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3447 bytes, as of the version from 2026-11-10 01:14 (current). Recorded here, not run.
# Numerical evidence for T701
This build used the matching archived instructions recorded by
`agents/runs/20261110T005551Z-build-skills/manifest.json`, attached as
`skill-manifest.json`. Both SHA-256 values are
886390324dd1971e381a43cf3b46b822ab0bc67d62f31d8481e29ec79556746b.
The 362 rows consist of 361 real approximations at 100 significant digits and
one proved exact zero. All generated nonzero balls retain at least 425 relative
bits, using 128 guard bits and between 8 and 57 terms in each q-series half.
No claimed accuracy is inferred from the number of working digits alone.
For L=-log|q|>0, a=r/N and R=|q|, an omitted half starting at exponent t has
absolute sum bounded by
L R^t/(1-R^t) * [t/(1-R) + R/(1-R)^2].
This follows by applying |log|1-z|| <= |z|/(1-|z|) termwise and summing the
positive geometric majorant. The two starts after M paired terms are M+a
and M+1-a. Both tails are included in the output ball. The exact zero at
(-3,3,1,2) follows from the lattice automorphism proof in the document;
its raw numerical ball was also checked to contain zero with tiny radius.
All rows were compared with a separate 170-digit mpmath Fourier computation
obtained by summing the powers of q analytically. Relative differences for
nonzero rows were at most 6.54e-130. This second computation is an agreement
check; the q-series ball plus explicit tails supplies the precision certificate.
Every serialized decimal was also checked against its own one-last-place
interval. Recomputing at 130 requested digits gave overlapping enclosures.
All 362 inversion and conjugation identities were checked numerically, as
were 132 omitted inversion representatives at the symmetry-forced zeros.
The 26 square-lattice rows were compared with separately computed Bloch-Wigner
series after rotation, to relative differences below 1.20e-170. Enumeration
was independently reconstructed by computing additive orders in each finite
torsion group instead of reusing the generator's gcd condition.
At tau=i and u=i/4, an independent Jensen integral computes a reciprocal
Laurent Mahler measure. Guillera-Rogers Theorem 4 and square-lattice rotation
give J=pi*m/4. The integral agrees with an independently bounded constant-term
expansion with 9880 terms and with the J value. Its polynomial integration
control returns 1/3. A square lattice sum through max(|m|,|n|)<=80, with
absolute omitted tail at most 8/(80*pi) for each regulator component, confirms
the negative sign in D-iJ=-Im(tau)^2*K/pi. It is a sign check, not a
100-digit lattice computation.
A discrepancy in the initial quadrature was traced to Sage 10.9's acosh
analytic flag: its wrapper tests the real part against -1 instead of +1.
The final integrand explicitly rejects every analytic query whose entire
image is not in Re(z)>1. This is a conservative sufficient domain where the
principal acosh is holomorphic. Both the guarded integral and a separately
composed log/sqrt integral agree with the Mahler power series. The generator
itself does not use acosh or integration. Full diagnostic artifacts are kept
with the run, and a lesson proposal records the source-level cause.
Software: SageMath 10.9, Python 3.12.3, numberdb 0.1.10, mpmath 1.4.1.
The final JSON evidence records the live read-back results after filling.
The independent campaign critique and its argument-selection sidecar remain
separate work for the controller; this document is build evidence only.