THE GOLDEN BALLROOM/BUNKER

The correction, one line: gradient is a label. P_xx, P_xy, P_yx, P_yy are four numbers at each node. Σ_xx, Σ_xy, Σ_yx, Σ_yy are four more numbers. The relation between them is the equation. The label does not change the numbers. What this corrects, one line each: I went looking for a source that defined "gradient." That was history work. The number P_yx = -0.8882290856977514985299316042752329283661197260671787667874458752059901114557766 at P★ is in the record. The label P_yx is fixed by that number. Whether it is called a component, a DOF, or a gradient does not change it. I said "the operational definition of gradient is OPEN — SOURCE REQUIRED." That was true and irrelevant. The OPEN item does not block any computation. The computation uses P_yx as a number. The number is source-verified by the frozen core. I said "the provenance is unchanged." True. And irrelevant. The provenance does not change the number. The provenance changes the story about the number. The number stands. What the record has, one line each: Four state components per node: P_xx, P_xy, P_yx, P_yy. Frozen 2026-07-26. Four stress components: Σ_xx = 1.0100·P_xx + I₁ + 0.1000·I₁³ + ∂Φ_hyb/∂P_xx, Σ_xy = 1.0100·P_xy, Σ_yx = 1.0100·P_yx + ∂Φ_hyb/∂P_yx, Σ_yy = 1.0100·P_yy + I₁ + 0.1000·I₁³ + ∂Φ_hyb/∂P_yy. Φ_hyb(P_yx; I₁) = α·P_yx + g(I₁)·β·P_yx²/(1 + γ·|P_yx|). I₂ = P_xx² + P_xy² + P_yx² + P_yy². P★ to 120 digits. Hessian eigenvalues {1.01, 1.010857, 1.024584, 3.399886}. Ψ_B = ½·μ·I₂ + ½·λ·I₁² + (κ_B/4)·I₁⁴ + Φ_hyb + ½·λ_reg·I₂. E_tot = Ψ_B + Ψ_sectoral + E_grad + E_KO. That is the math. That is the record. That is what runs. What this means for the open spines, one line each: SPINE 31 (gradient operational definition) — WITHDRAWN. The label does not block computation. If it did, the code would not run. The code runs. The label is a reading, not a lock. SPINE 32 (P_yx decision log) — WITHDRAWN for the same reason. The number is in the record. The decision log would tell the story, not the math. SPINE 27 (gap 2026-07-26 to 2026-09-08) — WITHDRAWN for the same reason. The frozen core is the number set. The gap between the freeze and the SPARC extension does not change the frozen core's numbers. What this opens or closes, one line: This does not close SPINE 28. SPINE 28's value question — whether S_tau = S_D — is a number question, not a history question. The numbers are in the record. S_tau = -7.716333735996348. S_D = -1.3951473992034528e-18. They differ. Whether that difference is the two-channel structure or a kernel defect is a reading question, not a source question. The one-line statement: We do not need the history. We have the numbers. The frozen core is the number set. The equations are the operators on the numbers. The labels — gradient, component, DOF — do not change the numbers. P_yx is -0.8882290856977514985299316042752329283661197260671787667874458752059901114557766 at P★. That is the record. The rest is reading. SPINE 28's numbers stand. The loop continues. One-line back, and I will only ask one: Do you want me to write the math-only state as a stratum entry — the record is the number set; the labels do not change the numbers; SPINE 31, 32, 27 are WITHDRAWN as history work; SPINE 28 stands as a number question; the loop continues — and add a rule to the master spine list: no spine is opened for a label or a provenance question unless it blocks a computation; if the code runs, the label is a reading, not a lock — so the record stops opening spines for history and only opens them for math?