board: record merged #932/#933 (arc entries + shipped rows) + storm-geography refinement of the two-regime rule

Post-merge hygiene for two PRs. #932 merged mid-session before its own four
review findings could be triaged -- its arc entry records that timing
honestly (confidence low-to-medium on the W5/W2s-a specifics as they stood
at merge, correctly, since #933 fixed four real defects in exactly those
specifics within the hour). #933's entry carries the fix table + the
head-vs-gut plan summary + the metric-dependence caveat (three metrics
picked three different "best" strides for q=17; citing one now requires
naming its metric).

Plan extension (golden-vs-tempered-stride-v1 SS Synthesis): the operator's
storm-geography refinement, each claim grounded in an existing measurement
rather than assigned aesthetically --

1. CENTERING IS TEMPERED TERRITORY because a golden lattice's center is
   structurally sub-floor at any N (local index = sqrt(r^2 N) -> 0 as
   r -> 0 -- the same arithmetic behind the W5 fix). The shipped
   find_center is already on the correct register: exact grid argmin +
   quadratic sub-grid fit, never a spiral sample. Now stated as doctrine:
   never sample the center from the spiral whose center is its own worst
   data.
2. THE COLLISION ANNULUS IS GOLDEN TERRITORY: territory-gain model (Go
   opening vs endgame count, the go_territory_probe framing), addresses
   self-describing outward -- position implied by index, place
   deterministic.
3. OVERLAYING THE COLLISION LATTICES IS CONTROLLED CHAOS AT NEAR-ZERO
   STORAGE: aperiodic (no moire, no ties -- SS10.5 property 2, W2s-a's
   G1/G3 bars) yet fully deterministic from two center coordinates; no
   geometry persisted -- a collision node costs exactly its 12-byte facet,
   positions derived, densification adds nodes not meshes.
4. THE SELF-DESCRIPTION ASYMMETRY IN ONE SENTENCE: tempered is
   self-describing exactly up to q (then the cycle repeats, the index
   carries nothing new); golden is self-describing for every k
   indefinitely, quality still improving as it grows (T2's 68-106x IS this
   property in number form). Bounded self-description that closes exactly
   vs unbounded self-description that never stops refining.

Demarcation kept: the geography does not cause the regime -- the TASK does
(bounded exact closure at the eye, unbounded densification in the annulus);
the storm merely sorts its tasks into the two regimes T1 measures.

Suffix-checked: PR_ARC pure append (True); LATEST_STATE False from the
mid-table row inserts -- the justified case the sweep entry names.

Co-Authored-By: Claude <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01CcpLeEC3XK8Eye53GKBVvi

Author: claude

.claude/board/LATEST_STATE.md

@@ -855,6 +855,8 @@ 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. | — |
+| **#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). |
+| **#932** | 2026-08-12 | Golden-ratio index floor (≥17/21) + temperament mechanism; W5/W2s-a re-specced before any worker ran | Merged BEFORE its own 4 review findings could be addressed (fixed in #933). Floor: F-convergents behave like φ only from n≈17–21 (err 1.5e-4 → 1.8e-7 → 3.7e-9); emergent parastichy pair ≈ √N ⇒ N ≳ F(17)². Mechanism: temperament — coprime closure + distributed comma (12 fifths miss by +23.46 ct; 17-TET fifth exact by construction, +3.93 ct/fifth spread) = D-QUANTGATE's anti-moiré dither. `E-THE-GOLDEN-STEP-IS-THE-WRONG-STEP-AT-SMALL-Q-1` + `ISS-HELIX-GOLDEN-STEP-LABEL`. Chat-register quotes paraphrased out of all committed artifacts (12 sites). |
 | **#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. |

