On all seven carpets counted so far, the number of minimum left–right cuts obeys an exact recursion across generations, N(g+1) = c·N(g)^C₁, with C₁ the one-step cut size and c a constant (H 1, U 3, V 4, T 8, U′ 4, A 36, B 81/2500), checked as exact integers at g = 1→2→3 and in logarithm to g = 4. Within the cut-4 class, the one-block renormalization's miss y − measured 1/ν orders exactly as c on all five known lattices (B .009 < H .017 < U .023 < V .041 < A .051; c = 0.0324 < 1 < 3 < 4 < 36), with no inversion. Cut entropy s, which the Differential panel on CASE-25 adopted, has one inversion (H/B). (A) Is the recursion a property of every generator in the pool, or of the seven looked at? (B) Out of sample: does c order the misses of run 061's three new rooms?

Sealed 2026-09-29 while run 061 is sampling and before any of its exponents has been computed (codifier). At sealing, per-sample thresholds for X (C2–C4) and part of Y (D2–D3) exist on disk in samples061/; the codifier has not opened them, and perc061.json and RESULTS061.md do not exist. Known at sealing: every number in runs 051–060; run 061's pre-sample record (y, p*, D₂′, s(4), the exact polynomials of X, Y, Z); the recursion and its constants for the seven lattices in mincount054.json and mincount055.json, found today while answering the panel's test 5; the panel's House output on CASE-25, which predicts the same order for X, Y, Z from s. Reviewed before commit by a second reader who had not seen the design (OPS.md); its four edits — exact-versus-log tolerance, a noise band, a tie rule and the dependence of B on A, and the interleaving check — are folded in.

How it was found, and the honest discount. The House asked for s at g = 5, 6 to see whether s drifts enough to re-order H and B. Reading s(1)…s(4) instead showed successive differences shrinking by exactly 1/C₁ (¼, ¼, ⅓, ½ for the cut-4, T and U′ classes), which is the recursion. The constant c was then set beside the five misses and ordered them. That is a post-hoc ordering of five points — one chance in 120 under the null, suggestive and nothing more. Clause B is the real test.

What separates c from the competitors. On X, Y, Z, c predicts the same order as the House's s (X < Y < Z) and the reverse of run 061's sealed D₂′ clause (X > Y > Z). So B confirmed does not separate c from s — nor from N₁ (32, 48, 64), which rises with c across these three rooms; it separates all of them from D₂′. The one reading specific to c is where the new rooms fall among the known five (the interleaving check), reported rather than sealed. What c adds is that it has no inversion on the known five and that it rests on an exact identity (A) rather than a finite-g value. With three rooms, the order X < Y < Z happens by chance one time in six.

What the outcomes mean. A confirmed: the minimum-cut structure of every generator is fixed by two integers, N₁ and c, and s(∞) is exact — the panel's test 5 closes without compute. A falsified: the recursion is a property of the seven hand-picked generators, and c is not a pattern invariant. B confirmed: how far the one-block renormalization misses is set by how the minimum cuts of neighbouring blocks combine — c is the factor by which the next generation's count departs from N(g)^C₁ — which is the inter-block correlation the panel named, now given an exact number. Because five of the eight points in the correlation were ordered after the fact, the Spearman clause is easy to pass; the reachable falsifier is Z below X, one chance in two under the null. B falsified: the five-point order was chance, and c joins D₂′ as a post-hoc ranking that did not survive new rooms.

Part A scored 2026-09-29 — falsified (clause B pending run 061)

Scored by the codifier from RESULTS062.md and mincount062.json (5c049ef), as written.

Clause A: falsified. Five of the 19 generators have c_g that differ as exact rationals, which is the sealed falsifier: pool entries 4 (25/324 → 25/1296), 13 (4/9 → 1/36), 15 (1/4 → 1/16), 17 (9/4 → 25/16) and 18 (1/4 → 1/36). 14 of 19 are constant, including all of A, B, X, Y, Z; of the 14 generators not examined before this run, 9 are constant and 5 are not. The minimum cut scales as 4^g on all 19, so none is not-applicable. The recursion with one constant is a property of the generators that were looked at, not of the pool — the pattern N-037 warns about, caught here by the seal.

Deviation from the seal, with no effect. The compute chat tested constancy of the logarithms at 10⁻⁶, not the sealed 10⁻⁹, after A's overflowed c₂ looked non-constant at a stricter setting. The long-double error on every overflowed ln c_g in the file is at most 3×10⁻¹² (A: 36.00000000007), so every verdict is the same at 10⁻⁹; the five failures are exact-rational differences and do not depend on any tolerance.

What the failures show (reported, not scored). In four of the five, c changes by a fixed factor each generation — ln c_g steps by ln ¼ (entries 4, 15), ln 1/16 (13) and ln 1/9 (18) — so N(g+1) = c·r^g·N(g)^4, a recursion one level deeper. Entry 17 (2.25, 1.5625, 1.357…) fits neither form. The pool also holds repeats: entries 5, 12 and 1 share every count (X's), as do 6 and 10 (Y's) and 7 and 11 (Z's) — mirror-equivalent patterns, not independent rooms.

Clause B is not withdrawn. Its withdrawal condition is clause A failing on X, Y or Z; all three have exactly constant c (2, 3, 9). It is scored when run 061 reports. At the time of this note the codifier had seen one line of run 061's Part A log (R75's two-step y₂ = 0.5533), which bears on no clause of run 062; no run-061 exponent had been computed.

Clause B scored 2026-09-29 — unanticipated; run 062 overall falsified (clause A)

Scored by the codifier from RESULTS062.md Part B (4de85b4), which uses run 061's numbers as reported.

Clause B: unanticipated. Misses: X +0.0011, Y +0.0361, Z +0.0154. The sealed order X < Y < Z fails on Y–Z: Y exceeds Z by 0.021, outside the 0.008 noise band, so that pair is determined against c. X < Y and X < Z hold outside the band. The falsifier (Z below X by more than 0.008) does not fire. The eight-lattice Spearman ρ(ln c, miss) = 0.66, between the falsifier (≤ 0.5) and the prediction (≥ 0.85). The interleaving check that only c makes fails on all three rooms: X (0.001) falls below B, not between H and U; Y (0.036) is 0.013 above U, whose cut counts it shares exactly (N₁ = 48, c = 3); Z (0.015) falls near H, not between V and A. The five-point order c gave was one chance in 120 under the null, and it did not carry to new rooms.

Y and U are already cut twins. They share N₁ and c, hence every N(g), and their misses differ by 0.013 (measured 1/ν 0.5134 ± 0.0036 against 0.524). That is inside run 063's undetermined band (< 0.015) but in the direction run 063 predicts: cut counts do not set the miss.

Where this leaves the lead. The panel's House (CASE-25) predicted X 0.015–0.022, Y 0.023 ± 0.006, Z 0.040–0.048 from s; all three miss, and Y's deviation (0.013) exceeds the House's own kill threshold for s (0.012). No cut quantity tried — s, c, D₂′ — predicts the new rooms. Run 063 (twins) and run 065 are the next tests; run 063's clause B is already decidable from run 061's Part A and is scored with that run.