# Sources checked for T679

The controlling skill archive is `agents/runs/20261102T134642Z-build-skills/manifest.json`;
local and live SHA-256 are both `a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`.

Read on 2026-11-02:

- Long, Tu, Yui, Zudilin, https://arxiv.org/html/1705.01663v4 , Introduction,
  Table 1, Section 5. The classical normalized series and fourteen parameter
  multisets agree with issue 301 and T674/T675. The lower classical vector has
  three ones; the fourth factorial belongs to the series definition.
- Bönisch, Klemm, Scheidegger, Zagier,
  https://arxiv.org/html/2203.09426v1 , Section 2.1, equations (2.1), (2.2),
  Table 1. Independently confirms all fourteen systems and conifold exponents
  0,1,1,2. Their x is mu times this table's z. The full title was checked at
  https://arxiv.org/abs/2203.09426 .
- Roberts, Rodriguez Villegas, https://arxiv.org/html/2109.00027v1 , Section 10,
  “Wild, tame, and good primes”. Potential tame primes depend on the reduced
  numerator/denominator of z and numerator of z-1. This supports the controlled
  ramification rationale, not a claim of modularity for every smooth fiber.
- DLMF https://dlmf.nist.gov/16.2 . Generalized hypergeometric series and excess
  criterion at 1. Here the excess is 1. The upper-bank choice is explicit in
  the family and table; it is not inferred from a software default.
- Rogers, Wan, Zucker, https://arxiv.org/html/1303.2259v2 , Section 5,
  equation (30). Dividing the equality (pi/2)L(f2,2)=(pi^3/32)4F3 gives
  F_all-half(1)=16 L(eta(2tau)^4 eta(4tau)^4,2)/pi^2. The adjacent L(f2,3)
  formula concerns a 7F6 and must not be substituted for this one.
- DLMF https://dlmf.nist.gov/5.11 . Gamma-ratio asymptotics motivate the
  independent conifold calculation. No unproved tail bound is represented
  as a certified error bound.
- PARI documentation https://pari.math.u-bordeaux.fr/dochtml/html/Transcendental_functions.html ,
  hypergeom. Generic 4F3 continuation at the boundary is outside the documented
  simple summation domain, so PARI hypergeom was not used as a general control.
  PARI modular-form L-functions supply the unrelated all-half control instead.

Live corpus reads are T25.json, T178.json, T323.json, T348.json, T665.json,
T674.json and T675.json. The actual long URLs were read from the pages and
recorded in link-evidence.json. The local arithmetic companions are populated
drafts at this time, so publication ordering needs the controller's attention.
No existing table was edited. The second proposal in issue 301 is unbuilt;
no identifier was invented for it.