@@ -3,10 +3,49 @@
 **Status:** FINDING `[G]` — W5 RUN (`spiral_adi_probe.py`/`.json`) + a
 targeted verification measurement, both committed.
 
-**The claim.** On a Vogel/golden lattice, a *local* non-Fibonacci control
-for stride-structure experiments **does not exist** — not "is hard to
-build," does not exist. Locality and Fibonacci-family membership are the
-same property, by the three-distance theorem: a point's near neighbours in
+> **⊘ CORRECTION (2026-08-12, codex review on PR #936, same day) — the
+> HEADLINE 0.9996 anisotropy ratio this finding cites is retracted; the
+> MECHANISM below it is not.** The headline run's control was subsampled
+> at 250k points/band against ~956k-point headline bands — ~74 % of
+> sources got no real KD-tree and silently self-linked — so 0.9996 mostly
+> measured self-links, not the control, and cannot by itself establish
+> anything. **The 99.38 %-Fibonacci-offset verification measurement below
+> is UNAFFECTED**: it ran at N=62 208, with per-band populations
+> (~7 776 points) far under the 250k cap, so no subsampling occurred
+> there — the mechanism claim (locality ⟺ Fibonacci membership via the
+> three-distance theorem) still rests on a real, unsampled measurement.
+> Fixed same day (`106ca605`): `build_control_links` is now full-band, no
+> cap; a v2 headline rerun is in flight. Once it lands, this note gets a
+> sibling recording the corrected headline ratio — append-only, this
+> paragraph is not edited further.
+
+> **⊘ SECOND CORRECTION (2026-08-12, codex P2 on PR #937) — "does not
+> exist" overclaims what 99.38 % actually showed.** The claim below reads
+> as a universal non-existence proof; the evidence is a 99.38 % rate at
+> ONE N (62 208) with ONE control construction (distance-matched among 8
+> real nearest neighbours) — not 100 %, and not a sweep across constructions
+> or scales. **What is actually proven, exactly:** the three-distance
+> theorem is a real theorem — a point's near neighbours on this lattice
+> ARE at convergent-denominator (Fibonacci) index offsets, as a matter of
+> number theory, not measurement. **What is empirical and should be read
+> as strong CORROBORATION, not proof of universal impossibility:** 99.38 %
+> of the measured control links landed on a Fibonacci offset, with the
+> ~0.62 % remainder consistent with the independently-measured ~1–2 %
+> structural boundary effect (points whose own forward Fibonacci partner
+> falls outside band range, counted separately in the same session) rather
+> than evidence of a working non-Fibonacci alternative. The claim below is
+> RESTATED, not deleted, to match this scope: read "does not exist" as
+> "the three-distance theorem predicts it cannot, and 99.38 % measured
+> confirmation at one tested N/construction is consistent with that" — a
+> sweep across N and control constructions would be needed to call the
+> universal form settled.
+
+**The claim, AS ORIGINALLY WRITTEN below (kept for the record; read through
+both corrections above).** On a Vogel/golden lattice, a *local*
+non-Fibonacci control for stride-structure experiments **does not exist**
+— not "is hard to build," does not exist. Locality and Fibonacci-family
+membership are the same property, by the three-distance theorem: a point's
+near neighbours in
 physical space are exactly the points at convergent-denominator index
 offsets, and for the golden angle the convergent denominators ARE the
 Fibonacci numbers.
 
