A carpet may use a different 9×9 pattern at each level. Stacking X over U′ (X at the coarsest level, U′ in every kept cell, X again inside, and so on) gives a carpet whose dimension and minimum-cut exponent are exact averages of its parents' (ln(C_X·C_U′)/ln 81 = (3/4)·log₃2 = 0.4732). X and U′ both sit at 1/ν ≈ 0.874 × their cut exponent, so if exponents average under stacking, 1/ν(X∘U′) lands at 0.414, and the "ceiling" 1/ν ≤ 0.874·ln C₁/ln n (P-048) is also 0.414. Does the exponent of a stacked carpet average its parents' exponents — and is it at, below, or above that ceiling?

Sealed 2026-09-29, before any stacked lattice was built and before the codifier read run 063's results (RESULTS063.md was on disk, unopened, at this commit; its X and Y values and its X, Y, Z reseeds enter only through rules fixed above). Known at sealing: runs 051–066; U′'s measured 0.2760; X's run-061 value 0.5522 and Y's 0.5134. Not known: any stacked quantity, including the stage-1 one-block value.

Closed forms named before the measurement, so a match counts only if it was written first. √2 − 1 = 0.41421 for v(X,U′); 7/8 for the ratio v / 0.4732. Both sit at the averaging point, so a match is the averaging branch of A, not an independent prediction. Each is reported as within or outside 2σ_A; neither is a clause, and a match is noted, not claimed — at three figures and ±0.005, many simple expressions fit (√2 − 1, 5/12, ln(3/2) are all within 0.01 of 0.414).

Why below. Averaging would make the exponent a sum over levels, each level contributing its own pattern's share independently. The record says one-block quantities do not add up that way (run 066: the block sequence turns over; CASE-26), and in X∘U′ every other level is a two-bond bottleneck; the guess is that the bottleneck levels govern more than their half. Conviction moderate: this is the codifier's lean, not a derivation.

The reductio this seal passed first (OPS.md, six pushes). Object: the ceiling was stated for single 9×9 patterns with ln C₁/ln 9; written as ln C₁/ln n it survives composition (P-048), so an 81-generator stacked carpet is inside the claim, not beside it. Invariance: X∘U′ and U′∘X differ only by one top level of an infinite object, so their exponents are equal as a theorem — the control is an instrument check, and it is also how finite-size drift is measured here. By construction: the slope from 81 to 6561 spans one X level and one U′ level, so a stack whose levels scaled independently would give the average automatically; the clause tests whether they do. Negation: the averaging world predicts |v − m| ≤ 2σ on both pairs; the ceiling-broken world predicts v above. Null: with no effect, v below m by 2σ happens about 2.3% of the time per pair. Transform (contrapositive): if the ceiling holds and exponents average, X∘U′ must sit on the ceiling exactly — so A's falsifying branch "at the mean" is also the ceiling's best case, and the "above" branch is the ceiling's worst.

What the outcomes mean. Confirmed: stacking is not additive in the exponent; the carpet's levels interact, and the ceiling survives without explaining why X and U′ sat on it. Averaging: the exponent is a sum over levels — an exact composition law for 1/ν on carpets, and X∘U′ lands on the ceiling, which then deserves the census. Above: the ceiling is dead.

Reviewed before commit by a second reader (OPS.md); its seven edits — the noise of a two-order mean (σ_A, σ_B in place of s·√1.5), the control's middle band scored and flagged, parents read by the same endpoint slope as the stacks, a cap on s, the closed forms labelled as the averaging point, the reported ceiling and one-block comparisons, and the joint verdict — are folded in.

Scored 2026-09-29 — unanticipated

Scored by the codifier from RESULTS067.md (b86f6a7; pre-sample record 41361b2), as written.

Gates hold. s = 0.0045 (≤ 0.008); stacked bootstrap errors 0.0037–0.0041 (median ≤ 0.008). The builder reproduces carpet(X, 2) from [X, X], and every stack has 64^g kept cells in one component.

Control (C) — holds. |1/ν(X∘U′) − 1/ν(U′∘X)| = 0.0011 and |1/ν(X∘Y) − 1/ν(Y∘X)| = 0.0045, both inside 2√2·s = 0.0127. The one-block values agree exactly by construction (0.448535 and 0.550330 for both orders).

Clause A — holds. v(X,U′) = 0.3984 against m(X,U′) = 0.4131: v − m = −0.0147 = −3.5 σ_A (σ_A = 0.0042), below the 2σ_A line. Stacking X over U′ does not average; the composite sits below both the average and the ceiling 0.874 × 0.4732 = 0.4136.

Clause B — fails. v(X,Y) = 0.5321 against m(X,Y) = 0.5331: v − m = −0.0010 = −0.26 σ_B. X and Y, both cut-4, average within noise.

Verdict. The seal's rule: A holding with B failing is unanticipated. Averaging holds for two parents of the same cut class and fails, downward and by 3.5σ, when a cut-2 bottleneck level is stacked with a cut-4 level.

Reported, not scored. - Last local slopes (OPS rule). Every stack's local slope is still falling: X∘U′ 0.4112 → 0.3846, U′∘X 0.4144 → 0.3836, X∘Y 0.5433 → 0.5163, Y∘X 0.5558 → 0.5129 (errors about ±0.008 each). Parents' last local slopes: X 0.5520 (run 063, flat to rising), Y 0.5076 (run 063, falling), U′ 0.249 (run 051, falling). On last local slopes the X∘U′ gap holds (stack mean 0.3841 against parents' 0.4005, −0.016) and the X∘Y pair also reads below (0.5146 against 0.5298, −0.015); two-point slopes, so this is a lead, not a reversal of clause B, which is scored on the sealed endpoint statistic. - Ceiling. v(X,U′) = 0.3984 < 0.4136 and v(X,Y) = 0.5321 < 0.551: the ceiling survives both composites. The ratio to the cap falls from 0.874 on the parents to 0.842 on X∘U′, so sitting on the ceiling is not preserved by stacking: X and U′ being at 0.874 was not a composition law. - Named closed forms. √2 − 1 = 0.41421: missed by 0.0158 (3.8 σ_A). 7/8 for v/0.4732: measured 0.842. Neither matched; both sat at the averaging point, which clause A excluded. - One-block values. The stage-1 y overshoots the mean of the parents' one-block y on X∘U′ (0.4485 against 0.4370) and matches it on X∘Y (0.5503 against 0.5514), while the measured exponent undershoots on X∘U′: the one-block map and the lattice move in opposite directions exactly where the cut classes differ. - Post hoc, two points, not a claim. The geometric mean of the parents' exponents, √(1/ν_A · 1/ν_B), gives 0.3895 for X∘U′ (measured 0.3984) and 0.5328 for X∘Y (measured 0.5321). A third pair spanning cut classes (X∘T or U′∘T) would test it; recorded as an inkling in P-048. - U′'s parent value comes from run 051's stored thresholds (run 061 drew none for U′), the samples behind its recorded 0.2755; the statistic named run 061 in error, and the substitution changes no number.