Taken as true, "the cut constant c sets the one-block miss" contradicts itself across block sizes — so is the block renormalization of an infinitely ramified carpet converging to its percolation exponent at all?

Why this exists. Filed 2026-09-29, before run 061's exponents exist, to put on record what follows from assuming run 062's lead rather than waiting for its score. The owner asked: take the idea as true, project it forward, and see where it breaks. Nothing here is a result.

The lead assumed. Within the cut-4 class, the one-block miss y − measured 1/ν is a monotone function of c, where N(g+1) = c·N(g)^4 (run 062; post-hoc order on five lattices, one in 120).

Deduction 1 — the variable must be c₁. On five of run 062's 19 pool generators c_g shrinks by a fixed factor each generation (Part A), so ln c_g → −∞. A miss monotone in ln c would run off to −∞ for them, which a fixed polynomial cannot do. Only c₁ = N(2)/N(1)^4, finite for every generator, can carry the law. A refinement, not a refutation.

Deduction 2 — the strong version contradicts itself. Where the recursion holds, the 81×81 block has the same c as the 9×9 block. If c alone set the miss, the two-step exponent y₂ would miss the true exponent by the same amount as y. Run 061's Part A log already shows Z (R75) at y₂ = 0.5533 against y = 0.5435 — a shift of +0.0098 at the same c. So "c sets the miss" cannot be a law of the percolation exponent; at most it describes how the one-block approximation errs. The strong hope — an exact correction to y as a formula in c — is ruled out before any exponent is measured. (The codifier saw this one log line while checking run times; it bears on no sealed clause.)

Deduction 3 — three assumptions, at most two true. (a) The block renormalization converges with block size to the carpet's exponent. (b) The Monte Carlo estimator is within about 0.02 of the truth. (c) Bigger blocks move carpet exponents up (seen on Z; expected on the others). With (c), (a) and (b) together need the true 1/ν(Z) above about 0.55 against a measured value near 0.50. Saving (b) by a low bias does not work: every carpet's local slope falls with L (runs 051–056), which puts the asymptote lower, not higher. So (a) is the assumption that breaks: on these carpets the block renormalization does not converge monotonically to the percolation exponent, if it converges to it at all. A candidate reason, not a proof: the carpets are infinitely ramified — blocks share whole edges — while the hierarchical lattices on which block renormalization is exact are finitely ramified.

Deduction 4 — the pool contains a sharp test. Run 062's pool holds cut twins: distinct D4-symmetric patterns with identical N(g) at every g. Entries 5 and 12 twin X (R25); 10 twins Y (R50); 11 twins Z (R75). Any law in cut counts alone predicts that twins have equal misses, so their 1/ν differ by exactly their y. Deduction 2 predicts that fails. This is the exact-degenerate pair the panel's House asked for on CASE-25. Sealed as run 063.

A free check once run 061 lands. The weak version (c describes the one-block error) still predicts that the two-step misses y₂ − measured order as c on the five known cut-4 lattices. Sealed as run 063's clause B.

What would show this probe wrong. y₂ < y on most carpets in run 061 (then (c) was Z alone and Deduction 3 dissolves); twins with equal misses to within noise (then cut counts do carry the miss).

Queued from the transforms pass (OPS.md, push 6), 2026-09-29 — not sealed, to be taken up after run 061 is scored. - Dual. Minimum cuts and shortest paths are planar duals; R(p) is set by cuts near p = 1 and by paths near p = 0, and y sits between. Does the shortest-path count obey its own recursion N′(g+1) = c′·N′(g)^ℓ, and does the miss track c against c′ rather than c alone? Exact and cheap. - Null case. The miss falls with c on the five (B smallest), and the square — c tiny, another class — misses by −0.029. If that trend is real the sign changes somewhere: find a generator with miss ≈ 0 among the pool's small-c₁ generators. Its existence, or not, says more than a fit. - Converse. "Equal misses ⇒ equal c" is not implied by run 062's lead; test on pool pairs with different c and similar misses. - Quantifier swap. This probe attacks "one block size works for every carpet"; "for every carpet some block size gets close" is weaker and untouched.

Back-links (2026-09-29)

Dated pointers added by the codifier from lab/backlinks.py; nothing above this heading was changed.

• Run 058 — confirmed (2026-09-29, measured). lab/runs/058-reliability-polynomial-rg.md: CONFIRMED 2026-09-29.