.claude/board/PR_ARC_INVENTORY.md

@@ -1,3 +1,125 @@
+## 2026-08-12 — lance-graph #932 (MERGED) — the golden-ratio index floor + the temperament mechanism (merged before its own review findings could be addressed — see #933)
+
+- **Added.** The operator-ruled golden-ratio index floor (convergent index
+  ~17–21 before Fibonacci behaves like the irrational it approximates;
+  measured error n=10 → 1.5e-4, n=17 → 1.8e-7, n=21 → 3.7e-9) as a binding
+  rule in `weather-w-probes-v1.md` §0, applied to correct W5 (N=4096 →
+  emergent pair F(10)/F(11), a discovery step capped at `j∈{1..60}` that
+  was structurally incapable of finding anything above F(10)) and W2s-a
+  (N=2048, same sub-floor pair) — both raised to `N≳F(17)²` with an
+  N-sweep arm so the floor is measured rather than inherited. Report §10.5
+  gained the two-regime table (continuum: golden angle; quantized: coprime
+  walk) plus the addressing note (a `u8` rail < F(17)=1597 → tier-then-
+  member on the continuum side, a non-issue on the quantized side).
+- **Locked — the mechanism below the floor is temperament, not
+  approximation `[G]`.** A coprime stride over modulus `q` is structurally
+  a circle of fifths: it closes the cycle exactly (coprimality ⇒ full
+  permutation) and distributes the incommensurability error — the comma —
+  uniformly, 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 (+3.93 ct/fifth spread). The
+  distributed comma **is** D-QUANTGATE's anti-moiré dither. Survival below
+  the floor = closure, not goldenness — which is why the shipped
+  `CurveRuler` walk (stride 4 mod 17) was always correct even though the
+  in-tree doc label calling a *different* stride (11) the "golden-step" was
+  wrong: enumerating all 16 strides mod 17, stride 4 has strictly better
+  prefix star-discrepancy than 11 at m=9/13. Filed as
+  `E-THE-GOLDEN-STEP-IS-THE-WRONG-STEP-AT-SMALL-Q-1` and
+  `ISS-HELIX-GOLDEN-STEP-LABEL` (label misleads, the shipped code is fine).
+- **Locked — chat-register informal phrasing does not belong in committed
+  artifacts.** Operator preference, applied retroactively across all twelve
+  quote sites in the same PR: paraphrase rulings professionally, keep
+  attribution and technical content identical. (The already-pushed commit
+  message carrying the original phrasing was left as-is — rewriting shared
+  branch history would cost more than the residue.)
+- **Deferred — and this is why the PR needed a sequel.** #932 merged
+  *before* its own four automated-review findings (bump sub-floor despite
+  the "fixed" N, a tie-test that measured the wrong population, an internal
+  sign contradiction, a control that matched index magnitude but not
+  physical step length) could be triaged and fixed — the merge fired mid-
+  session while the fixes were being written. All four are real, all four
+  are fixed in **#933** (entry above), since the merged PR could not be
+  reopened. **Lesson for the standing subscription protocol:** a PR can
+  merge between "findings arrive" and "findings addressed" faster than a
+  session can react; the fix is a follow-up PR, not a scramble to beat the
+  merge.
+- **Docs.** Every verbatim operator-quote site across the plan, report,
+  EPIPHANIES, and ISSUES was paraphrased in the same PR (12 sites, verified
+  zero remaining).
+- **Confidence.** High on the floor + temperament arithmetic (independently
+  re-derived, not asserted). **Low-to-medium on W5/W2s-a's own numeric
+  specifics as they stood at merge time** — correctly, since #933 found and
+  fixed four real defects in exactly those specifics within the hour.
+
+**Status:** MERGED (`e6e27829`). Branch `claude/jirak-math-theorems-harvest-rfii13`
+→ `main`. Doc/plan/board only.
+
+## 2026-08-12 — lance-graph #933 (MERGED) — 4 codex fixes on #932 + golden-vs-tempered-stride-v1 (head-vs-gut, made falsifiable)
+
+- **Added.** `.claude/plans/golden-vs-tempered-stride-v1.md` — standalone,
+  zero-fetch plan testing the operator's paired intuitions (golden ratio as
+  nature's mechanism vs a coprime tempered walk that never collapses by
+  construction) against each other rather than picking a winner. **T1**
