Golden-ratio index floor (≥17/21) + the temperament mechanism — W5/W2s-a re-specced before any worker ran

.claude/board/EPIPHANIES.md

@@ -1,3 +1,105 @@
+## 2026-08-12 — E-THE-GOLDEN-STEP-IS-THE-WRONG-STEP-AT-SMALL-Q-1
+
+**Status:** FINDING `[G]` — arithmetic, fully reproducible, no fetch. Operator
+ruling + three measurements run this session.
+
+**The ruling (operator, three messages, paraphrased):** golden-ratio
+structure counts only from convergent index ~17–21 upward, below that it is
+unusable · the preferred small-q combination is modulus 17 with stride 4 ·
+the stride-11 alternative is explicitly not a golden-section step.
+
+**Measured, and it splits into two regimes with two different generators.**
+
+1. **The index floor is real and my specs were below it.** `F(n+1)/F(n)` is a
+   RATIONAL of period `F(n)`; convergent error n=10 → **1.5e-4**, n=13 →
+   8.2e-6, **n=17 → 1.8e-7**, n=21 → **3.7e-9**. Below the floor the ratio
+   *resonates* — the exact moiré the golden construction exists to prevent, so
+   a sub-floor lattice demonstrates the OPPOSITE of the property. The emergent
+   parastichy pair of an N-point Vogel lattice sits at `≈ √N`, so index ≥17
+   needs **N ≳ F(17)² = 2 550 409**. **W5 was specced at N=4096 (emergent pair
+   F(10)/F(11)) and its discovery step searched `j ∈ {1..60}` — structurally
+   incapable of returning anything above F(10). The sub-floor answer was
+   hardcoded and every bar would have been measured on it.** W2s-a likewise at
+   N=2048. Both corrected; both now carry an N-sweep so the floor is measured,
+   not inherited.
+2. **The angle is NOT what the floor binds.** `2π(1−1/φ)` in f64 is irrational
+   to ~1e-16 at any N. What the floor binds is the *addressable stride family*.
+   Keeping these apart is load-bearing: "fix the angle" would be the wrong
+   repair.
+3. **Below the floor, do not approximate φ at all — ENUMERATE.** This is the
+   payload. `helix/KNOWLEDGE.md:320` labels `(i·11)%17` the **"golden-step"**
+   because `17/φ = 10.51 → 11`. Enumerating all 16 strides mod 17, prefix
+   star-discrepancy at m = 5/9/13:
+
+   | stride | m=5 | m=9 | m=13 | |
+   |---|---|---|---|---|
+   | **4** | **0.2000** | **0.1111** | **0.0769** | shipped `CurveRuler`, D-QUANTGATE |
+   | 11 | 0.2000 | 0.1503 | 0.0905 | the "golden-step" |
+
+   **Stride 4 is never worse than 11 and strictly better at m=9 and m=13.**
+   And `17/11 = 1.5455` is **7.3e-2** from φ — an order of magnitude worse
+   than `13/8` (7.0e-3). At q=17 there is no irrational to approximate, and
+   the φ-derived selector picks the measurably worse integer. *(Honest
+   caveat: under worst-case-over-all-m, strides 10–15 tie at 0.5000 and
+   stride 4 reads 0.7647 — that metric is dominated by m=2 where every stride
+   is degenerate. The useful-prefix reading is reported as the one that
+   matters, and the other is stated rather than hidden.)*
+
+4. **The MECHANISM below the floor is TEMPERAMENT, not approximation**
+   (operator framing: the stride-11-region walk behaves like a 5/3
+   circle-of-fifths with a distributed Pythagorean-style comma — not a
+   genuine golden step, yet it does not collapse; and that last property is
+   the whole theory). A coprime stride `s` over `q` is
+   structurally a **circle of fifths**: it does not *approximate* the
