Fix 4 codex findings on merged #932 + golden-vs-tempered-stride-v1 (the head-vs-gut plan) - #933
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…tempered-stride-v1 head-vs-gut plan #932 merged before its automated review findings were addressed. Four real defects, all verified by re-deriving the numbers, all fixed here in a fresh commit since the merged PR cannot be reopened: 1. W5's bump sat at r=0.45 on a lattice sized to put ONLY the RIM at the index floor -- local parastichy index scales as sqrt(r^2*N), so the bump's actual local index was ~719, still sub-floor. The disk's inner half is structurally sub-floor at any finite N (index -> 0 as r -> 0); no N fixes that, only excluding those bands does. 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 and reported under B1 only. B4's sweep scales the same margin+exclusion logic per n. 2. W2s-a's tie test counted GLOBAL duplicate rounded distances across the whole million-point population -- blind to the actual claim (does one H-point have two equally-near T-candidates) and, at these sizes, prone to unrelated-pair float collisions regardless of mechanism. Redefined G1/G4 per-source: d1/d2 ratio > 1-1e-6 for each H-point's own two nearest T-candidates. 3. EPIPHANIES' 17-TET interval-error table used just-minus-TET for four entries and TET-minus-just for the fifth, contradicting its own "+3.93 ct/fifth" statement one paragraph above (stride 10 was written as -3.9, needed +3.9 to match). Recomputed with one consistent convention throughout. 4. W5's B3 control (1500/2600) matched Fibonacci INDEX magnitude but not GEOMETRIC step length -- physical distance is governed by the angular residue (stride*golden_frac mod 1), which for 1597/2584 is ~0.00028/0.00017 (near-zero, that's why they're parastichy numbers) while 1500/2600 sit at ~0.05/0.11, two to three orders larger. So the control would have failed for the same wrong-scale reason as the FIRST draft's 12/18, just disguised by same-magnitude integers. Fixed: distance-matched shuffled-neighbour control -- for each point, the control partner is its nearest REAL lattice neighbour (by measured physical distance, via cKDTree) that is NOT the true Fibonacci partner, guaranteeing near-identical step length while breaking arithmetic coherence by construction. New: .claude/plans/golden-vs-tempered-stride-v1.md -- the actual head-vs-gut test plan requested, standalone from the weather arc. T1 sweeps 8 values of q finding the crossover m* (point where golden's O(log m/m) refinement overtakes a coprime tempered walk's frozen ceiling) -- sits at m~=q in every case, 68-106x golden advantage by m=200q. T2 confirms the asymptotic golden claim as a measured pass/fail bar. T3 shows tempered GUARANTEES zero empty cells at closure (proof) where golden's fill count is a genuine variable (124/140 measured at non-Fibonacci q=140). T4 is the sharpest form of "does not collapse": naive round(golden*q) without a coprimality check collapses in 39.0% of q in [8,300) -- a real, common hazard a coprimality-checked tempered search cannot have by construction. Synthesis: bounded/fixed-budget regime (a rail, a facet byte) -> tempered; unbounded/growing regime (continuum lattice) -> golden. Both instincts right, different regimes, crossover at m~=q. Explicitly flags that three different metrics across this session picked three different "best" strides for q=17 -- none contradicts another, each scoped to its own metric. Board hygiene: INTEGRATION_PLANS prepend + STATUS_BOARD rows D-GVT-T1..T4. No probe run -- all numbers here are hand/script-verified arithmetic pending worker execution. Co-Authored-By: Claude <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01CcpLeEC3XK8Eye53GKBVvi
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| range to golden's score in the same range, and separately find `m*`, the | ||
| first prefix length beyond `q` at which golden's discrepancy drops below | ||
| the tempered stride's (permanently, since tempered is frozen at its `m=q` | ||
| value forever after). |
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The tempered prefix discrepancy is not frozen for every m > q: although the points repeat, a prefix ending partway through a later cycle weights some cells more than others. Consequently, comparing golden only with the m=q value does not establish a permanent crossover; for example, with the specified star-discrepancy calculation at q=34, golden loses again at m=67, despite the table claiming permanent overtake at 35. Recompute m* against the actual repeated tempered prefix at each m, otherwise the plan's central m* ≈ q conclusion is invalid.
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| > With N=7 651 227: **`r_floor = 1597/√N ≈ 0.5774`** — only annuli with | ||
| > `r ≥ r_floor` have a local index ≥ the floor. Under the 8-equal-area | ||
| > annulus scheme (`r_i = √(i/8)`), that is **bands 3–8** (`r ≥ 0.6124`); | ||
| > **bands 1–2 are structurally sub-floor and MUST be reported under B1 only, |
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With edges r_i = sqrt(i/8), band 3 spans sqrt(2/8)=0.5 through sqrt(3/8)=0.6124; it does not start at 0.6124. Since r_floor=0.5774, most of band 3 is below the stated floor, yet the later B2 sweep includes all of bands 3–8. Either split band 3 at the floor or qualify only bands 4–8, otherwise B2 still judges sub-floor points and cannot validate the intended floor rule.
