Stacking two carpet patterns A and B gives, at the one-block level, the 2-cycle of their crossing polynomials, with y_AB = ln(R_A′(r)·R_B′(q))/ln 81 at q = R_A(r), r = R_B(q). Its deviation from the parents' mean, D = y_AB − (y₉(A) + y₉(B))/2, was +0.0115 (X,U′), +0.0022 (X,T), +0.0052 (U′,T) and −0.0011 (X,Y). Panel PN-004 read D as governed by the separation of the fixed points δ = p*_B − p*_A rather than by cut class, and its House final stated as forced that D is second order in δ. Expanding the 2-cycle gives a first-order term instead, D₁ = δ(λ_A − 1)(λ_B − 1)(s_A − s_B) / [ln 81 · (λ_Aλ_B − 1)], with λ = R′(p*), a = R″(p*) and s = a/(λ(λ − 1)) one number per pattern; D₁ vanishes only when δ = 0 or s_A = s_B. Over every pair of distinct census polynomials: is D first order in δ, what sign does it take, and does cut class matter once δ is known?

Sealed 2026-09-30, after panel PN-004 was filed and before any two-map value beyond the four recorded pairs was computed (codifier). Known at sealing: every pattern's p*, λ, y₉, C₁ and N₁ (census); run 075's polynomials and g₁ values; the four recorded pairs' y_AB. Not known: any other pair's y_AB or D, any pattern's R″(p*) or s. Counted from census p* and C₁ only, before sealing: 49 distinct functions, 1,176 pairs; 123 with 0 < |δ| ≤ 0.01; 976 with |δ| > 0.02; |δ| quintile cuts 0.023, 0.050, 0.086, 0.123 with (equal C₁, unequal C₁) pairs per bin (154, 82), (144, 91), (104, 131), (60, 175), (10, 225). C₁ bands of p*: cut 2 0.801–0.943, cut 3 0.827–0.860, cut 4 0.684–0.827, cut 5 0.665–0.715.

Where the first-order term comes from. ln R_A′(r) − ln λ_A ≈ (a_A/λ_A)(r − p*_A) and likewise for B. The linearized 2-cycle, r₁ − p*_B = λ_B(q₁ − p*_B) and q₁ − p*_A = λ_A(r₁ − p*_A), gives r₁ − p*_A = δ(λ_B − 1)/(λ_Aλ_B − 1) and q₁ − p*_B = −δ(λ_A − 1)/(λ_Aλ_B − 1), both inside the interval, and so the closed form above. The House's second-order statement is the special case s_A = s_B for every pattern. The codifier checked the expansion on made-up cubic maps, R(x) = p + λ(x − p) + (a/2)(x − p)² + c(x − p)³ with (p, λ, a, c) = (0.70, 3.0, 1.0, 0.3) for A and (p_B, 2.5, −2.0, −0.2) for B, p_B = 0.72, 0.701, 0.7001: D/D₁ = 0.996, 0.9998, 0.99998. Control (ii) repeats that check in the lab's code.

Why B, C and D. To first order D < 0 exactly when s_A < s_B with p*_A < p*_B, so clause B asks whether s fails to decrease monotonically with p*; Kendall τ(p*, s) is reported. The recorded X,Y pair is already negative. Nothing in the expansion refers to C₁; clauses C and D ask the data to agree once δ is held fixed, since C₁ and p* are themselves correlated (the bands above), so a raw comparison would pass by construction.

Reported, not scored. D against δ, δ², ΔC₁, Δy₉ and Δ(measured 1/ν) where both parents are measured; Kendall τ(p*, s); the log-log slope of |D| on |δ|; D₁ against D over the whole range of δ with the |δ| beyond which |D/D₁ − 1| first exceeds 0.2; the 20 largest |D|. For the seat record (PN-004): cut-4 pairs with |δ| > 0.03 and the share with D > +0.003 (Bound); the cut-4 pair with the largest |Δy₉| (Lateral: +0.008 to +0.016); every cut-4 pair with |δ| ≥ 0.15 (the House's test 1; none exists at sealing, since cut-4 p* spans 0.684–0.827, a width of 0.143) and the widest cut-4 pair instead.

The reductio this seal passed first. Object: y_AB is the same one-block 2-cycle value runs 067 and 070 computed, extended to every pair; control (i) ties it to those. By construction, caught: a first draft scored D against D₁ without asking whether s varies (a Taylor theorem wherever it does), compared raw Spearmans of |D| on |δ| and on |ΔC₁| (passes because C₁ tracks p*), and set a threshold on equal-C₁ pairs with no comparison group; all three are replaced above. Null: if D were second order with a fixed sign, clause A's first part and clause B fail. Negation: a world where cut class matters for the map at fixed separation shows equal-C₁ bins with much smaller |D|; clause C is written for it. Cost: minutes.

Reviewed before commit by a second reader (OPS.md); its eight edits are folded in: clause A rebuilt around the spread of s with a filtered ratio test; the toy check and a translated-pair check made controls; a first-order reading of clause B; clause C made a comparison at matched separation; clause D made a partial correlation; set sizes counted from the census before sealing; exact root counting for the 2-cycle; and rules for merged patterns and unscorable clauses.

Scored 2026-09-30 — falsified

Scored by the codifier from RESULTS076.md (991d9e3), as written; the clause-A set computed from pairs076_raw.json by the seal's definitions. Controls (i)–(iii) pass; no pair has more than one root.

(A) First order — unanticipated. s varies widely: IQR 2.93 against median |s| 3.21 (ratio 0.91, far above 0.2), so D₁ is not identically zero and the House's "second order" statement is false. On the filtered set (0 < |δ| ≤ 0.01, |s_A − s_B| ≥ 0.32; 46 pairs) the median |D/D₁ − 1| is 0.23: between the prediction's 0.1 and the falsifier's 0.5. D approaches D₁ as δ → 0 (the top |Δs| quartile: median ratio 0.94; the translate control: D₁ = 0 and D ∝ h²), but the linear regime is narrow: by |δ| > 0.02 the median D/D₁ is 0.05–0.07. Beyond δ ≈ 0.01 the first-order term is almost entirely cancelled by higher orders.

(B) Both signs — confirmed. D < 0 on 319 of 976 pairs with |δ| > 0.02 (33%).

(C) Cut class does not protect — unanticipated, leaning against. At matched separation, equal-C₁ pairs have much smaller |D|: bin ratios 0.105, 0.153, 0.260, 0.328, 0.971 (median 0.260, between 0.2 and 0.5), with the first four bins at p ≤ 3e-3.

(D) Separation beats class — falsified. The partial Spearman of |D| with |ΔC₁| given |δ| is +0.596, beyond the falsifier's 0.3. Cut class carries information about the deviation that the fixed-point separation does not.

Outcome. Falsified on D. The codifier's reading — deviation set by the separation, cut class a confounded proxy — is wrong at the one-block level; so is the House's. The case's own framing (matched cut class averages) is closer to the one-block map than either rival.

Reported, read. |D| ranks best against |Δy₉| (Spearman 0.81) and |Δ(1/ν)| where measured (0.79), ahead of |δ| (0.77). D is positive when a high-cut, high-exponent pattern is stacked with a low-cut one (the twenty largest are all cut 5 or 4 with cut 2, D ≈ +0.017 to +0.021). s tracks p* almost monotonically (Kendall −0.91), so the first-order coefficient is nearly a function of p*; what cancels it beyond δ ≈ 0.01 is not known.