+   irrational target, it **closes the cycle exactly** (coprimality → full
+   permutation) and **distributes the incommensurability error — the comma —
+   uniformly around the cycle** instead of letting it accumulate at a seam.
+   Measured: 12 pure fifths miss closure by the Pythagorean comma
+   **+23.46 ct**; 17-TET's fifth (stride 10) closes **exactly by
+   construction** with **+3.93 ct/fifth** spread around the circle. That
+   distributed comma is precisely the deterministic **anti-moiré dither**
+   D-QUANTGATE names. So the survival property below the floor is
+   **CLOSURE, not GOLDENNESS** — which is why the shipped integer walk was
+   always right even while its "golden-step" rationale was wrong.
+   - **The operator's tentative 5/3 identification resolves exactly:** the
+     5/3 major sixth (884.36 ct) lands on **stride 13** (917.65 ct, +33.3 ct)
+     — and **13 ≡ −4 (mod 17)**: `4·13 ≡ 1`, they are inverses. **Stride 4 IS
+     the descending-5/3-sixth circle.** Stride 11 sits at 776.5 ct ≈ 8/5, the
+     neighbouring sixth — the hedge was right, and the measured answer is
+     13 = −4, i.e. the operator's own stride 4 read backwards.
+   - Interval map for the record (17-TET): stride 3 ≈ 9/8 (−7.9 ct), 7 ≈ 4/3
+     (+3.9), **10 ≈ 3/2 (−3.9, the fifth)**, **4 ≈ 7/6 (−15.5)**,
+     **13 ≈ 5/3 (+33.3)**.
+   - The two-regime table thus gets its mechanism column: **continuum** =
+     equidistribution by irrationality (φ, needs the index floor);
+     **quantized** = temperament — exact closure + distributed comma
+     (coprime walk, needs no φ at all).
+
+**Why this is the same defect as two others found this week — third instance
+of one shape.** A rule true in its asymptotic home, applied where it does not
+hold: **R² "structurally near-blind to encoder bias"** (true at +1.59 Pa →
+6th decimal, false at +92.76 Pa → 3rd); **"zero removed lines proves a pure
+prepend"** (proves *additive*; an end-append also deletes nothing); and now
+**"the golden step is the best step"** (true as N→∞, false at q=17). **The
+repair is identical each time: measure/enumerate in the regime you are
+actually in, instead of inheriting the asymptotic label.** Corollary for this
+workspace: a name carrying a theory ("golden-step", "lossless", "pure
+prepend") is a claim, and claims get falsifiers — the label is not the
+evidence. *(And the temperament frame shows the deeper reason the label was
+seductive: the walk really does share φ's PURPOSE — even coverage without
+collapse — it just achieves it by closure + distributed comma rather than by
+irrationality. Same goal, different mechanism, wrong name.)*
+
+**Consequences.** Report §10.5 carries the two-regime table + the
+addressing note (a `u8` rail holds 256 < F(17)=1597, so the continuum side
+must read tier-then-member — while the quantized side never has the problem,
+since the 17-alphabet fits a byte fifteen times over). `weather-w-probes-v1`
+§0 carries the enumerate-don't-approximate rule so every worker inherits it.
+`helix/KNOWLEDGE.md:320`'s "golden-step" label is filed in `ISSUES.md` as
+misleading-but-not-wrong-code — the walk it names is fine, the *reason given
+for choosing it* is not, and a future session picking a stride by that
+rationale would pick 11.
+
 ## 2026-08-12 — E-THE-CONTROL-SCORED-THE-HEADLINE-1
 