Checked 2026-09-29, post hoc on the eight cut-4 carpets (H, U, V, A, B, X, Y, Z) — every full-occupation invariant is blind to the exponent. Euler-type counts (bonds, loops b₁ = E − 63, unit squares, holes): Spearman with measured 1/ν 0.2–0.3; H and V are identical in every count (E 88, b₁ 25, 16 squares, 9 holes) yet 1/ν 0.547 against 0.477, and A and B likewise (0.429 against 0.517). Left-to-right effective conductance of the 9×9 and 81×81 blocks with every bond present, and its generation ratio: Spearman −0.02; H and V conduct almost equally (0.603, 0.611). Shortest-path counts: 2 or 4, no ranking. The cut twins X/X1/X2, Y/Y1/U, Z/Z1 are also Euler twins. Reading (a lead): anything evaluated at p = 1 sees the arrangement's topology and transport but not its critical behaviour; the one object that ranks — the crossing polynomial — is evaluated at the fixed point. Next object, generalised: the anisotropic crossing polynomial R(p_h, p_v), horizontal and vertical bonds open with separate probabilities. Symmetry forces ∂R/∂p_h = ∂R/∂p_v at the symmetric point, but the mixed response ∂²R/∂p_h∂p_v at p* measures how series (along the crossing) and parallel (across it) structure couple near criticality — directed, exact, and not a count.

Sealed 2026-09-29 16:5x, before run 063's twin exponents exist (RESULTS063.md absent at commit) — the edge share of the pivotal field. By Russo's formula R′(p*) = Σ_e P(e pivotal), and pivotal ("red") bonds grow as L^{1/ν} (Coniglio); the one-block map treats every block alike although blocks on a parent's edge and in its interior see different surroundings. Statistic: ring share = pivotal weight on bonds with both ends on the 9×9 block's outer ring ÷ total pivotal weight, at the one-block p*, by Monte Carlo (60,000 samples; control: Σ P(pivotal) matches the exact R′(p*) to about 1%). Post hoc on the eight cut-4 carpets (ring share, miss = y − 1/ν): X 0.277, 0.001 · Z 0.313, 0.015 · H 0.316, 0.017 · U 0.349, 0.023 · Y 0.359, 0.036 · V 0.371, 0.041 · A 0.415, 0.051 — monotone on seven — and B 0.426, 0.009, the one outlier (B is also the one pattern with c < 1). Spearman over all eight 0.50; with measured 1/ν −0.83. H and V, identical in every Euler count, separate (0.316 against 0.371) as their misses do. Prediction for the twins, by interpolating the seven-point monotone relation (B excluded): misses X1 ≈ 0.010 (share 0.307), X2 ≈ 0.020 (0.337), Y1 ≈ 0.038 (0.367), Z1 ≈ 0.019 (0.326); hence measured 1/ν X1 ≈ 0.551, X2 ≈ 0.543, Y1 ≈ 0.514, Z1 ≈ 0.509. Sharp consequences: X2 below X (the panel's House predicts X2 above X by ~0.014); Z1 below Z by ~0.019; X1 level with X; Y1 level with Y. Scored by the order of the four twins' misses against the order of their ring shares (predicted X1 < Z1 < X2 < Y1), and by X2 against X. Falsified if the twins' misses order opposite to their ring shares (Spearman ≤ 0) or X2 measures above X by more than 0.008. Post hoc on eight points with one outlier: a lead, not a law.

Reductio pass on the queue, 2026-09-29 16:58, existing data only (before run 063's twins). - Edge share, limit push (the square lattice, not in the fit): pivotal ring share 0.104 (control: Σ P(pivotal) 4.878 against exact R′ 4.879). The seven-carpet line 1/ν = 0.816 − 0.891·share predicts 0.723 against the exact 0.75 — an out-of-family point within 0.03. The miss changes sign at low share as the square's does (−0.020). Survives; still post hoc. - Duality → fixed-point drift → the rise-then-fall of y_L: ρ(p* − p∞, rise 9→81) = 0.21, ρ(p* − p∞, fall 81→729) = −0.14. The quantitative claim is dropped; duality stays a description (holes collapse to dual hubs, so nothing pins the carpet's critical point), not a predictor. - Dual path counts: shortest crossing paths on these blocks are the straight rows (2 or 4); nothing positional to recurse. Removed from the queue. - Still queued: harmonic (Hodge) content of the critical current; the anisotropic polynomial R(p_h, p_v).

