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3055 bytes, as of the version from 2026-10-29 01:41 (current). Recorded here, not run.
# Argument selection for T596
The only quantity is r(m,n), the effective resistance between (0,0) and (m,n)
divided by the common edge resistance R0. Edges join nearest neighbors of Z^2.
The infinite-network convention is the limit of periodic square tori at fixed
displacement. Cserti, arXiv:cond-mat/9909120v4, section II, equations (9)–(18),
and section II.C, equations (25)–(32), establish these conventions for arbitrary
lattice sites. The positive combinatorial Laplacian is 4I minus adjacency.
Both integer parameters m and n have role `discrete_index`. They are the two
coordinates of a vertex displacement on a fixed network, with m >= n >= 0
and m > 0. Neither chooses a coupling, a continuous sample input, or another
quantity. Sign changes and coordinate interchange identify equivalent
resistances, so each displacement orbit occurs once. The normalization R0
is fixed by taking the ratio and is not a free parameter.
We select all nonzero representatives with m+n <= 20: 120 entries, consisting
of 20 axial, 10 diagonal, and 90 asymmetric representatives. These groups have
the same discrete role and the same joint graph-distance bound. Enumeration
is by increasing m+n, then increasing n. The origin is a computational seed,
not an entry. No independent Cartesian product of tunable arguments is taken.
This is a bounded reference for short separations in the square resistor
network, encompassing all displacement directions within the graph ball.
The radius 20 is a noncanonical practical choice, independent of numerical
notation. It supplies angular breadth before extending only axial or diagonal
separations. We do not claim that every vertex pair has an individually
documented experiment. Values can arise in voltage-drop computations and
discrete Green-function evaluations on this specified network. A larger radius
would mainly deepen the same family; different lattice geometries are separate
quantities requiring their own review. Keeping just the adjacent and diagonal
closed forms would omit asymmetric and longer short-range displacements.
The recurrence has exact coefficients in Q + Q/pi. At this range certification
and storage are inexpensive; the build measures cancellation and written size
rather than using entry count as a target. The mathematical domain is unbounded;
`complete: no` and the completeness note specify the finite graph ball and its
purpose. The generator has no data-source dependency controlling enumeration.
Policy basis: the coordinated skill manifest is
`agents/runs/20261029T011133Z-build-skills/manifest.json`. Both archived copies
have SHA-256 `28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
The local build's justification is not the required independent critique.
Build measurement: the 119 irrational entries are written to 100 significant
digits, with at least 413 relative accuracy bits retained from 461 working
bits. The longest written number is 102 characters; the measured serialized
value block is about 16.4 KiB. The adjacent value is exactly 1/2.