 **Status:** FINDING `[G]` — `comet_tail_f16.py` / `.json`, bars committed

.claude/board/ISSUES.md

@@ -1,5 +1,20 @@
 # Issues Log — Open + Resolved (double-entry, append-only)
 
+## ISS-HELIX-GOLDEN-STEP-LABEL (2026-08-12) — OPEN, misleading-but-not-wrong-code
+
+`crates/helix/KNOWLEDGE.md:320` labels the `(i·11)%17` walk **"golden-step"**
+(rationale: `17/φ = 10.51 → 11`). The label's THEORY is measured wrong twice
+over (`E-THE-GOLDEN-STEP-IS-THE-WRONG-STEP-AT-SMALL-Q-1`): (a) stride 4 has
+strictly better prefix star-discrepancy than 11 at m=9/13 (0.1111/0.0769 vs
+0.1503/0.0905); (b) at q=17 the correct frame is TEMPERAMENT (coprime closure
++ distributed comma — operator framing: not a genuine golden step, yet it
+does not collapse), not φ-approximation, so *"golden"* names the wrong mechanism
+entirely. **The code is fine** — `CurveRuler` uses stride 4; only the doc
+label misleads, and a future session choosing a stride BY that rationale
+would pick 11 (the measurably worse one). Fix when helix is next touched:
+rename the label (e.g. "tempered-step" / "coprime walk") + one line citing
+the epiphany. Not urgent; filed so the rationale cannot silently recruit.
+
 ## ISS-D-IGN-B-REAL-CORPUS-PATH-IS-UNVERIFIED (2026-08-06) — OPEN, SURFACED BY THE CORPUS FIX
 
 `crates/lance-graph-supervisor/tests/d_ign_b_lenses.rs` takes one of two corpus

.claude/board/LATEST_STATE.md

@@ -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. | — |
+| **#930** | 2026-08-12 | #929 hygiene → grew into an open-review sweep of #920–#930 + report §10 (product-lead program) + `weather-w-probes-v1` (Sonnet worker briefs) | MIXED (started as pure hygiene, corrected its own description twice per the #927 lesson). Sweep found 3 ledger figures wrong (R² "5th decimal" claim, "10 probes" undercount, "+13/−0,+10/−0,+0/−0" audit figures) and replaced the append-only audit itself (zero-deletions → suffix check, both halves measured, the new check correctly flags this very PR). §10 = measurement standard + dipole vector-sum model incl. stranded-storm regime + corridor α + queue-and-bow + sunflower/spiral-ADI substrate. Worker briefs W5/W2s-a/W6 ready; CT-F17 gated on W6 + independent adversarial audit. See sweep entry, `.claude/board/PR_ARC_INVENTORY.md` for the correction table — the figures in #928's/#929's rows below are SUPERSEDED by that entry, not edited in place. |
 | **#929** | 2026-08-12 | CT-F16 kills the steering rescue; the control scores the headline; circular resultant replaces the sign test | 2 probes (`comet_tail_f16`, `comet_tail_resultant_instrument`) + report §5.12/§5.13 + `E-THE-CONTROL-SCORED-THE-HEADLINE-1`. Steering FAILED both bars (0.579 vs 0.70; residual +28.4 % wider; sweep monotone to surface, best 850 hPa); rotated control scored 0.684 = CT-F14's headline; resultant resolves the same rows at p=0.0050, offset estimated −30.2°. |
 | **#928** | 2026-08-12 | Board hygiene for #927 — chain terminator | Pure prepend (+13/−0, +10/−0). Living-documents vs append-only-ledgers correction discipline banked; zero-removed-lines diff = structural append-only audit. |
 | **#927** | 2026-08-12 | Board hygiene for #926 + 4.7×-not-5× correction + append-only revert | Mixed. 9/10 figure self-verification caught the 6 % favourable rounding; an in-place edit of a MERGED EPIPHANIES entry reverted same-PR (the rule being cited was the rule broken). |