Sealed 2026-09-29 17:4x, before run 063's stage 2 has reported (RESULTS063.md absent at commit) — the reseed floor for a twin difference. Run 063 clause A calls a twin gap |Δmiss| ≥ 0.015 real and ≤ 0.008 equal. Neither line was set against a measured run-to-run spread of the carpet estimator; the only one on record is the square's (eight repeats, spread 0.004, run 061). Origin, and its reductio: the proposal was a mirror pair — a pattern with the four rotations but no mirror symmetry, and its reflection. The reflected carpet is the same graph with the same crossing event, so its y₉ equals its twin's exactly and its 1/ν is the original's measured again with other seeds: a reseed with an orientation-reversed build file, nothing more. Run 063 already contains three reseeds — X, Y, Z measured again with fresh seeds by the same estimator — so the floor is sealed on those, and the mirror pair is kept only as an optional code check. Statistic: d = 1/ν(063) − 1/ν(061) for X, Y, Z, read from RESULTS063.md. The carpet per-run noise is s = rms(d)/√2 (three differences — a rough estimate, stated as such). Prediction: all three |d| ≤ 0.012 (two combined errors at 0.004 per run) and rms(d) ≤ 0.008, i.e. the carpet estimator is no noisier than the square's. Falsified if any |d| > 0.015 or rms(d) > 0.011 (s above about 0.008, twice the square's). Anything else is unanticipated. Consequence, fixed now: run 063 is scored as written. Alongside it, since each original is the mean of two runs and each twin is one, a twin gap carries noise s_gap = s·√1.5; with s = max(0.004, rms(d)/√2) each of the four gaps is reported in units of s_gap, and a gap under 2·s_gap is labelled "within reseed spread" beside its score. At s = 0.004, s_gap ≈ 0.005, so clause A's 0.015 line is about 3 s_gap per comparison, and a chance crossing on any of the four is about 1%. The reseed measures sampling noise only; it says nothing about convergence in L (Y's slow drift is not a reseed effect). Second reader's six edits — the RMS clause scored, the per-run scale from the differences rather than their maximum, the √1.5 gap scale, the label threshold fixed in advance, the family-wise rate, and the square-versus-carpet assumption stated — are folded in.

Scored 2026-09-29, from RESULTS063.md (cdd879b). - Reseed floor — confirmed. d = 1/ν(063) − 1/ν(061): X −0.0028, Y +0.0040, Z −0.0099; all |d| ≤ 0.012; rms(d) = 0.0064 ≤ 0.008. s = 0.0045, s_gap = 0.0055; the label threshold is 2·s_gap = 0.011. Run 063's entry 10 – Y gap (0.0076) is labelled within reseed spread; the other three are not. - Edge-share twin prediction — not falsified, order not met: unanticipated. Measured misses X1 0.0253, X2 0.0425, Y1 0.0417, Z1 0.0433 (predicted 0.010, 0.020, 0.038, 0.019): order X1 < Y1 < X2 < Z1 against the predicted X1 < Z1 < X2 < Y1, Spearman(share, miss) = 0.2 — above the falsifying line (≤ 0) and far from the predicted order. X2 measures below X by 0.030 (predicted below; the House predicted above by 0.014), so the second falsifier is not met. Consequences: X2 below X, held; Z1 below Z, held (0.0385 against a predicted 0.019); Y1 level with Y, held (0.5104 against a predicted 0.514); X1 level with X, failed (0.0149 below, 2.7 s_gap). All four twins' misses exceed the seven-point line by 0.004–0.024: the line is biased low on twins, and its rank information was weak. The edge share already failed composition (the 3×3 carpet has no interior); it stays in the queue only as the 9×9 view of a level profile.

