Run 068 measured 14 of the 63 patterns and left a hierarchy, post hoc: the minimum cut C₁ sets a band of exponents (cut 2: 0.260–0.349; cut 3: 0.372–0.427; cut 4: 0.429–0.551; cut 5: 0.588–0.613), and within a band the number of minimum cuts N₁ sets a sub-band, more minimum cuts lower (cut 2: N₁ = 4 at 0.303–0.349, N₁ = 16 at 0.260–0.276; cut 3 monotone in N₁). The exact one-block y₉ of all 63 shows the same layering. Does the hierarchy hold on patterns chosen before their exponents exist?

Sealed 2026-09-30, after run 068 was scored and before any exponent of the selected patterns was computed (codifier). Known at sealing: runs 051–070 as scored or running; run 068's census, including the exact y₉, C₁, N₁ and connectivity of all 63 patterns — so the codifier has seen the one-block values of every candidate, and the predictions lean on the layering those show. That is declared, not hidden: y₉ is exact and was committed before this seal; what this run tests is whether the measured exponent follows the same layers on patterns whose exponents do not yet exist.

Why these predictions. In run 068's data the layers are clean at the cut-2/cut-3 and cut-4/cut-5 boundaries and touch at cut-3/cut-4 (0.427 against 0.429); clause A's margin is set so that the touching boundary can only falsify on a real crossing. Cut-2's two sub-bands are disjoint in both y₉ and the measured values. Cut 4 is where N₁ is a trend with scatter (its N₁ = 18 member sits above N₁ = 16 in y₉), hence a correlation clause rather than an ordering.

The reductio this seal passed first (OPS.md, six pushes). Object: C₁ and N₁ are run 062's bond-cut quantities from the census, the same objects the hierarchy was read in. Invariance: only connected lattices are used, so a component count cannot masquerade as a layer. By construction: the selection is a fixed seed over a fixed order, written before any value; clause C pools old and new cut-4 members, so it cannot be passed by the new members alone. Negation: a world without the hierarchy shows new cut-4 members below 0.415, or an N₁ = 16 cut-2 pattern above the N₁ = 4 floor. Null: with 26 cut-4 members and no trend, Spearman ≤ −0.5 is rare (well under 1%). Transform: the contrapositive of B — if a cut-2 N₁ = 16 pattern beats an N₁ = 4 one, the count of minimum cuts is not a sub-band label — is its falsifier.

Reviewed before commit by a second reader (OPS.md); its six edits — candidates restricted to unmeasured patterns, clause C's n and tie rule and connectivity stated, a per-pattern error gate, a rule for failed patterns, the census commit pinned, and the one-sided test of the band boundaries declared — are folded in.

Cost. Sixteen lattices at L = 6561, about 75 minutes each in two streams: about 10 hours.

Erratum to the stated count, 2026-09-30, committed during sampling and before any output of this run was read (codifier). The selection rule is fixed and unchanged. The count written beside it was wrong. At census commit 84a5fce only 11 cut-4 (C₁, N₁) cells contain an unmeasured connected pattern (N₁ = 4, 16, 18, 36, 64, 72, 96, 144, 152, 176, 324), so the rule gives 15 patterns (4 cut-2, 11 cut-4), not 16. Clause C's pool is the 13 old connected cut-4 patterns plus the 11 new, n = 24, not 25 (the reductio's "26" is wrong on the same count). No threshold depends on n. The null still holds: with no trend, Spearman ≤ −0.5 at n = 24 has a one-sided probability of about 0.6%. The selection log select071.log (4636bcd), committed before compute, records the 15 and flags the discrepancy. Errors in the codifier's run prompt, not the seal: it named a 0.0045 reseed floor and called seeds 71101+ reseeds. The seal governs. Seeds 71101+ are bootstrap seeds, no reseeds are drawn, and the 0.008 gate is checked against the bootstrap error.

Scored 2026-09-30 — falsified

Scored by the codifier from RESULTS071.md (b71ebcf), as written. All 15 selected patterns are inside the 0.008 error gate; the median bootstrap error (about 0.004) is under the 0.006 withdrawal line.

(A) Bands hold — falsified. The new cut-2 patterns all lie below 0.3718 (0.2602–0.3180). Among the new cut-4 patterns, #20 (N₁ = 324) measures 0.4078 ± 0.0036, below 0.4270 − 0.012 = 0.415: a cut-4 pattern inside the cut-3 band. Its local slopes fall (0.4306 → 0.3849), so its limit is lower still. At the other end, #25 (N₁ = 4) measures 0.5923, inside the cut-5 range (0.5878–0.6130), which no clause addressed.

(B) Cut-2 sub-bands hold — confirmed. N₁ = 4 runs 0.3030–0.3493 over five members; N₁ = 16 runs 0.2602–0.2763 over five. The lowest N₁ = 4 exceeds the highest N₁ = 16 by 0.027.

(C) Within cut 4 the exponent falls with N₁ — confirmed. Spearman(N₁, 1/ν) = −0.765 over the 24 connected cut-4 members (p = 1.4e-5).

What it shows. Cut class does not set disjoint bands: within cut 4, the number of minimum cuts moves the exponent from cut-5 territory (N₁ = 4, 0.592) to cut-3 territory (N₁ = 324, 0.408), a span of 0.18 against gaps between class maxima of about 0.06–0.12. The exponent is a function of both C₁ and N₁, with N₁ strong enough to carry a pattern across class lines. The bands of run 068 were a sampling of the middle of each class.

Reported, read against runs 076–077. In the one-block composition the per-order amplitude (ln N₁)/C₁ drops out (run 077); in the exponent itself N₁ matters as much as C₁. The Feigenbaum reading (order universal, amplitude not) holds for how two patterns compose, and fails for what a single pattern's exponent is.