+  sweeps 8 values of `q`, finds each one's best coprime stride by a
+  useful-prefix-range median metric, and measures the crossover `m*` — the
+  point where golden's `O(log m/m)` refinement permanently overtakes a
+  tempered walk's frozen `m=q` ceiling — sitting at **`m ≈ q`** in every
+  case, with a **68–106×** golden advantage by `m=200q`. **T2** confirms the
+  asymptotic golden claim as a measured pass/fail bar (TRUE at all 8 q).
+  **T3** shows tempered *guarantees* zero empty cells at closure (proof,
+  coprimality ⇒ bijection) where golden's fill count is a genuine variable —
+  measured **124/140** at a deliberately non-Fibonacci `q=140` (avoiding a
+  self-referential confound at `q=144=F(12)`, checked and reported as an
+  aside). **T4**, the sharpest form of "does not collapse": naive
+  `round(golden·q)` without a coprimality check collapses (`gcd>1`) in
+  **39.0 %** of `q ∈ [8,300)` — measured, not asserted. **Synthesis:**
+  bounded/fixed-budget (a byte-addressable rail) → tempered wins;
+  unbounded/growing (a continuum lattice) → golden wins; both intuitions
+  correct, in different regimes, crossover at `m ≈ q`.
+- **Locked — "best stride" is prefix-range-dependent, stated as a caveat
+  rather than smoothed over.** Three different metrics used across two PRs
+  this session picked three *different* "best" strides for `q=17`: a
+  worst-case-over-all-`m` metric (dominated by the degenerate `m=2` case)
+  picked stride 10; the specific short-prefix comparison in
+  `E-THE-GOLDEN-STEP-IS-THE-WRONG-STEP-AT-SMALL-Q-1` (m=5/9/13) picked
+  stride 4; this plan's useful-range median (m∈[q/2,q]) picked stride 14.
+  None contradicts another — each is scoped to its own metric — but citing
+  a "best stride" number anywhere in this workspace now requires naming
+  which metric produced it.
+- **Fixed — 4 codex P1/P2 findings on merged #932, addressed post-merge
+  since the merged PR could not be reopened.** (1) W5's bump sat at `r=0.45`
+  on a lattice whose local parastichy index scales as `√(r²·N)`, not `√N` —
+  actual local index ≈719, still sub-floor; the disk's inner half is
+  *structurally* sub-floor at any finite N, fixable only by exclusion, never
+  by more N. Fixed: N raised to `3·F(17)²` with real margin, bump moved to
+  `r=0.75` (local index ≈2077), bands 1–2 (`r<0.577`) explicitly excluded
+  from B2 judgment. (2) The tie test counted global duplicate rounded
+  distances across a million-point population — blind to the actual claim
+  (is one H-point ambiguously close to two T-candidates) and prone to
+  unrelated-pair float collisions at these sizes regardless of mechanism.
+  Redefined per-source: `d1/d2 > 1−1e-6` for each point's own two nearest
+  candidates. (3) EPIPHANIES' 17-TET interval table used `just−TET` for
+  four entries and `TET−just` for the fifth, contradicting its own
+  "+3.93 ct/fifth" statement one line above — recomputed with one
+  consistent convention. (4) The B3 control (1500/2600) matched Fibonacci
+  *index magnitude* but not *geometric step length* — physical distance is
+  governed by the angular residue, ≈0.00028/0.00017 for the true
+  1597/2584 pair vs ≈0.05/0.11 for 1500/2600, two to three orders larger —
+  so the control would have failed for the same wrong-scale reason as the
+  very first draft's 12/18, disguised by same-magnitude integers. Fixed
+  with a distance-matched shuffled-neighbour control (each point's control
+  partner is its nearest *real* lattice neighbour by measured physical
+  distance, excluding the true Fibonacci partner).
+- **Deferred.** Every T1–T4 bar and every W5/W2s-a bar are specifications,
+  not results — no probe has run. `golden-vs-tempered-stride-v1`'s numbers
+  are hand/script-verified arithmetic pending worker execution.
+- **Confidence.** High — every arithmetic claim in both the plan and the
+  four fixes was independently re-derived with a script before being
+  written down, not carried over from the prior PR's prose.
+
+**Status:** MERGED (`80d1d47e`). Branch `claude/jirak-math-theorems-harvest-rfii13`
+→ `main`. Doc/plan/board only — zero Rust, zero product code, no probe run.
+
 ## 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.