Inklings, 2026-09-29 evening — unjudged, one line each, recorded so a later compaction cannot choose. Not claims; each becomes a probe or a seal only when it can be stated so it could fail. - Composition test: any carpet law must give the same answer for H at 9 and the Sierpinski carpet at 3. Dimension and ln C₁/ln n pass; one-block y and edge share fail (the 3×3 has no interior). - Edge share → level profile: pivotal weight on level-1 against level-2 block boundaries; H must match the Sierpinski carpet regrouped in pairs. - Discrete scale invariance: log-periodic corrections with period ln 9 are aliased to a constant by sampling only at L = 9^g; H alone can be built at 3^k (27, 243, 2187). - Round tiles: disk packings (Apollonian) are finitely ramified, so p_c = 1; round-hole carpets stay carpets (Whyburn) but keep only D4 (Bonk–Merenkov rigidity, recalled). - Stacking X∘Y: order-independence is a theorem (control); averaging of 1/ν is the test — run 067. - 17 = 9² − 8² = 9 + 8, prime by accident; the factor 17 and odd parity persist under stacking. - Ceiling constant as ln λ / ln C₁: two per-stage multipliers compared (Feigenbaum-style); composition-invariant. - Feigenbaum ratio estimator g·y_g − (g−1)·y_{g−1} removes the ln A offset (mean miss +0.0003 against +0.024 over ten carpets, post hoc); noise ×4, so a precision run is needed. - Second eigenvalue = the anisotropy direction R(p_h, p_v); it sets the convergence rate of the ratio estimator. - Universality inside one carpet: site against bond; weakly filled holes with w·p < 1/2 keep the carpet exponent, above → 3/4; threshold w ≈ 0.68. - Julia set of R_G: self-similar at p* under zoom by λ; one-block y is the zoom factor in units of ln 9. Zeros of finite-size polynomials near it (Derrida–De Seze–Itzykson 1983, recalled). - Parameter hypercube of the nine orbit weights: carpets are corners; the Mandelbrot analogue is the boundary where holes fill. - Monotone R forbids period doubling; frustrated models (an antiferromagnet on the carpet) are the route to chaotic renormalization (McKay–Berker–Kirkpatrick 1982, recalled). - Crossing-curve shape as a class fingerprint (the analogue of Feigenbaum's g*), free from stored thresholds; interpretation table fixed before looking. - Gelfond–Schneider: ln(algebraic)/ln 9 is rational or transcendental, never √2 − 1; 7/8 would need λ = 3^(7/4). - 1/ν is itself a fractal dimension (red bonds, Coniglio); the plane's critical cluster has dimension 91/48 ≈ 1.896, against the carpets' 1.893. - Twins break the y₉ ranking (4 of 5 twin pairs invert); y₉ may ride on cut structure. All four twins sit below their originals — check run 062's selection rule. - Lineage, checked on disk: run 049 (the first carpet-percolation run) has no builds_on; it came from the dictionary's §43/§45 (room against dimension), a separate root from the intermediate-growth cell (runs 031–050 on the Grigorchuk coset graphs: bisection, barriers, expansion and code ceiling, quantum walks, seam orbits). The two met only in runs 064–065, which falsified the cell's coset tower as a spectral-decimation object.

Bridge to the intermediate-growth cell, 2026-09-29. This thread's genesis is run 049 (from the dictionary's §43/§45), not the cell; the two met in runs 064–065. The cell's code-ceiling probe P-026 now carries the translation (cut ↔ distance, cut count ↔ minimum logicals, threshold ↔ erasure threshold, ramification ↔ bounded distance) and lists this thread's runs in related:, so the back-link check flags it whenever one is scored and not yet read there.

Bridge to the training-dynamics thread, 2026-09-29. P-028 (edge of stability as a Feigenbaum cascade; grokking course Chapter 4) is this thread's Feigenbaum counterpart: its double-well table of superstable parameters converges to δ geometrically, the benchmark against which this thread's slow ratio estimate should be compared. Linked both ways in related:.

Record status, 2026-09-29. Run 061 falsified; run 062 falsified (clause A; clause B unanticipated); run 063 confirmed; runs 064 falsified and 065 confirmed; run 066 confirmed; run 067 sealed, computing.

Record status and inkling, 2026-09-29 (late). Run 067 unanticipated: stacking averages 1/ν for two cut-4 parents (X∘Y, −0.26σ) and falls below the average by 3.5σ when a cut-2 level is stacked with a cut-4 one (X∘U′, 0.3984 against 0.4131); the ceiling survives but is not preserved (ratio 0.874 → 0.842). Inkling, post hoc on two points: the composite's 1/ν sits near the geometric mean of the parents' (0.3895 and 0.5328 against 0.3984 and 0.5321); the next seal is a third cross-class pair (X∘T or U′∘T).

Record status and inkling, 2026-09-29 (night). Run 069 falsified: at 8,000 samples the width-standardized crossing curve is indistinguishable across carpets, sizes and reseeds by KS distance (scaled 0.46–1.13 everywhere). Inkling from its reported moments: skewness is positive on every carpet (+0.11 to +0.55) and near zero on the square (+0.011), and in the three twin pairs with separated exponents the lower-exponent member has the lower skewness (4.5–7σ, normal-theory). Next seal: skewness reproduced across reseeds and stable across sizes, then read against the exponent.