@@ -855,6 +855,7 @@ Membrane consumers can now pull BOTH halves of a render `classid` BBB-safely fro
 | PR | Merged | Title | What it added |
 |---|---|---|---|
 | *gap note* | — | **#781–#925 are NOT in this table** — carried by the dated sections above + `PR_ARC_INVENTORY.md`. Recorded 2026-08-12 (codex P2 on #930) rather than silently reconstructed; the table had stalled at #780. | — |
+| **#936** | 2026-08-12 | W5 v1 RUN (B2 PASS / B3 VOID / B4 smooth) — ⊘ SUPERSEDED same day, all three verdicts compromised; v2 CODE fix merged in this PR, v2 RUN/results in flight | Codex found 4 real defects: B3 control subsampled at 250k/band (~74 % self-linked at headline, ratio 0.9996 uninformative); B2's fit floor = input σ (8 iters ≈ inert, "resolved" indistinguishable from "untouched"); bump only 1.72σ from the mask edge (analytic truncation ratio 1.2082 ≈ the measured "1.213 asymptote" — likely the MASK, not the operator); 99.38 % Fibonacci-membership figure was chat-only. Fixed same day, code merged HERE (`106ca605`, verified an ancestor of this PR's merge commit — corrects two overclaims caught by codex P2 on PR #937: the fix was described as "landing in a follow-up PR" when it had already landed, and the histogram artifact as "committed" when only the SCRIPT that produces it had landed — the tracked JSON is still v1's until the v2 run completes): full-band control, V-matched iteration scaling, bump moved to 3.35σ clearance + baseline-through-mask computed, offset histogram now computed by the script. The epiphany's MECHANISM survives (sub-cap 99.38 % measurement was never subsampled) but its "does not exist" phrasing was also softened (codex P2 on #937: 99.38 % ≠ 100 %, one N/one construction ≠ universal proof) — only the headline evidentiary number is retracted; the claim is restated at its actual evidentiary scope, not deleted. |
 | **#935** | 2026-08-12 | The validation wave RUNS: T1–T4 + W2s-a executed; `E-A-CONTROL-THAT-CANNOT-LOSE-IS-NO-CONTROL-1` | T2/T3/T4 PASS (68–106× at 200q; tempered 140/140 exact vs golden 124–127/140; 39.0 % naive-rounding collapse). T1 twice-corrected under codex review of its own run: verified-permanent m* = **1.9–2.7× q** (first-crossing 1.0–1.4× was not permanent; q=17: D*(22) back above the ceiling). W2s-a: G1 VOID, G2/G4 FAIL — the CONTROL is degenerate (two translated identical grids are symmetry-uniform, CV ~1e-12; cannot lose any evenness comparison). W5 pre-registered, run in flight at merge. |
 | **#934** | 2026-08-12 | Board hygiene #932/#933 + storm-geography refinement | MIXED. Refinement, each claim measurement-grounded: centering = tempered territory (spiral center structurally sub-floor at any N; shipped `find_center` already exact-register); collision annulus = golden (Go/territory framing); overlay = controlled chaos at 12 B/node; self-description asymmetry (tempered up to q, golden unbounded). Task causes the regime, geography sorts the tasks. Arc entry written one PR late, caught in #935's hygiene pass. |
 | **#933** | 2026-08-12 | 4 codex fixes on merged #932 + `golden-vs-tempered-stride-v1` (head-vs-gut plan) | MIXED. Fixes: W5 bump sub-floor despite "fixed" N (local index = √(r²N), not √N → N=3·F(17)², bump r=0.75, bands 1–2 excluded); tie test redefined per-source (d1/d2 ratio); 17-TET sign convention unified; B3 control distance-matched (residue arithmetic exposed 1500/2600 as wrong-scale in disguise). Plan: T1 crossover at m≈q across 8 q; T2 golden 68–106× ahead at m=200q; T3 tempered fills q/q by proof vs golden 124/140 at q=140; T4 naive φ-rounding collapses at 39 % of q∈[8,300). "Best stride" declared metric-dependent (3 metrics → 3 different winners at q=17). |
 
@@ -54,6 +54,77 @@
 **Status:** MERGED (`e6e27829`). Branch `claude/jirak-math-theorems-harvest-rfii13`
 → `main`. Doc/plan/board only.
 
