Run 034's instrument (Franz–Parisi at T = 1) failed its control and was withdrawn, but its second look stood unsealed — at T = 0, greedy pair-swap paths between minimum bisections of the level-4 ⟨b,c,d⟩-coset graph climb ~50 edges above the endpoints (28% of the 176 cut), against ~2 on a random 4-regular graph of the same size and ~0 on the level-3 coset graph. Is that barrier extensive — does it stay a fixed fraction of the cut at level 5, a thousand times larger — and does it stay separated from the random graph's?

Sealed before barrier.py was run on any graph (2026-09-27, codifier). Between prediction and falsifier is unanticipated. Clause 1 runs on the cloud box tonight; clause 2 is a Claude Code build on the M5 against the spec in this file, scored when it lands. The two clauses are scored separately.

Why the seal says extensive. The level-4 minima are lengthwise a-edge bisections of the coset graph along different seams of the Schreier-path structure (run 032); moving from one seam to another by balanced swaps means carrying a front across the graph, and a front costs a fixed fraction of the cut for a fixed fraction of the way. Random regular graphs are the Fu–Anderson spin glass too, so their barriers should also grow — but at level 4 they were 0.7% of the cut, so the prediction is that they grow slower than the cut. The falsifier's second clause is the outcome that would matter most: if the coset graph's barrier is not separable from the random glass's at N = 2²⁰, then "crystalline minimum, glassy landscape" is not a distinction this statistic can see, and the classical-memory reading of the host loses its comparison.

Spec for clause 2 (Claude Code, M5). - Minima: run R24's refine pipeline on grig5_q with seeds 1–9; record each cut (90,112 expected from some, slightly above from others) and the pairwise |overlap| matrix; A = smallest, ties by seed order. - Interpolator: C, on the coset graph (2²⁰ vertices, degree 4). Gains are integers in {−4, −2, 0, 2, 4} per vertex, so bucket lists suffice: maintain g_v = (same-side neighbours − other-side neighbours) for every v; the best pair is (argmin over U, argmin over V) unless those two are adjacent, in which case also check the next candidates — the pair cost is g_u + g_v + 2·[u ~ v]. Swap, update the ≤ 8 affected gains, record the cut. Path length ≈ N/2 · (1 − |q|)/2 swaps; O(1) amortised per swap. Ties by vertex index, so the level-4 cross-check is exact. - Control first: read b040_coset4_pairs.txt (row 0 = A, rows 1–8 = B), run the C interpolator on coset4 (R23_ising_barrier/coset4.edges), compare to barrier.json's greedy list. ±2 on all eight or stop. - Random control: a random 4-regular graph on 2²⁰ vertices (configuration model, simple), same .adj format, same nine-seed refine, same interpolation. - Report: nine cuts, |q| matrix, eight barriers each for coset and random, medians, wall times. Commit the C source, the .bits of the nine minima, and the JSON; not the random graph itself (regenerable from its seed, which is committed).

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Clause 1, measured the same evening (seeds 200–249, one minute of compute)

Randomised interpolation, best of ten (unsealed tightness check): coset level 4 → 48, 44, 42, 48, 46, 48, 48, 50 (median 48); random → 14, 6, 8, 10, 4, 12, 22, 22 (median 11). The greedy upper bound is not loosened by randomising the path at this size, on either graph.

Scored as written: clause 1 CONFIRMED. Δ₃ = 0 ≤ 6; Δ₄ = 47 ∈ [35, 75]; Δ_rand(1024) = 12 ≤ 12 — on the boundary, inclusive. Neither falsifier fires (Δ₄ > 20; Δ_rand = 12 < Δ₄/2 = 23.5).

Recorded, not scored. Run 034's random-graph barriers (median 2) were a lucky seed set: with fresh anneals the random 4-regular graph's minima are separated by 4% of the cut, not 1%. The random graph is a glass too — Fu–Anderson says so — and this instrument sees it. The separation from the coset graph is 6× in cut fraction, not 25×. Nine distinct minima of exactly 176 among 50 anneals at level 4, mean overlap 0.19: the crystalline minimum is degenerate and its copies are nearly orthogonal, and every path between two of them climbs a quarter of the cut.

Clause 2 (level 5, Claude Code on the M5) is open; state stays open until it is scored.

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Clause 2, measured 2026-09-28 (Claude Code, M5) — UNANTICIPATED

Cross-instrument control: the C interpolator on the level-4 endpoints returns the eight level-4 barriers exactly. Wall: seventeen coset quenches at ~190 s; random graph 26 s to build, nine minima at ~200 s; every interpolation under 0.15 s. Artifacts in R24_grig5_bisection/barrier5/.

Scored as written. Δ₅ = 39,235 ∈ [13,500, 40,500]: hit. Δ_rand(2²⁰) = 25,062 > 8,000: miss. Neither falsifier fires (Δ₅ ≫ 4,500; 0.435 ≫ 2 × 0.0865). Control exact. Outcome: unanticipated.

What the seal got wrong. The random regular graph's minimum-bisection landscape — the Fu–Anderson glass — has extensive barriers under this instrument, 8.65% of the cut at 2²⁰ against 4.3% at 1024, doubling in fraction per thousandfold in N. The codifier expected it to grow sub-extensively. It grows. The host's fraction also grew, 27% → 43.5%. Both landscapes harden with size; the host's is five to six times harder at both sizes.

Three things the measurement found that the seal did not ask for. 1. Twins. The 90,112 minima come in pairs at |q| = 0.953 — the same seam up to 2.35% of cosets — and a twin interpolates to its partner with barrier 0. Every batch of quenches produced one. Seventeen minima clustered into ten classes at |q| > 0.95. So the crystalline minimum is not a point but a flat valley of near-copies connected by zero-cost local rearrangements, with walls of ~39,000 edges between valleys. The one low barrier, 5,750, is to the |q| = 0.80 partner: the barrier tracks the overlap. 2. Inter-basin (unsealed extra). From the best 90,112 minimum to a 131,072 METIS minimum (|q| = 0.0025): peak 139,716. Above the plateau end that is a barrier of 8,644; above the crystal end it is a climb of 49,604 — higher than the 39,235 between crystal copies. So from the crystal, another crystal is nearer than the plateau; from the plateau, the crystal is behind a low wall. 3. Instrument. The interpolator's hierarchical bitset skipped 4,096 indices at a time in its first descent, and the level-4 control could not see it — at N = 1024 the hierarchy is one word deep and that path never runs. It failed loudly on the first level-5 step. Controls at both sizes.

Classical-memory reading, updated. The wall between two copies of the host's minimum is 39,000 edges at 4.2 million spins. The random glass's is 25,000 at the same N and a cut three times larger; a 3D lattice's domain wall (run 030's comparison) is ≈ 52,000. The host beats the random glass in fraction and sits below the 3D lattice in absolute edges: a glass, hardened, not a crystal's cleavage plane.