Record status, 2026-09-30. Run 068 falsified on clause B: the ceiling 1/ν ≤ 0.874·ln C₁/ln 9 is dead (cut-2 #16 at 0.3493 against 0.2757, connected, 17 errors above; it also exceeds the bare cut exponent 0.3155). Clause A confirmed: class maxima rise strictly with cut (0.349, 0.427, 0.551, 0.613). Cut class sets the ceiling of a class's exponents only loosely and bounds nothing; within cut 2, y₉ orders the measured exponents exactly.

Record status, 2026-09-30 (morning). Run 072 confirmed: the skewness of the threshold distribution reproduces across reseeds (X, Y, Z within 1.7 errors) and is stable from 729 to 6561 on 10 of 14 carpets, the clause's floor. It still drifts on four (T by 5.2 errors). It is uncorrelated with 1/ν (Spearman +0.16), so it is a second coordinate if it is anything. The X/X1 twin ordering reverses between 729 and 6561, so any twin clause is sealed at a named size. Run 071 (bands and sub-bands) is sampling 15 patterns, not 16 (erratum in the seal).

Record status and inkling, 2026-09-30 (late morning). Run 073 falsified: the skewness drift is not a single shrinking correction. g₁ is near zero at L = 81 on several carpets and rises by 729 on thirteen of fourteen; after that, T and X1 turn back, six carpets level off, and X and Z keep climbing at a constant step per factor of 9. Inkling, post hoc: every carpet traces one hump, built over the first generations as the minimum cuts repeat, then relaxing, with the peak at a carpet-dependent depth — T and X1 past it by 6561, X and Z not yet. The hump's depth, not its height, would then be the fingerprint, and it may be what the falling local slopes of the width are also seeing.

The hump programme, 2026-09-30. Four lines pursue the hump filed with run 073. Each result is appended here and folded into the lines still unsealed before they are sealed; sealed runs are answered, never edited. 1. Run 074, five sizes of H (stored data, minutes). Asks whether H's rise is one rise without a dip and whether it is concave from 81 or sigmoidal. Feeds line 4 the shape of a rise at factor-3 resolution. 2. Run 075, the exact one-block map (deterministic, minutes). The iterated map's skewness is one analytic function of λ⁻ᵏ; the prediction is that it does not turn over at the lattice's depths, so the turnover on T and X1 comes from correlations between blocks. Also returns the map's limit g∞ and peak depth for all 63 patterns. 3. Mechanism (sealed after 075 returns; sampling at L = 729, minutes per carpet, Lab_Tree_Model after 071). The observable is chosen by 075. If the turnover is not in the map: per sample, the times at which the top-level minimum-cut faces are first bridged, with the prediction that conditioning on early bridging removes the skewness. If it is in the map: the same conditioning on the map's pivotal bonds inside one block. 4. The decisive size, L = 59049 (cloud, 2,000 samples, about 20 hours per carpet; X, Z and T). Sealed last, its numbers taken from lines 1–3. The standing forecast: X and Z turn down, T does not rise again.

Hump programme, update 1 (run 074, unanticipated). H's skewness has no dip over five sizes, but its steps alternate with generation parity (large into even generations 3⁶ and 3⁸, small or negative into odd ones), in g₁ at 2.1 errors and in g₂ at 1.4, post hoc. Inkling: a correction that flips sign each generation (a negative subleading eigenvalue at scale 3), invisible on the factor-9 carpets, which are sampled every second generation. Folded into the unsealed lines: line 3 should compare parities where a carpet allows it; line 4's forecast for the factor-9 carpets is unaffected, but no factor-3 carpet is extrapolated from two sizes. A stored-data check before any seal: whether H's width local slopes over the same five sizes alternate with the same parity, which would tie the falling local slopes to the same term.

Hump programme, update 2 (a record reading, not a run). The width check proposed in update 1 needed no sampling and admits no seal: run 051 recorded H's width at all five sizes (RESULTS051.md, "Carpet H, full range"). Its local slopes, −Δln w / ln 3: 0.539 ± 0.016 (81→243), 0.580 ± 0.016 (243→729), 0.529 ± 0.016 (729→2187), 0.539 ± 0.015 (2187→6561). The parity contrast, slopes into even generations minus slopes into odd ones, is +0.051 ± 0.042 (1.2 errors): the same sign as the skewness alternation (g₁ 2.1 errors, g₂ 1.4), with the width shrinking faster where the skewness grows faster. The square over 81–2187 shows none (slopes 0.746, 0.750, 0.756). Not independent evidence: width and skewness come from the same samples. So three readings of one data set lean the same way at 1–2 errors each; the parity term remains an inkling. What would settle it cheaply is a fresh reseed of H5 and H7 (L = 243 and 2187, minutes and about two minutes of sampling), sealed with the parity contrast as its prediction, since the stored H files are now spent for this question.