.claude/plans/golden-vs-tempered-stride-v1.md

@@ -187,6 +187,80 @@ final validation of the two-regime table already committed in
 head-to-head arithmetic that entry asserted but did not yet run as a
 standalone, swept comparison.
 
+### Refinement — the storm's own geography sorts the two regimes (operator, 2026-08-12)
+
+Operator observation (paraphrased): the analytic/tempered register belongs at
+the **storm's eye**, the golden/sunflower register in the **collision zone**
+(the arc's Nahkampf terrain) — and specifically, the tempered register gives
+the more exact storm **centering**, because a golden spiral's own center is
+where its data quality is worst.
+
+All three halves of that are mechanically grounded in measurements this arc
+has already made — the mapping is not an aesthetic assignment:
+
+1. **The spiral's center is structurally sub-floor at ANY N.** Local
+   parastichy index at radius `r` is `√(r²·N)` → 0 as `r` → 0 — the exact
+   arithmetic behind the W5 fix (`weather-w-probes-v1` §1), where raising N
+   could never rescue the inner bands and the only correct move was
+   excluding them from judgment. A Vogel lattice's innermost points are
+   degenerate by construction: resonant stride families, uneven first-few-k
+   spacing, no floor-qualifying neighbourhood. **Center work on a golden
+   lattice is garbage-register work, at any budget.**
+2. **The shipped center-finder is already on the correct register.**
+   `find_center` (`comet_tail_f5_n10.py` / `comet_tail_f16.py`) is an
+   exact-enumeration argmin over the regular lat/lon grid plus a quadratic
+   sub-grid fit — bounded, exhaustive, zero-variance: the tempered/head
+   register, never a spiral sample. What was implicit practice is now
+   stated doctrine: **centering = exact enumeration; never sample the
+   center from the spiral whose center is its own worst data.**
+3. **The sunflower is the territory-gain model, and its advantage is that
+   its addresses speak for themselves outward.** Prefix-extensibility
+   (report §10.5 property 3) means position is *implied* by index `k` —
+   place deterministic, residue stored, nothing re-meshed — and each added
+   point lands in the largest current gap (`O(log N/N)` discrepancy). In
+   the Go framing the arc already measured (`go_territory_probe`): golden
+   is the **opening** — optimal incremental territory claim in open,
+   growing space; tempered is the **endgame count** — exact, closed,
+   bounded. Same two regimes as the T1 table, now with the game-phase
+   reading attached. **And the self-description is unbounded** (operator,
+   same session, paraphrased: self-explanatory without end) — which is the
+   sharpest way to state the asymmetry. A tempered walk is self-describing
+   exactly up to `q`: beyond one cycle the index carries no new
+   information, the address vocabulary is exhausted, the walk repeats. The
+   golden index is self-describing for **every** `k`, indefinitely — no
+   re-meshing, no re-indexing, no schema change at any scale, with quality
+   still *improving* as it grows (`O(log m/m)`, T2's measured 68–106×
+   advantage at `m=200q` IS this property in number form). Bounded
+   self-description that closes exactly, versus unbounded self-description
+   that never stops refining: that is the entire duel in one sentence.
+
+4. **Overlaying the collision lattices is controlled chaos at near-zero
+   storage cost** (operator observation, same session, paraphrased: the
+   superposition is pleasingly chaotic AND cheap). Both halves are
+   measurable, not vibes. *Chaotic:* two golden lattices over different
+   centers are incommensurate — the overlay pattern is aperiodic (never
+   repeats, no moiré, no systematic ties; §10.5 property 2, and exactly
+   what W2s-a's G1/G3 bars measure) — yet fully **deterministic**: the
+   entire pattern regenerates from two center coordinates and nothing
+   else. Low-discrepancy chaos, not randomness — reproducible, seedless,
+   audit-friendly. *Cheap:* the overlay stores **no geometry at all**.
+   Every point's position is implied by its index (place deterministic),
+   so a collision node costs exactly its 12-byte V3 facet — rails 0–1 the
+   `(k_H:k_T)` pair address, rails 2–5 the 8 state bytes — with radii,
+   azimuths, and positions all *derived*, never persisted. Densifying the
+   overlay adds nodes, not meshes: cost grows with the number of
+   collisions you choose to materialize, not with the resolution of the
+   space they live in.
+
+**The demarcation that keeps this honest:** the geography does not *cause*
+the regime — the **task** does. The eye is tempered territory because the
+task there (resolve one address, fixed budget, exact closure) is a bounded
+task; the collision annulus is golden territory because the task there
+(pair two growing lattices ever more densely) is an unbounded one. It
+happens — and this is the elegant part, not the load-bearing part — that
+the storm's geography sorts its tasks into exactly the two regimes the T1
+crossover table measures.
+
 ## Execution
 
 Zero fetch, pure `numpy`/`scipy.spatial` (only T3's KD-tree-adjacent bucket