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Original ledger classification: External MMST fact pinned at 4-point [E]/[C]: the edge four-point is quasi-free (G^2=G) and Cauchy-convergent to the free-fermion conformal cross-ratio 2+sqrt(3) (vs an off-scale exponential bulk control), extending v444's two-point scaling limit to 4-point order. The one external MMST existence fact is empirically supported at both orders; SEAM.EQUIV.01 stays [O]

Recorded statement: Pinning the ONE external MMST fact empirically (2026-06-30) -- the edge FOUR-point function is quasi-free and conformally convergent, extending v444's two-point scaling limit to the next order. v441 isolated the keystone's single EXTERNAL…

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SEAM.EQUIV.EDGE.FOURPOINT.01

Original ledger classification: External MMST fact pinned at 4-point [E]/[C]: the edge four-point is quasi-free (G^2=G) and Cauchy-convergent to the free-fermion conformal cross-ratio 2+sqrt(3) (vs an off-scale exponential bulk control), extending v444's two-point scaling limit to 4-point order. The one external MMST existence fact is empirically supported at both orders; SEAM.EQUIV.01 stays [O]

Original claim text

Pinning the ONE external MMST fact empirically (2026-06-30) -- the edge FOUR-point function is quasi-free and conformally convergent, extending v444's two-point scaling limit to the next order. v441 isolated the keystone's single EXTERNAL hypothesis (continuum existence of the chiral scaling limit, MMST); v444 grounded it at the TWO-point level; this module takes the FOUR-point step on the same v367/v368 collar. [E] QUASI-FREE/WICK (CAR hypothesis): the ground-state correlation matrix is an exact projector G^2=G (~1e-13), so the state is quasi-free and all n-point functions are Wick/Pfaffian sums of the two-point -- the MMST quasi-free CAR hypothesis (ledger entry 5) literally holds on the collar (structural: the BdG state is free). [E] FOUR-POINT CAUCHY CONVERGENCE: the edge four-point cross-ratio Q=[G01 G23]/[G02 G13] at commensurate proportional positions (1,2,4,7)*(Nx/12) is Cauchy-convergent under refinement (successive spread shrinks, Nx=36..60) -- the four-point converges, extending v444's two-point scaling-collapse. [E] CONFORMAL FOUR-POINT FORM: Q converges to the free-fermion conformal cross-ratio sin(5pi/12)/sin(pi/12)=2+sqrt(3)~3.732 (chord distance d(r)=(Nx/pi)sin(pi r/Nx)) -- the edge four-point has the chiral-CFT cross-ratio structure (eta=1), not just the two-point. [E] BULK NEG CONTROL: the bulk-row four-point is orders of magnitude off the conformal value (exponential decay, gapped) -- only the EDGE four-point is conformal. [C] VERDICT: the one external MMST fact (continuum existence) is now empirically supported at BOTH two-point (v444) and four-point order; every measured n-point converges to its conformal limit. SEAM.EQUIV.01 stays [O] -- the rigorous MMST uniform-convergence theorem (v336) is the cited backbone.

Original classification detail

Numerical

Dependencies as recorded

SEAM.EQUIV.01; SEAM.EQUIV.CONTINUUM.EDGE.01; SEAM.EQUIV.APPLICABILITY.01; v444; v441; v336

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  • v448_seam_edge_fourpoint.pyRegistered verification module · frontier
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    SEAM.EQUIV.EDGE.FOURPOINT.01: pinning the ONE external MMST fact empirically -- the edge FOUR-point is quasi-free and conformally convergent, extending v444's two-point scaling limit. [E] QUASI-FREE/WICK: the ground-state correlation matrix is an exact projector G^2=G (~1e-13), so the state is quasi-free and all n-point are Wick sums -- the MMST quasi-free CAR hypothesis (ledger entry 5) literally holds (structural: the BdG state is free). [E] FOUR-POINT CAUCHY CONVERGENCE: the edge four-point cross-ratio Q=[G01 G23]/[G02 G13] at commensurate positions (1,2,4,7)*(Nx/12) is Cauchy-convergent (spread shrinks, Nx=36..60). [E] CONFORMAL FOUR-POINT: Q converges to the free-fermion conformal cross-ratio sin(5pi/12)/sin(pi/12)=2+sqrt(3)~3.732 (eta=1). [E] BULK NEG CONTROL: the bulk four-point is orders of magnitude off (exponential). [C] the one external MMST fact (continuum existence) is now empirically supported at BOTH 2-point (v444) and 4-point order; SEAM.EQUIV.01 stays [O]. Python-only (numpy).

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