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2591 bytes, as of the version from 2026-11-10 23:40 (current). Recorded here, not run.
# Research for T711
Checked source: Báez-Duarte, arXiv:math/0011254v1, §4.1 pp.16–17,
definition immediately before Proposition 4.3; §§1.1–1.2 fix fractional
parts, lambda, Mertens and distinguish the dual approximation. The original
R_N has upper endpoint N-1 and coefficients M(N/k)/k. The stated L2
divergence is not used as a computational claim or as convergence to zero.
BBLS arXiv:math/0306251v1, §4 Vasyunin definition and Proposition 89 were
inspected for kernel signs, coprime reduction and V(p,1)=0.
DLMF 25.11.1/.3/.17 were inspected for the Hurwitz sum and its shifts.
Derived here: zero slope from Mobius inversion, cancelled Mellin cross term,
and direct periodic endpoint integration; full derivation.md records these.
They are deductions, with independent executable checks, not identities
borrowed from sibling tables. No unresolved normalization alternatives.
Live checks: catalogue (including drafts) fetched once; text screen
already_here and already_asked run; plausible T640/T641/T642/T706–T709
metadata refreshed. Three 30-digit sample lookups returned no matches.
T709 differs in weights and target. Related T639/T640/T16/T94/T226 were
read, never used as precision-bearing inputs. Existing tags number theory,
functional analysis, integral verified. Nyman-Beurling absent; recommend it
for T640/T641/T642/T706–T709, without changing those tables.
Issue #315 is this exact proposal; only #273 is a direct originating wanted
issue, explicitly contributes to, not answers. Checked both live issues.
Source-access note: both attempted EMIS PDF URLs redirected to a zbMATH
HTML catalogue, despite search-engine cached PDF text. The canonical arXiv
preprint was successfully downloaded and inspected instead. No claim of
checking the unavailable published PDF. Sources and log paths follow.
- `baez-duarte-2000.pdf` SHA-256 `951ecc56eaae5b80eb8128ab4f98b5184d06ed97da608a130d65940daea8e94c`
- `bbls-2003.pdf` SHA-256 `4c786619a6d2a81b1de6808f489a8a4f8c85de42d4a50d5c20f58f4a518fd9f9`
- `catalogue.json` SHA-256 `52f7350e41a17239e61725ec6933c7d4c3c294184781bfd23d2bb82bc8e95294`
- `screen.json` SHA-256 `b922da7ef3848451911eb11d28084bfcc4cadd7589840e554e1a365eb9b25865`
- `lookup.json` SHA-256 `0b38d982c890752b44e8eaa149273cf8efa49a6f9d43b2ac1361ac6c956a3d05`
- `skill-manifest.json` SHA-256 `c5ee30e128246f511fb7c0e8e37f8b7d2419d5fad25227688a6111fdf9686049`
- `argument-selection.md` SHA-256 `1b9201dd20b2324dae6e5810e4e1ba21bb942d532e022e252532c168d6b6d484`
- `derivation.md` SHA-256 `69b4e4db82d3a9cf73ece07115cd74657e36110fcd5513c01b178653203f3596`