back to table · edit · history · where entries came from · files · download
1576 bytes, as of the version from 2026-11-02 13:07 (current). Recorded here, not run.
# Checked mathematical sources
- Balazard and Martin, https://arxiv.org/pdf/1305.4395: §§2.1–2.2, equations (10), (14), (19), Propositions 6–9, and Theorem 1. Checked natural logarithms, beta[-1]=1, first term log(1/x), alternating sign, convergent weights, functional equation, and equivalence of Wilton convergence with the continued-fraction criterion for differentiability of fractional-part autocorrelation. The assertion is differentiability at convergent irrational arguments, not equality of W and the derivative.
- Waldschmidt (2016), https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/NouakchottCoursCIMPA2016.pdf: §3.6, Lemmas 46–47, pp. 36–38. Checked eventual periodicity and the reduced-quadratic criterion for purely periodic continued fractions, applied here to 1/x.
- Corless, https://www.cecm.sfu.ca/organics/papers/corless/confrac/html/node6-an.shtml: Theorem 1 and its corollary state that Gauss-map periodic points are reciprocals of reduced quadratic irrationals. Used as a supplementary source, not an additional table reference.
The web research tool could read these sources. Direct PDF archival from this build machine timed out; no downloaded full PDFs are claimed. Screenshots were attempted to check formula glyphs, but the Waldschmidt screenshot was unavailable. The explicit indexing was also checked in the definitions and functional equation.
Skill evidence: agents/runs/20261102T123618Z-build-skills/manifest.json. Both archived skill versions hash to a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278.