Record status, 2026-09-30 (afternoon). Run 070 unanticipated (U′,T withdrawn for order disagreement; X,T +2.7σ above its parents' mean, the wrong side): the rule "mixing cut classes pulls the stack below the mean" is refuted in substance. Three cross-class stacks now give three answers (X∘U′ below, X∘T above, U′∘T above), and no single-number summary of the parents orders them.

Hump programme, update 3 (run 075 confirmed). The iterated one-block map's skewness rises monotonically at every depth on all 63 patterns, and its limit's sign is fixed by the minimum cut (m₁ = C₁ against the shortest crossing m₀ = 8, 63 of 63). So the bottleneck origin of the skewness is exact at the one-block level, and the lattice's turnover (T, X1) is not in the one-block map: it comes from what the map discards, the correlations across block boundaries. Folded into the unsealed lines: - Line 3 (mechanism) will be sealed at block boundaries: per sample at L = 729, the time at which each top-level minimum-cut face is first bridged, with the prediction that conditioning on early bridging removes the skewness on a turning carpet (T) and does less on a still-climbing one (X). - The order gap of run 070 (0.023 at 6561 on U′,T) is a direct, engineered measurement of a generation-parity term: a stack alternates generators every level. It joins the parity inkling from run 074 as its test bed. - Line 4 (L = 59049) is not feasible as specified. The L = 6561 lattice already peaks at 1.2 GB (2.2 GB for U on the M5); the next generation holds 81 times as many cells, so on the order of 100–180 GB, beyond both the M5 and the cloud container, and the container runs about 4× slower. Line 4 waits on a memory-lean threshold algorithm (strip-by-strip, holding a boundary rather than the lattice), to be specified for Claude Code, or on hardware with that memory.

Record status and inkling, 2026-09-30 (evening). Runs 076 (falsified) and 077 (unanticipated): in the one-block two-map composition, cut class C₁ carries information beyond the fixed-point separation, and across classes the per-order amplitude (ln N₁)/C₁ drops out entirely (partial +0.015) while C₁ stays (+0.72). Inkling, held with conviction: C₁ is the order of contact of the crossing polynomial at the wall (1 − R ≈ N₁q^{C₁}), and it plays the part of the order of the maximum in Feigenbaum's universality, with N₁ as the non-universal amplitude. Where it breaks: N₁ still moves the exponent inside a class (run 068), and the exponent gap carries information across classes that neither C₁ nor the amplitude explains (077 reported).

Record status, 2026-09-30 (night). Run 078 unanticipated: the cut-class effect on the one-block composition is carried mostly by curvature mismatch at the fixed point (matched on it, the equal/unequal gap falls from 3–10× to 1.4×), with a small direct residue (+0.185). The order-of-contact inkling survives in weakened form: C₁ sets the curvature offset (partial +0.57 given δ) more than it acts on its own.

Record status, 2026-09-30 (late). Run 071 falsified on clause A: cut-4 pattern #20 (N₁ = 324) measures 0.408, inside the cut-3 band, and #25 (N₁ = 4) measures 0.592, inside the cut-5 range. Cut-2 sub-bands and the cut-4 trend in N₁ (Spearman −0.77) hold. The exponent depends on (C₁, N₁) jointly and the bands overlap; the order-not-amplitude split of run 077 belongs to composition, not to the exponent. Next: whether one combination of C₁ and N₁ orders all measured exponents (y₉ already orders cut 2 exactly).

Record status, 2026-10-01 (morning). Run 079 falsified: on fresh seeds at six times the samples, H shows no period-two term in generation, either in skewness (Δ⁴g₁ −0.54 errors) or in width (−0.20). Run 074's alternation was two low draws at the odd generations. H's skewness builds as one concave rise, and its local 1/ν falls steadily (0.553 → 0.533). The hump on the factor-9 carpets is therefore not an aliased alternation. Line 3 (the block-boundary mechanism) goes ahead as drafted: file the hump case, put it through the gate, then seal.