The construction (a 9×9 pattern keeping 64 cells, outer ring kept, symmetric under the eight symmetries of the square, centre removed) admits exactly 63 patterns. By minimum cut they fall into classes of cut 2, 3, 4 and 5; only one cut-2 pattern (U′), one cut-3 (T) and none of cut 5 have been measured. The "ceiling" 1/ν ≤ 0.874·ln C₁/ln 9 (P-048) rests on X and U′, and run 067 showed it is not preserved by stacking. Across the whole family, do the classes order by cut, and does any member break its class ceiling?

Sealed 2026-09-29, after run 067 was scored and before any quantity of the unmeasured patterns was computed (codifier). Known at sealing: runs 051–067; the enumeration's class sizes from the codifier's own count (cut 2: 19, cut 3: 6, cut 4: 36, cut 5: 2), computed earlier today with a site-based max-flow, which stage 1 replaces with run 062's bond definition — if the class sizes change, the selection rule applies to the new classes as stated. Glimpse declared: while counting, the codifier printed a few cut-3 grids; no exponent, polynomial or pivotal value of any unmeasured pattern was computed.

Why these predictions. Among the measured patterns the exponent falls with cut class (cut-4 0.43–0.55, cut-3 T 0.374, cut-2 U′ 0.276), and more parallel minimum paths should raise 1/ν, so the two cut-5 patterns are expected to top the family. The ceiling is the weaker bet: it was fitted on two points and failed to survive stacking (run 067, ratio 0.874 → 0.842), but no measured single pattern has yet exceeded it.

The reductio this seal passed first (OPS.md, six pushes). Object: the minimum cut here is run 062's bond cut on the pattern's lattice, the same object the ceiling was stated with, not the site count used for today's enumeration. Invariance: mirror images are the same graph; the construction already requires all eight symmetries, so no member is counted twice. By construction: the selection is drawn by a fixed seed from a fixed order written before any value exists, so no outcome can steer it. Negation: a world in which cut does not order the classes shows a cut-3 or cut-2 member above a cut-4 or cut-3 maximum; the record's twins (same cuts, gaps up to 0.039) say within-class spread is large, which is why the clause compares maxima, not means. Null: with no class effect, strict ordering of four maxima happens by chance about 1 time in 24 at most. Transform: the contrapositive of (B) — if some member breaks its ceiling, 0.874 was a coincidence of X and U′ — is exactly the falsifier, so the clause cannot be rescued after the fact by refitting the constant.

Reviewed before commit by a second reader (OPS.md); its seven edits — the scored value named, the sample-maximum reading of (A), a tighter power gate, a multiplicity-aware break line for (B), rules for changed classes and short classes, the 0.5514 arithmetic, and per-clause outcomes — are folded in.

Cost. Fourteen new lattices at L = 6561 at about 75 minutes each in two streams: about 9 hours. Stage 1 is minutes.

Scored 2026-09-30 — falsified (clause B)

Scored by the codifier from RESULTS068.md (c4f4112; stage 1 84a5fce, committed before any sample), as written.

Gates hold. Class sizes by run 062's bond cut: 19 / 6 / 36 / 2, as counted before the seal, so the changed-class rules did not apply. Pivotal control within 1% on all 63 (largest 0.83%). Bootstrap errors on the new exponents 0.0036–0.0042, median under 0.006.

Clause A — confirmed. Class maxima rise strictly with cut: cut 2 0.3493 (#16) < cut 3 0.4270 (#44) < cut 4 0.5508 (X) < cut 5 0.6130 (#2), each adjacent gap far beyond 0.012 (0.078, 0.124, 0.062). The two cut-5 patterns top the family, as predicted.

Clause B — falsified. Three cut-2 patterns exceed the cut-2 ceiling 0.2757 by more than 0.016: #16 0.3493 (+0.074, 17 errors), #50 0.3051 (+0.029), #53 0.3030 (+0.027); #38 sits on it (+0.0006). #16 is connected at generation 2, so the break does not rest on the disconnected patterns (#50 and #53 have more than one component at generation 2). No member of cut 3, 4 or 5 exceeds its ceiling (margins −0.010, −0.0006, −0.027). The ceiling 1/ν ≤ 0.874·ln C₁/ln 9 is dead: U′ sat on it by chance, and #16 exceeds even the bare cut exponent ln 2/ln 9 = 0.3155 (ratio 1.107), so no constant ≤ 1 bounds 1/ν by the minimum-cut exponent across the family.

Last local slopes (OPS rule). #16 0.3684 → 0.3302, still falling; its last local slope stands 0.055 above the cut-2 ceiling, so the break does not depend on the fit window. Cut-5 #5 is flat (0.5882, 0.5873); #2 falls (0.6274 → 0.5986).

Reported, not scored. Within cut 2, the one-block y₉ orders the five new members exactly as the measured exponents (#16 > #50 > #53 > #38 > #47); within cut 3 the top three are tied within errors in the measurement (0.4204–0.4270) while y₉ spreads them by 0.012. X remains the cut-4 maximum among 14 measured members (the two new cut-4 draws, #4 and #24, measure 0.507 and 0.501). The ceiling's closest survivor is cut 4, where X sits 0.0006 below it — the constant 0.874 was X's ratio, not a law.