Each 9×9 pattern has an exact one-block map, the crossing polynomial f(p) of run 058 (rg058.poly). Iterating it, R₀(p) = p and Rₖ = f ∘ Rₖ₋₁, gives at every depth k a cumulative distribution on [0, 1] (R₀ is the uniform threshold of a single site, R₁ = f is the exact L = 9 lattice, and depth k matches L = 9ᵏ). With Ψ the map's Poincaré function (Ψ(λx) = f(Ψ(x)), Ψ(0) = p*, Ψ′(0) = 1) and φ = Ψ⁻¹, the depth-k threshold is exactly Tₖ = Ψ(λ⁻ᵏ φ(U)) with U uniform, so its skewness is g₁ₖ = g(λ⁻ᵏ) for one analytic function g with g(1) = 0 and g(0) = g∞, approaching g∞ geometrically at rate 1/λ without oscillation. On the lattice, run 073 found g₁ turning back between 729 and 6561 on T and X1 and still climbing on X and Z. Is that turnover in the one-block map, which would need g(ε) to peak between λ⁻⁴ and λ⁻², or does it live in what the one-block map leaves out?

Sealed 2026-09-30, after run 073 was scored and before any moment of any iterated map was computed (codifier). Known at sealing: every pattern's degree M, p*, λ and y₉ from the census; the lattice's g₁ at 81, 729 and 6561 for the fourteen named carpets (run 073). Not known: any Rₖ beyond f itself, any moment.

What this run is for. The second of four lines pursuing the hump (P-048). In a one-dimensional map the skewness is a single analytic function of λ⁻ᵏ, so a turnover at the lattice's depths is possible only if that function happens to peak in a narrow window. The prediction is that it does not: the lattice's turnover on T and X1 is not a property of the one-block renormalization but of what it discards, the correlations between neighbouring blocks, which is also what made the one-block y₉ fail on twins in run 068. If confirmed, the hump is a multi-block effect and line three (the mechanism test) should look at block boundaries, not inside one block. If falsified, the hump is already in the map, its depth can be read for all 63 patterns at no cost, and line four's prediction for L = 59049 comes from the map.

Reported, not scored. For all 63 patterns: g₁ₖ and g₂ₖ for k = 1 … 20; the depth and height of the maximum of g₁ₖ; g∞ with the last change as its convergence check; g(ε) on a fine grid of ε over [λ⁻⁵, 1]; λᵏ·σₖ against its limit. For k = 1 … 4: the mass within 0.01 of each wall and the share of κ₃ from |T − p*| > 4σₖ, flagging any scored carpet where that share exceeds one half at k = 2 (there Δ₁ is wall-driven, not shape-driven). For each pattern, m₀ (lowest degree of f, the shortest crossing) and m₁ (lowest degree of 1 − f(1 − q), the minimum cut), with the tail forecast sign(g∞) = sign(m₀ − m₁) against the computed sign. The fourteen named carpets' map values beside the lattice's at k = 2, 3, 4; Spearman of peak depth and of g∞ against C₁, N₁, y₉ and the measured 1/ν; the twin orderings at each depth and at the limit. A sign change of g₁ₖ − g∞ for k ≥ 5 is impossible in exact arithmetic and flags a numerical error.

The reductio this seal passed first. By construction, caught: a first draft scored "g₁ rises from depth 2 to 3 on at least 12 of 14". With g(1) = 0 and a tail-set positive g∞ approached monotonically, that passes without the lattice playing any part; it is now reported only, with the tail forecast beside it. The draft's second clause, sign matching on four carpets with a 5% null, assumed a quarter chance per carpet; given the first clause it was a half (31%), and the map's own structure scores it at exactly two of four, so it measured the map's genericity rather than anything about the lattice. It was replaced by the clause above, which scores the one non-generic event, a turnover, and states which way the codifier expects it. Negation: a world where the one-block map already carries the hump shows Δ₂ < 0 on T and X1; that is the falsifier. Cost: seconds to minutes per pattern.

Reviewed before commit by a second reader (OPS.md); its edits are folded in: the exact representation Tₖ = Ψ(λ⁻ᵏφ(U)) and its consequence (no oscillation, geometric approach) added to the question; the numerical method specified (60-digit p*, warm-started inverse iterates, tanh-sinh on both sides of p*, per-depth tolerance); the withdrawal rule made precise; the scored clause rebuilt around the one non-generic outcome; the null corrected; the tail-exponent forecast and wall-share diagnostics added to what is reported.

Scored 2026-09-30 — confirmed

Scored by the codifier from RESULTS075.md (4b529ec), as written.

Withdrawal checks first — not triggered. Every depth k ≤ 4 converged within 322 nodes (cap 2¹⁶); every scored |Δ| is above 1e-6. The quadrature matches exact rationals at k = 1 to 5.5e-18.

Prediction — holds on all four. (Δ₁, Δ₂): T (+0.2717, +0.1183), X (+0.1529, +0.0489), Z (+0.1559, +0.0513), X1 (+0.1463, +0.0462). The map's Δ₂ has the sign of its Δ₁ on every scored carpet: no turn between depths 2 and 4. On the lattice, T and X1 turn back over the same depths (run 073). The turnover is not in the one-block map.

Reported, read. - Monotone everywhere. g₁ₖ rises strictly from k = 1 to 20 on all 63 patterns; no pattern has an interior maximum, so peak depth is not a coordinate of the map at all. - The tail forecast is exact. m₀ (shortest crossing) is 8 on every pattern and m₁ (lowest degree of the complement) equals the minimum cut C₁ on every pattern; sign(g∞) = sign(m₀ − m₁) on 63 of 63. In the one-block map the skewness is set by the minimum cut: the bottleneck tail, exactly. - The map's limit tracks the cut. Spearman(g∞, C₁) = −0.81, (g∞, 1/ν) = −0.77 over 28 measured patterns: the smaller the cut, the more skewed. The lattice at 6561 does not show this (Spearman(g₁, 1/ν) = +0.16, run 072); e.g. U′: map g∞ +0.71, lattice +0.36; T: +0.51 against +0.17. - Twin orderings. The map orders X above X1 and X2 at every depth and in the limit (+0.064, +0.156); Z above Z1 (+0.016); Y below Y1 (−0.009).