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3051 bytes, as of the version from 2026-11-10 20:59 (current). Recorded here, not run.
# T708 build research
Checked in this run (build evidence, not an independent verdict):
- Báez-Duarte math/0011254v1 §1.1 (1.4) defines g(x)=sum_{k<=x}mu(k)/k;
§1.2 (1.17) defines V_n=sum mu(k)rho(1/(kx))-g(n)rho(1/x).
(1.18) calls the untapered sum S_n; (1.19) reserves F_n for the dual.
- math/0202141v2 §1 (1.1) instead calls the untapered sum F_n and targets
-chi in L²(0,infinity). No source conflict after translating notation.
- BBLS math/0306251v1 §4 gives the signed fractional-part cotangent sum;
§9 Propositions 87/89 give A(1)=log(2pi)-gamma and the rational formula.
Source HTML and its hashes are in source-archives.json. Relevant equations
were inspected directly; sources are not being treated as numerical data.
- All parameters and normalizations are specified in derivation.md.
argument-selection.md justifies every N=1,...,30 as a discrete prefix.
- Live catalogue fetched once, filtered locally; candidate metadata T639,
T640, T641, T642, T706, T707 read. No matching Vasyunin-error family found.
screen.already_here and already_asked rerun. Lookup of 1 has generic matches;
0.48013961458004106 has none. These matches do not define duplication.
A further computed sample lookup is recorded with discovery evidence.
- Both tag pages checked: number theory and functional analysis exist;
Nyman-Beurling criterion absent. Recommend it for this family and T639–T642;
no tag changes to existing tables are authorized or performed.
- T640 supplies the kernel context, T641 the variational lower bound, and
T706 the untapered baseline. T707 uses the distinct moving-endpoint correction.
No sibling's stored decimal is an input or independent evidence.
- Reused gram_system and integral_kernel.py from the shared T707 artifact
directory after checking its manifest hashes. Both primary formula and
integral remainder were rechecked here. All kernels and errors were freshly
computed. mu is checked by a separate trial-division implementation.
- All 30 norms, 465 symmetric Gram entries, small whole residuals N=1,2,3,4,6,
correction identities, nonsquarefree repetitions, and least-squares bounds
passed executable build checks. Known-answer and wrong/wide/NaN controls
are retained. No numerical agreement is asserted to prove an asymptotic claim.
- Exact binary endpoints use exact_rational(), not QQ(real). The numerical
evidence and readback preserve full intervals, not just decimal midpoints.
- Skill archive: ../20261110T205245Z-build-skills/manifest.json, attached as
skill-manifest.json. Both bundle hashes match
d6661c2f21613524889fa3a57d3c95f8330344ca62e5a856211c08a282b7dbab.
Unresolved: the independent critic's scientific and argument-selection verdicts.
No outstanding convention alternatives were found. T708 remains a private draft;
only the controller may offer it after independent validation. Proposal #313
contributes to wanted #273; it does not complete that request. Provenance belongs
in the revision message and issue reply, not the mathematical prose.