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| magnitude-matched:** for each point, its true Fibonacci partners are its | ||
| neighbours at index offset `±1597`/`±2584`; the control partner is chosen | ||
| as the point among its **8 real nearest lattice neighbours (via | ||
| cKDTree)** whose PHYSICAL distance is closest to the true Fibonacci | ||
| partner's distance, **excluding the true Fibonacci partner itself**. This |
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Selecting a nearest alternative independently for each point does not produce the (start, j) chains used by the Fibonacci tridiagonal sweep: the resulting links can be asymmetric, duplicated, or branch into an arbitrary graph. Thus an anisotropy difference can come from changing the diffusion operator's topology rather than breaking Fibonacci recurrence, and the brief does not specify how this mapping can run the same sweep. Define a distance-matched control that preserves bijective chains/degrees and directional treatment before interpreting B3 causally.
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| - **G1 TIES (per-source, corrected):** for each H-point in the overlap band, | ||
| find its 1st- and 2nd-nearest T-lattice points (`d1 ≤ d2`, via cKDTree, | ||
| k=2). Define **near-tie** as `d1/d2 > 1 − 1e-6` (the two candidates are | ||
| ambiguously close FOR THAT SOURCE POINT — the actual pairing-quality | ||
| question). Count near-ties: golden = **0** (irrational angle ⇒ generic | ||
| position, no H-point is equidistant between two T-points except by | ||
| measure-zero coincidence); grid control **> 0** (regular lattices produce |
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Irrationality rules out a generic exact equality, but the bar counts d1/d2 > 1-1e-6, which includes non-equal candidates whenever a source lies near a Voronoi boundary. With the planned million-point population, such arbitrarily close pairs are not measure-zero, so a nonzero golden count would not show that the angle mechanism or index-floor claim is wrong as G4 states. Calibrate and compare a near-tie rate, or test exact equality separately, instead of requiring zero under a finite tolerance.
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…eography 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
…e run Full post-#933 brief: N=3*F(17)^2=7,651,227 headline, bump at r0=0.75 (local index ~2077 > floor 1597), KD-tree stride discovery with no capped window, band qualification by the INNER-radius >= r_floor rule (bands 4-8; the brief's "bands 3-8" label is off-by-one against its own parenthetical r>=0.6124 -- the rule wins, discrepancy reported not silently adopted), distance-matched shuffled-neighbour B3 control (same 0.25/0.5/0.25 stencil both arms; control prev = reverse map where uniquely defined, else hold -- documented implementation choice), B4 sweep n in {8,10,12,14,17,19} at 3*F(n)^2 each, n=21 recorded NOT RUN per budget. Smoke-tested at n_idx=8 (N=1323, machinery-only, sub-floor by design): discovery correctly returns the F(8)/F(9)=21/34 pair, both arms run, JSON shape complete. The smoke run's poor isotropy at that N is exactly the sub-floor behaviour B4 exists to expose and is not a code defect. Co-Authored-By: Claude <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01CcpLeEC3XK8Eye53GKBVvi
Two things in one PR — the merge timing forced it
#932 merged before its automated review findings landed. All four are real (each re-derived independently, not taken on faith) and are fixed here in a fresh commit, since the merged PR itself can no longer be reopened.
The four fixes
√(r²·N), not√N— the bump atr=0.45had local index ≈719, still far below the floor, and the disk's inner half is structurally sub-floor at any finite N (index → 0 as r → 0; only exclusion fixes that, not more N). Fixed: N raised to3·F(17)²with real margin, bump moved tor=0.75(local index ≈2077), bands 1–2 (r < 0.577) explicitly excluded from B2 judgment.d1/d2 > 1−1e-6for each point's own two nearest candidates.just − TETfor four entries andTET − justfor the fifth, directly contradicting the "+3.93 ct/fifth" statement one line above it. Recomputed with a single consistent convention.(stride·golden_frac) mod 1, which for 1597/2584 is ≈0.00028/0.00017 (near-zero — that's why they're parastichy numbers) while 1500/2600 sit at ≈0.05/0.11, two to three orders larger. The control would have failed for the same wrong-scale reason as the 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 that is not the true Fibonacci partner — matches step length by construction, breaks arithmetic coherence by construction.The new plan — the actual head-vs-gut test requested
.claude/plans/golden-vs-tempered-stride-v1.md, standalone from the weather arc:q, finds each one's best coprime stride by a useful-prefix-range metric, and finds the crossoverm*— the point where golden'sO(log m/m)refinement permanently overtakes a tempered walk's frozen ceiling — sits atm ≈ qin every case tested, with a 68–106× golden advantage bym=200q.q=140(avoiding a self-referential confound atq=144=F(12)).round(golden·q)without a coprimality check collapses (gcd>1) in 39.0 % ofq ∈ [8,300)— a real, common hazard a coprimality-checked tempered search structurally cannot have.Synthesis: bounded/fixed-budget regime (a rail, a facet byte) → tempered wins; unbounded/growing regime (a continuum lattice) → golden wins. Both intuitions correct, different regimes, crossover at
m ≈ q. The plan also flags honestly that three different metrics used across this session's work picked three different "best" strides forq=17— none contradicts another, each is scoped to its own metric, stated as a caveat rather than smoothed over.Board hygiene same-commit: INTEGRATION_PLANS prepend + STATUS_BOARD rows D-GVT-T1..T4.
No probe run — every number here is hand/script-verified arithmetic pending worker execution. Doc/plan/board only, zero Rust, zero product code.
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