← Session 37 — Paper A revisions: certificate retraction + margin fix
thinking (375 chars)
All done. Summarize concisely for the user: what was done per item, verification status, commit, and the two follow-up flags. Also note the λ_n = nΛ_n verification I did (independent derivation) since it's the "biggest new issue" — the user will want to know the factor direction was checked, not just transcribed. And mention the one extra fix I caught ("those five" → six).
All 8 items actioned, committed as `4001c5d`. Paper A: **12 pp, zero overfull boxes, zero undefined refs**.
**What changed, item by item:**
1. **Johansson normalization** — Step 5 now displays his Keiper series $\log\xi(\frac1{1-x}) = -\log 2 + \sum\Lambda_n x^n$ and states $\lambda_n = n\Lambda_n$. I independently re-derived the factor before writing it (equate coefficients in $x\frac{d}{dx}\log\xi(\frac1{1-x})$; the Li and Keiper generating functions coincide by the $\rho\leftrightarrow1-\rho$ symmetry — factor direction confirmed, $\lambda_n^{\text{Li}} = n\Lambda_n$). The endpoint is converted: $\lambda_{100000} \approx 462\,580.78$, and the table range is written $\Lambda_1,\dots,\Lambda_{100000}$.
2. **T-notation** — separated exactly as you prescribed, matched against the Lean source: actual contour height $\tau_n\in[\sqrt n,\sqrt n+1]$ (`exists_zero_avoiding_T_wide`, clearance $1/(9C_0(\sqrt n{+}2))$), deterministic majorant $T_n := \sqrt n+1$ (matches `Bn`'s `let T := √n + 1`), dog-leg $U_n := \tfrac32\tau_n$ (matches LiDogLeg's `(3/2)*T`). Also corrected the left-vertical charge text to the actually-charged $\tfrac{\sqrt n+1}{4}(e^{5/2}+1)$.
3. **Trust boundary** — "seven explicit perimeter inputs" everywhere; Appendix B now has the 4-column provenance table (hypothesis / statement / source / status: 3 published Trudgian bounds + 4 computational certificates).
4. **NoLowZeros** — its own paragraph: logically separate from RHUpTo; provenance = the zero-location stage of the Platt–Trudgian computation (Riemann–Siegel isolation + Turing's count, $\gamma_1 = 14.134725\ldots$).
5. **Reconciliation sentence** added immediately after Theorem 2.
6. **Voros sentence** on page 3 replaced with the precise tail formulation.
7. **Oesterlé** now "Voros [12] reports an unpublished result of Oesterlé… (typescript uncirculated; we rely on Voros's citation)"; novelty recentered on the constant-traced strict-positivity assembly + dog-leg + formal verification.
8. **Affiliation** → "Independent researcher" (memory directive updated too).
**One extra fix caught while actioning item 3:** the abstract's "machine-proved from those five" was wrong — `sfBoundProp` takes six hypotheses (all but `LiVerifiedUpTo`); corrected.
**Two follow-ups for your call:**
- `paperB.tex` carries the same "Research Ai" block — change it now, or when Paper B is next touched?
- NGUYEN.md (Ledger #6, §5B ii′-7), R-004, and STATE.md still say "2 computational + 5 analytic". Add a one-line erratum/reclassification note to the archive (4 computational + 3 published), or leave the archive as the historical record?
raw content_json (database row)
[{"type":"thinking","thinking":"All done. Summarize concisely for the user: what was done per item, verification status, commit, and the two follow-up flags. Also note the λ_n = nΛ_n verification I did (independent derivation) since it's the \"biggest new issue\" — the user will want to know the factor direction was checked, not just transcribed. And mention the one extra fix I caught (\"those five\" → six).","signature":""},{"type":"text","text":"All 8 items actioned, committed as `4001c5d`. Paper A: **12 pp, zero overfull boxes, zero undefined refs**.\n\n**What changed, item by item:**\n\n1. **Johansson normalization** — Step 5 now displays his Keiper series $\\log\\xi(\\frac1{1-x}) = -\\log 2 + \\sum\\Lambda_n x^n$ and states $\\lambda_n = n\\Lambda_n$. I independently re-derived the factor before writing it (equate coefficients in $x\\frac{d}{dx}\\log\\xi(\\frac1{1-x})$; the Li and Keiper generating functions coincide by the $\\rho\\leftrightarrow1-\\rho$ symmetry — factor direction confirmed, $\\lambda_n^{\\text{Li}} = n\\Lambda_n$). The endpoint is converted: $\\lambda_{100000} \\approx 462\\,580.78$, and the table range is written $\\Lambda_1,\\dots,\\Lambda_{100000}$.\n2. **T-notation** — separated exactly as you prescribed, matched against the Lean source: actual contour height $\\tau_n\\in[\\sqrt n,\\sqrt n+1]$ (`exists_zero_avoiding_T_wide`, clearance $1/(9C_0(\\sqrt n{+}2))$), deterministic majorant $T_n := \\sqrt n+1$ (matches `Bn`'s `let T := √n + 1`), dog-leg $U_n := \\tfrac32\\tau_n$ (matches LiDogLeg's `(3/2)*T`). Also corrected the left-vertical charge text to the actually-charged $\\tfrac{\\sqrt n+1}{4}(e^{5/2}+1)$.\n3. **Trust boundary** — \"seven explicit perimeter inputs\" everywhere; Appendix B now has the 4-column provenance table (hypothesis / statement / source / status: 3 published Trudgian bounds + 4 computational certificates).\n4. **NoLowZeros** — its own paragraph: logically separate from RHUpTo; provenance = the zero-location stage of the Platt–Trudgian computation (Riemann–Siegel isolation + Turing's count, $\\gamma_1 = 14.134725\\ldots$).\n5. **Reconciliation sentence** added immediately after Theorem 2.\n6. **Voros sentence** on page 3 replaced with the precise tail formulation.\n7. **Oesterlé** now \"Voros [12] reports an unpublished result of Oesterlé… (typescript uncirculated; we rely on Voros's citation)\"; novelty recentered on the constant-traced strict-positivity assembly + dog-leg + formal verification.\n8. **Affiliation** → \"Independent researcher\" (memory directive updated too).\n\n**One extra fix caught while actioning item 3:** the abstract's \"machine-proved from those five\" was wrong — `sfBoundProp` takes six hypotheses (all but `LiVerifiedUpTo`); corrected.\n\n**Two follow-ups for your call:**\n- `paperB.tex` carries the same \"Research Ai\" block — change it now, or when Paper B is next touched?\n- NGUYEN.md (Ledger #6, §5B ii′-7), R-004, and STATE.md still say \"2 computational + 5 analytic\". Add a one-line erratum/reclassification note to the archive (4 computational + 3 published), or leave the archive as the historical record?"}]