[{"type":"thinking","thinking":"The MZeroProp paragraph renders exactly as intended — certified by interval arithmetic (E-023b), 16 813 boxes, the FE form with the pole shift, certified ≤ 1.3331 < 1.3352, supersedes E-023. The table cell now says \"this project (E-023b), interval arithmetic\". All seven perimeter inputs are now genuinely rigorous certificates/bounds.\n\nCommit: paperA.tex, paperA.pdf, the E-023b script, CSV, JSON, research.db. Then final summary.","signature":""},{"type":"text","text":"The trust boundary is now fully rigorous. Committing everything."},{"type":"tool_use","id":"Bash_167","name":"Bash","input":{"command":"cd /d/Python/Quantum && git add research/paper/paperA.tex research/paper/paperA.pdf research/numerics/scripts/E-023b-mzero-boxcover.py research/numerics/data/E-023b-mzero-boxcover.csv research/numerics/data/E-023b-mzero-boxcover.json research/research.db && git -c user.name=\"NGUYEN-RH-1\" -c user.email=\"research@local\" commit -m \"$(cat <<'EOF'\nSession 043: E-023b COMPLETE — MZeroProp now interval-rigorous; the whole perimeter is certified\n\nE-023b (new, ALL CHECKS PASS): adaptive Arb box cover (16 813 boxes)\nof the segment Re s = -5/2, |t| <= 10; zeta'/zeta evaluated boxwise in\n128-bit ball arithmetic via the functional-equation form\n  log pi - psi((1-s)/2)/2 - psi(s/2)/2 + sum Lambda(n) n^{s-1}\nwith the psi(s/2) pole shift psi(w) = psi(w+3) - 1/w - 1/(w+1) - 1/(w+2)\nand a certified integral series tail; x10 adaptive subdivision;\nV1 mpmath cross-check, V2 exact coverage, V3 certified bound,\nV4 consistency with E-023's sampled 1.33237. Certified global bound\n|zeta'/zeta(-5/2+it)| <= 1.3331 < 1.3352 — the sampled-Lipschitz\ningredient of E-023 is eliminated from the trust boundary.\n\nPaper A: MZeroProp paragraph + table cell now describe the certified\nE-023b method/result (superseding E-023); Remark (iii) editorial:\nJohansson's table described as Keiper coefficients transferred via\nlambda_n = n kappa_n. Compiles clean: 13 pp, zero overfull/undefined.\n\nAll seven perimeter inputs are now rigorous: 3 derived explicit bounds\n(Rosser Thm 19) + 4 interval-arithmetic certificates (Platt-Trudgian,\nJohansson, Platt/Gram low-zero, E-023b).\nEOF\n)\" && git log --oneline -3","description":"Commit E-023b certification and paper updates"},"extra_content":null}]