.claude/board/PR_ARC_INVENTORY.md

@@ -1,3 +1,14 @@
+## 2026-08-12 — lance-graph #930 (MERGED) — #929 hygiene that became a review sweep, a product-lead program, and a replaced audit method
+
+- **Added.** `probes/weather-p1/COMET_TAIL_REPORT.md` **§10** (the product-lead program: §10.1 measurement standard · §10.2 the dipole **vector-sum model** with the **stranded-storm regime** via `v_rel = v_storm − v_env` · §10.3 corridor α · §10.4 queue-and-bow anchors · §10.5 sunflower-facet / spiral-ADI substrate · §10.6 roadmap · §10.7 worker model) + `.claude/plans/weather-w-probes-v1.md` (Sonnet worker briefs; §0 is a **verbatim-paste preamble** carrying the iron rules, the `fetch()`/t-guard/`wrap_deg`/`circular()` code, controls-FIRST with the VOID rule, and the **stranded-rescue** checkpoint protocol — per-storm `<name>.partial.jsonl` + resume-skip + `exec-runs/` heartbeat, so a killed worker resumes instead of re-fetching ~GBs). Board: INTEGRATION_PLANS prepend, STATUS_BOARD rows D-W5 / D-W2sA / D-W6 / D-W2sB / D-W7 / D-CT-F17 (all **Queued**), the #929 arc entry + LATEST_STATE, and the sweep entry below.
+- **Locked — three ledger figures corrected and one audit method replaced.** Detail in the entry immediately below (kept as its own record because the sweep is the reusable part, not the PR).
+- **Locked — a MIXED PR must correct its own description the moment it drifts.** #930 opened as "pure hygiene, the chain stops here" and was twice falsified by its own later commits. Both times the title and body were rewritten **proactively**, before a reviewer found them — the #927 lesson applied rather than re-learned. Consequence honoured here: a mixed PR owes an arc entry, so this one exists.
+- **Deferred.** Every W-probe (operator go-ahead pending). **CT-F17 additionally gated** on W6's result **and** an independent adversarial spec audit before any bar is committed. The ~30 older CodeRabbit findings on #920/#921 remain **UNVERIFIED** by deliberate choice, recorded rather than absorbed.
+- **Docs.** Report §5.13 + §6.1 carry dated correction notes; merged #929's PR body was patched post-merge for the same false relation (precedent: #922).
+- **Confidence.** High on everything measured (every figure re-derived from the committed JSONs or from `git` in this session); the W-probe designs are **specifications, not results** — nothing in this PR was run.
+
+**Status:** MERGED (`9da349ac`). Branch `claude/jirak-math-theorems-harvest-rfii13` → `main`. Zero Rust, zero product code — docs, plans, board.
+
 ## 2026-08-12 — open-review sweep of #920–#930 — three frozen figures corrected, and the append-only audit replaced with one that can actually fail
 
 - **Scope, stated at the coverage actually achieved.** Operator asked for the open comments on #930, then the previous five, then five more. All 68 review comments on **#920–#930** were enumerated; the checking depth is **not uniform and is not claimed to be**: #922–#930 were verified finding-by-finding against the tree, while **#920 (27 findings) and #921 (5) were spot-checked only** on their P1/governance items — both clean (`p1_noise_floor.py` carries an explicit `SUPERSEDED by p1_ci_vs_floor.py` header that fixes the decoded-error framing *and* the 255-vs-256 bucket-edge bug; the merged **#917** entry has exactly one commit in its whole history, `4be809c8`, so it was never mutated). **The remaining ~30 older coderabbit findings on #920/#921 are UNVERIFIED here** — recorded as such rather than absorbed into a clean-sweep claim. Result within the verified range: **#922 / #924 / #925 / #929 carry zero review comments**; **all 27 findings on #926 are fixed in the tree** (verified individually: `grid_pts` returns exactly `n` and the E2 JSON is regenerated at 64/64/64 · 256/256/256 · 1024/1024/1024; `subgrid_min` wraps longitude via `np.take(..., mode="wrap")`; `find_center` returns `None` on an empty mask; F7d tests `>= 40.0` matching its key; `CT_F12` emits `NO-VERDICT-INSUFFICIENT-N` instead of `pass: true`; storm metadata persisted; `d_dx` uses `np.roll`; `go_territory` writes `__file__`-relative; E6 requires a net decline; the 93–97 % headline superseded by 90.9–94.3 %); **#923's plan-status P2 is resolved**. Three findings on **#927/#928** were genuinely open, and all three were numbers already frozen in append-only ledgers.