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A registered result in its source context

Original ledger classification: Numerical [I] (lattice determinants vs exact conical constants) + [A/O] (continuum leg + anchor stay open)

Recorded statement: SEAM-HORIZON REPLICA CHAIN AT COLLAR LEVEL (the kernel-identification premise of SEAM.THEOREM.01, exercised numerically; SEAM.EHMODEL.03's residual list sharpens again, the gate stays OPEN): (1) REPLICA => EH FORM ON A REAL OPERATOR [I] -…

Statement, assumptions and sources

Paper context: Origin Theory

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SEAM.EHMODEL.04

Original ledger classification: Numerical [I] (lattice determinants vs exact conical constants) + [A/O] (continuum leg + anchor stay open)

Original claim text

SEAM-HORIZON REPLICA CHAIN AT COLLAR LEVEL (the kernel-identification premise of SEAM.THEOREM.01, exercised numerically; SEAM.EHMODEL.03's residual list sharpens again, the gate stays OPEN): (1) REPLICA => EH FORM ON A REAL OPERATOR [I] - matched conical deficit G(gamma,m) = log det L(gamma,m) - (gamma/2pi) log det L(2pi,m) of the discretized gapped cone operator (finite-volume polar grid, geometric tip grading, identical stencil across geometries so extensive terms cancel exactly) is linear in ln m with slope 2C(gamma), verified on deficit cones gamma/2pi = 1/4, 1/2, 3/4 (rel. err 0.01-0.05%) AND on REAL replica sheets gamma/2pi = 2 (0.8%), 3 (1.5%) - beyond linearisation, the regime the replica trick uses; (2) COEFFICIENT FORCED, SCALE = ANCHOR [I] - the EH slope is stable under IR/size refinement (0.5% drift) while the intercept (zeta-scale mu_lat 146.9 -> 153.1) drifts with the discretization: the v152 anchor exhibited on data; NO canonical ln(m/mu) = 3/4 emerges (recorded honestly - the anchor stays declared, not derived); (3) BFK SPLIT MEASURED ON THE DISCRETIZED CALDERON KERNEL [I] - Schur identity log det L = log det(halves_D) + log det S exact (~1e-16); across three cut geometries the Calderon/Schur factor's deficit slope follows a PURE CUT-EDGE law E(1-q) with tip term 0 (power check: the same law fails on the full determinant), the halves carry the whole tip 2C_cone via Kac doubling (exact) - v151's 'conically clean' measured on the kernel itself, not inferred from corner constants; (4) THE SEAM'S OWN SPECTRUM [I] - the v302 transfer masses m2 = 6 ln(3/2), m3 = 6 ln 3 (bend ln3/ln(3/2), v124/v147) sit ON the calibrated EH line (<=0.05%): det'(collar) inherits the EH variation mode-wise; the Perron/attractor mode (m=0) is IR-DIVERGENT, running exactly as -2C ln(IR ratio) - THE RECOVERY GAP Delta = 6 ln(3/2) IS WHAT MAKES THE INDUCED-GRAVITY COEFFICIENT FINITE (the same gap that makes the attractor unique, v56, makes 1/G finite). RESIDUAL [A/O]: the kernel premise is now discharged at the finite/model level; what remains of SEAM.THEOREM.01 is the CONTINUUM scaling limit of this statement (the MMST class - the same single residual as SEAM.EQUIV.01, v336) plus the one dimensionful anchor (v152). NOT claimed: a continuum proof, or a derivation of ln(m/mu) = 3/4

Original classification detail

Numerical [I]: kernel premise discharged at collar level; residual = continuum leg (MMST class) + anchor; gate stays open

Dependencies as recorded

SEAM.EHMODEL.03; SEAM.EHMODEL.02; SEAM.EHMODEL.01; SEAM.THEOREM.01; SEAM.AREACOEFF.03; v56; v73; v90; v150; v151; v152; v302; v336

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Registered verification modules

  • v471_seam_horizon_replica.pyRegistered verification module · horizon
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    SEAM.EHMODEL.04: the Seam-Horizon replica chain exercised numerically on a discretized seam collar -- the kernel-identification premise of SEAM.THEOREM.01 (residual of v150/v151/v152) discharged at the finite/model level for the seam's own kernel, with real replica sheets. Replica => EH form on a real operator: dG/d ln m = 2C(gamma) on deficit cones (0.01-0.05%) and replica sheets n=2 (0.8%), n=3 (1.5%); EH coefficient cutoff-independent (0.5% drift) while the zeta-scale mu_lat drifts = the v152 anchor exhibited (no canonical ln(m/mu)=3/4 emerges); BFK/Schur split exact (~1e-16) with the Calderon factor conically clean (pure cut-edge law, tip term 0, power check) and the halves carrying 2C_cone (Kac doubling exact); the v302 transfer masses 6ln(3/2), 6ln3 sit on the calibrated EH line (<=0.05%) and the Perron/attractor mode (m=0) is IR-divergent -- the recovery gap makes the induced-gravity coefficient finite. Honest scope: finite level; SEAM.THEOREM.01 stays open, residual = continuum leg (MMST class, = the SEAM.EQUIV.01 residual) + the anchor. Numerical, Python-only by nature.

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