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2652 bytes, as of the version from 2026-10-29 01:41 (current). Recorded here, not run.
# Sources and decisions for T596
Checked J. Cserti, arXiv:cond-mat/9909120v4, section II equations (9)–(18),
section II.C equations (25)–(32), and its arXiv bibliographic record. The paper
uses a negative discrete Laplacian and a Green function with a compensating
sign; the table explicitly uses L=4I-A. Equation (25) has exactly the proposed
resistance normalization. Periodic boundary conditions are introduced in
(10)–(14), and the infinite integral follows in (15)–(18). The recurrence (32)
uses the same normalization as the adjacent value 1/2 and diagonal value 2/pi.
The checker rewrites cosh(s)=2-cos(y) as s=2 asinh(sin(y/2)) on [0,pi]. It
uses expm1 and sin(ny/2)^2 to avoid subtractive loss near zero. The endpoint
integrand limit is m. These are analytic transformations of the published
single integral, independent of the coefficient recurrence.
The finite-torus check diagonalizes L=4I-A. For side N, its resistance is the
normalized Fourier sum (1-cos(m*x+n*y))/(2-cos(x)-cos(y)) excluding the zero
mode. At adjacent vertices symmetry gives (1-1/N^2)/2 exactly, which is the
control. The finite computations are diagnostic convergence checks, not a
claimed rigorous error bound for the infinite lattice.
All finite extents and conventions in the proposal were retained after the
current-skill review. The radius 20 is practical, not a theorem. No anisotropy,
continuous coupling, or alternate quantity was introduced. Every entry is a
displacement in a discrete network, and the coverage includes all directions.
Corpus checks found T400 (Kirchhoff indices of connected graphs) and T393
(Watson integrals of the cubic lattices) as related but different families.
Their actual addresses and full documents were read and saved in neighbors.json.
The existing physics, lattice sums, and random walks tags were verified.
No graph theory tag was found. Such a tag would fit at least T400, the table
of distance spectral radii of connected graphs, and T596; propose it separately.
The initial third exploratory numeric lookup contained a transcription error
in the expected axial value and is not used as evidence of absence. The other
lookups include correctly written 2/pi, 2-4/pi, 4/pi-1/2, and the exact 1/2.
Nontrivial resistance lookups returned no existing entries; rational 1/2 had
many unrelated matches. Family absence, not absence of a common value, justified
the claim. Title creation succeeded for T596.
The exact policy evidence is the manifest at
agents/runs/20261029T011133Z-build-skills/manifest.json. Both archived skill
copies match SHA-256 28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199.