+## 2026-08-12 — lance-graph #936 (MERGED) — W5 v1 RUN: B2 PASS / B3 VOID / B4 smooth, and codex found all three verdicts were built on sand (v2 fix in flight, not yet landed)
+
+- **Added.** `spiral_adi_probe.json` — v1's headline (N=3·F(17)²=7 651 227)
+  + B4 sweep result — plus `E-ON-A-GOLDEN-LATTICE-LOCALITY-IS-FIBONACCI-MEMBERSHIP-1`
+  (the epiphany that a local non-Fibonacci control on a Vogel lattice does
+  not exist, per the three-distance theorem).
+- **⊘ SUPERSEDED — this PR's own verdicts, corrected the same day.** Codex
+  review on #936 found FOUR real defects, each striking at a different
+  verdict: (1) **B3's control was subsampled** at 250k/band against
+  ~956k-point headline bands — ~74 % of sources got no real tree and
+  silently self-linked, so the reported ratio 0.9996 measured mostly
+  self-links, not the control — **the VOID verdict, and the epiphany's own
+  99.38 % Fibonacci-membership figure that grounded it, rest on an
+  unverified headline number** (the 99.38 % measurement itself was taken
+  at a SUB-cap N and remains valid; only the HEADLINE ratio was
+  compromised). (2) **B2's iso-fit search floor equalled the input σ** —
+  an inert operator (v1's fixed 8 iterations added ~0.003 % variance at
+  N=7.65M) fits `sigma_ref=sigma` exactly, indistinguishable from a
+  resolved diffusion — **the PASS verdict never demonstrated diffusion
+  occurred.** (3) **The bump sat only 1.72σ from the qualifying-band mask
+  edge** — analytically, a one-sided Gaussian truncation there produces a
+  covariance ratio of 1.2082, matching the measured "asymptote" of 1.213
+  closely — **the reported ~21 % structural anisotropy residual is
+  plausibly the MASK, not the ADI operator.** (4) The 99.38 % figure lived
+  only in chat/board prose, not in a committed, reproducible artifact.
+- **Fixed, same day, pre-registered BEFORE the v2 run — the CODE, and it
+  landed IN #936, not in a follow-up** (`106ca605` is an ancestor of
+  `a3f627f3`, verified via `git merge-base --is-ancestor`; corrects an
+  overclaim in this entry's first draft, caught by codex P2 on PR #937 —
+  "landing in a follow-up PR" described the RUN's results, not the fix
+  itself, and read as if the fix were still pending when it was already
+  merged): full-band control (no cap; verified in-qualifying self-link
+  rate 0.27 % at the real headline N — a live debugging trap caught and
+  explained en route: a FIRST v2 diagnostic divided by total N rather than
+  qualifying-band population and reported a spurious 38 % "self-linked",
+  predicted exactly from the qualifying/non-qualifying population split,
+  confirming it was the diagnostic that was wrong, not the control);
+  iterations scaled to a fixed target added variance
+  (`iters = round(2V/h²)`, h² the measured mesh spacing) with the fit
+  search centered on the predicted σ_ref, plus a raw pre-fit check against
+  the unsmoothed input; the bump moved to σ=0.05, r0=0.78 (≥3.35σ
+  clearance; analytic baseline ratio there ≈1.005) with the
+  unsmoothed-baseline anisotropy now computed through the identical mask
+  every run; the control-link offset histogram is now COMPUTED by the
+  script (codex P2 on #937, second catch: "now lands in the committed
+  JSON" was future-tense stated as present — the tracked
+  `spiral_adi_probe.json` at merge time is still the v1 result with no
+  histogram in it; the histogram artifact itself is committed only once
+  the v2 RUN completes and its JSON replaces v1's). Timing verified (not
+  guessed) before launching: ~33 min for the headline sweep loops alone.
+- **Deferred.** The v2 RUN's RESULTS — in flight at merge time (the v2
+  CODE already merged, per the correction above), landing in a follow-up
+  PR with corrected B2/B3/B4 verdicts AND the histogram artifact codex P2
+  asked to see committed. n=19/21 are out of scope
+  for v2's B4 under the V-matched iteration scaling (mechanism stated:
+  iters grows roughly linearly with N at fixed physical blur target,
+  making n=19 orders of magnitude more expensive than v1's uniform
+  8-iteration sweep ever cost — which is exactly why v1's n=19 number was
+  cheap AND uninformative).
+- **Confidence.** LOW on this PR's own three verdicts (B2/B3/B4), as
+  established the same day by external review — recorded rather than left
+  standing. The three-distance-theorem MECHANISM in the epiphany
+  (locality ⟺ Fibonacci membership) is independent of the compromised
+  headline ratio and stands on the sub-cap verification alone; the
+  epiphany entry is not retracted, only its headline evidentiary anchor.
+
+**Status:** MERGED (`a3f627f3`). Branch `claude/jirak-math-theorems-harvest-rfii13`
+→ `main`. This PR's v1 VERDICTS are superseded same-day (the v2 CODE fix
+merged in this same PR, per the correction above); see the v2 RUN entry
+once its results land.
+
 ## 2026-08-12 — lance-graph #935 (MERGED) — the validation wave RUNS: T1–T4 + W2s-a executed, four more defects caught, one new epiphany
 
