644
--- a/VERIFICATION_LOG.md
+++ b/VERIFICATION_LOG.md
@@ -99,7 +99,29 @@ agree before the formula is accepted.
 | 004 | P2: Idempotence C(C(p))=C(p) | ✅ VERIFIED | All diffs = 0 | 2026-06-23 |
 | 005 | P3: Contraction d_F(C(p),C(q))<d_F(p,q) | ✅ VERIFIED | 0.100441 < 0.440258 | 2026-06-23 |
 | 006 | P4: Information loss I_loss(p) | ✅ VERIFIED | 0.106727 nats | 2026-06-23 |
-| 007 | P5: Φ-corkscrew f(n) | ⬜ PENDING | — | — |
+| 007 | P5: Φ-corkscrew f(n) | ✅ VERIFIED | f(20121)=(-137.80079576,-33.64432624), dist=264.41810784 | 2026-06-23 |
+
+---
+
+## VERIFICATION 007: P5 — Φ-Corkscrew f(n)
+
+**Formula:** f(n) = (√n·cos(nψ), √n·sin(nψ)), ψ = 2π/φ²
+
+**Test values:** n₁ = 20121, n₂ = 20122
+**Verified by:** Alpha, Beta, Gamma
+**Consensus:**
+- φ = 1.61803399
+- ψ = 2.39996323
+- f(20121) = (-137.80079576, -33.64432624)
+- f(20122) = (124.33952368, -68.27651757)
+- Distance = 264.41810784
+- Different: YES (consecutive integers produce different points)
+**Date:** 2026-06-23
+**Status:** ✅ VERIFIED
+
+**Note:** Injectivity follows from ψ/2π = 1/φ² being irrational. If f(m)=f(n)
+with m>n, then (m-n)ψ ∈ 2πℤ, requiring ψ/2π ∈ ℚ. But φ² = φ+1 is irrational,
+so 1/φ² is irrational. Contradiction. Therefore f is injective.
 
 **Rule:** Status PENDING → 3-agent verification → VERIFIED or REJECTED.
 No formula moves from PENDING to VERIFIED without all 3 agents agreeing.