← Session 37 — Paper A revisions: certificate retraction + margin fix
thinking (564 chars)
Done. Final summary for the user:
1. E-023b complete: the certified bound 1.3331 < 1.3352, method description, all checks pass, registered in db.
2. Paper updated: MZeroProp paragraph + table cell + Remark (iii) editorial.
3. The trust architecture is now exactly the user's diagram: 3 derived explicit bounds + 4 rigorous certificates.
4. Committed as eca7fab. 13 pp clean.
One technical note worth surfacing: no ζ′ in python-flint → used the FE route; box digamma nan/segfault on wide boxes → pole shift; direct box cover avoids the sampled Lipschitz entirely.
**E-023b is complete — the entire perimeter is now rigorous.** Committed as `eca7fab` (13 pp, zero overfull/undefined).
**The certificate** (`E-023b-mzero-boxcover.py`, ALL CHECKS PASS, registered in research.db):
- No derivative access in python-flint's `acb.zeta`, so $\zeta'/\zeta$ is evaluated by the functional-equation form $\log\pi - \tfrac12\psi(\frac{1-s}{2}) - \tfrac12\psi(\frac{s}{2}) + \sum \Lambda(n)n^{s-1}$ (series converges at $1-s = 7/2-it$; truncated at $N=400$ with a certified integral tail, 8e-7).
- Adaptive Arb box cover of the segment: 17 570 box evaluations → 16 813 recorded boxes; each box's output ball rigorously encloses the range (ball arithmetic preserves the χ/series cancellation — no triangle inflation).
- Wide-box digamma returned nan/segfaulted; solved by the pole shift $\psi(w) = \psi(w{+}3) - 1/w - 1/(w{+}1) - 1/(w{+}2)$ (exact ball reciprocals, zero-free denominators).
- **Certified: $|\zeta'/\zeta(-\tfrac52+it)| \le 1.3331 < 1.3352$ for all $|t| \le 10$** (headroom 0.0022), cross-checked against mpmath (V1, sanity only) and consistent with E-023's sampled 1.33237 (V4). Coverage of [0,10] verified exactly; symmetry covers $t<0$.
- The sampled-Lipschitz ingredient is eliminated from the trust boundary — no wording softening was needed anywhere.
**Paper updates:** the MZeroProp paragraph now describes the certified method and result ("supersedes E-023, whose sampled maximum 1.33237 it confirms"); the table cell reads "this project (E-023b), interval arithmetic"; Remark (iii) now says "Johansson's rigorous Keiper-coefficient table, transferred to the present Li normalization via $\lambda_n = n\kappa_n$".
The trust architecture is now exactly your diagram: 3 derived explicit bounds (Rosser Thm 19) + 4 interval-arithmetic certificates (Platt–Trudgian, Johansson, Platt/Gram low-zero, E-023b) ⟹ `lambda_pos_finite_height_closed`, everything else machine-checked. Paper A is a release candidate for independent expert review.
raw content_json (database row)
[{"type":"thinking","thinking":"Done. Final summary for the user:\n\n1. E-023b complete: the certified bound 1.3331 < 1.3352, method description, all checks pass, registered in db.\n2. Paper updated: MZeroProp paragraph + table cell + Remark (iii) editorial.\n3. The trust architecture is now exactly the user's diagram: 3 derived explicit bounds + 4 rigorous certificates.\n4. Committed as eca7fab. 13 pp clean.\n\nOne technical note worth surfacing: no ζ′ in python-flint → used the FE route; box digamma nan/segfault on wide boxes → pole shift; direct box cover avoids the sampled Lipschitz entirely.","signature":""},{"type":"text","text":"**E-023b is complete — the entire perimeter is now rigorous.** Committed as `eca7fab` (13 pp, zero overfull/undefined).\n\n**The certificate** (`E-023b-mzero-boxcover.py`, ALL CHECKS PASS, registered in research.db):\n- No derivative access in python-flint's `acb.zeta`, so $\\zeta'/\\zeta$ is evaluated by the functional-equation form $\\log\\pi - \\tfrac12\\psi(\\frac{1-s}{2}) - \\tfrac12\\psi(\\frac{s}{2}) + \\sum \\Lambda(n)n^{s-1}$ (series converges at $1-s = 7/2-it$; truncated at $N=400$ with a certified integral tail, 8e-7).\n- Adaptive Arb box cover of the segment: 17 570 box evaluations → 16 813 recorded boxes; each box's output ball rigorously encloses the range (ball arithmetic preserves the χ/series cancellation — no triangle inflation).\n- Wide-box digamma returned nan/segfaulted; solved by the pole shift $\\psi(w) = \\psi(w{+}3) - 1/w - 1/(w{+}1) - 1/(w{+}2)$ (exact ball reciprocals, zero-free denominators).\n- **Certified: $|\\zeta'/\\zeta(-\\tfrac52+it)| \\le 1.3331 < 1.3352$ for all $|t| \\le 10$** (headroom 0.0022), cross-checked against mpmath (V1, sanity only) and consistent with E-023's sampled 1.33237 (V4). Coverage of [0,10] verified exactly; symmetry covers $t<0$.\n- The sampled-Lipschitz ingredient is eliminated from the trust boundary — no wording softening was needed anywhere.\n\n**Paper updates:** the MZeroProp paragraph now describes the certified method and result (\"supersedes E-023, whose sampled maximum 1.33237 it confirms\"); the table cell reads \"this project (E-023b), interval arithmetic\"; Remark (iii) now says \"Johansson's rigorous Keiper-coefficient table, transferred to the present Li normalization via $\\lambda_n = n\\kappa_n$\".\n\nThe trust architecture is now exactly your diagram: 3 derived explicit bounds (Rosser Thm 19) + 4 interval-arithmetic certificates (Platt–Trudgian, Johansson, Platt/Gram low-zero, E-023b) ⟹ `lambda_pos_finite_height_closed`, everything else machine-checked. Paper A is a release candidate for independent expert review."}]