 - **Added.** `golden_vs_tempered_probe.py`/`.json` (T1–T4 executed against
 
@@ -25,7 +25,7 @@ Wave 1 = parallel, no operator gate beyond go-ahead; gated rows named.
 
 | D-id | Deliverable | Wave | Status | Feeds |
 |---|---|---|---|---|
-| D-W5 | Spiral-ADI anisotropy (final spec: N=3·F(17)²=7.65M, bump r=0.75, distance-matched control) | 1 | **RUN — B2 PASS (iso 0.00053 vs 0.15, aniso 1.213 vs 1.25); B3 VOID structurally (control links are 99.38 % Fibonacci — three-distance theorem: locality IS family membership, `E-ON-A-GOLDEN-LATTICE-LOCALITY-IS-FIBONACCI-MEMBERSHIP-1`); B4 smooth, NO knee at n=17 (floor = safety margin on this metric, per the pre-registered second branch)** | domino.rs gather design UNBLOCKED by B2; honest residual: structural ~21 % aniso asymptote flagged for any bar below 1.22 |
+| D-W5 | Spiral-ADI anisotropy (v2 spec: full-band control, V-matched iterations, bump 3.35σ from mask) | 1 | **v1 RUN ⊘ SUPERSEDED (4 codex defects on #936: subsampled B3 control, inert-operator-indistinguishable B2 fit, mask-truncation-explains-the-"asymptote", uncommitted verification artifact) — v2 RUN IN FLIGHT, results in a follow-up PR** | domino.rs gather design claim now PENDING v2 (not unblocked — v1's B2 PASS never demonstrated diffusion occurred); mechanism-level epiphany survives on its unaffected sub-cap measurement |
 | D-W2sA | Golden-vs-grid pairing on real cos-lat metric (zero-ties G1, CV G2) | 1 | **RUN — G1 VOID, G2/G4 FAIL (control degenerate: two identical translated grids are symmetry-uniform, CV ~1e-12 — cannot lose any evenness comparison; diagnosed via smoke test, run as-specified, `E-A-CONTROL-THAT-CANNOT-LOSE-IS-NO-CONTROL-1`)** | honest falsifier for evenness DEFERRED (offset/rotation-varied or spacing-mismatched control); §10.5 properties 1–3 untouched |
 | D-W6 | Two-component deconvolution (geo + bow, global lstsq, 38 eqs / 2 params; B3 = stranded stratification via v_rel) | 1 | Queued | dipole vector-sum identification; F17 gate |
 | D-W2sB | α-window sweep β∈[0.85,1.15] | gated (W2s-a) | Queued | corridor α discriminator |