← Session 25 — ii′-5 R-bound: design + level-2 EM disc bound
thinking (393 chars)
Also update the gotchas line in STATE.md's handoff to point at journal-024, and update NGUYEN.md's Phase 5B checklist (the ii′-5c entry). Let me also add a short line to the Lean gotchas section in STATE.md — actually the NEXT ACTION already references journal-024 gotchas. Let me add the session-024 entry to the NGUYEN.md §8.6 session log and update the ii′-5c checklist line in §5 Phase 5B.
Now the NGUYEN.md checklist updates.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\NGUYEN.md",
"old_string": " plan: loose disc bound as the GROWTH INPUT for the\n partial-fraction identity (5e), tight constants from D-056's\n analysis of the identity (5f). **ii\u2032-5c HALF (session 023)**:\n LiDisc.lean \u2014 zeroDiscFinset + zeroDisc_isNontrivial; scaledZeta\n (unit-disc scaling) + F(0) = 1 via Zeta23 zeta_lower_bound_two\n (\u2016\u03b6(2+it)\u2016 \u2265 1/3, no \u03bc-series build); the multiplicity-invariance\n chain (analyticOrderNatAt_riemannZeta_affine/const_mul/\n scaledZeta); scaledZeta_jensen_count (ZerosBound, \u2264\n log((9/4)|t|\u00b2)/log(33/32)). Next: 5c back half (R-gap, g, BC).",
"new_string": " plan: loose disc bound as the GROWTH INPUT for the\n partial-fraction identity (5e), tight constants from D-056's\n analysis of the identity (5f). **ii\u2032-5c COMPLETE (sessions\n 023\u2013024)**: LiDisc.lean \u2014 zeroDiscFinset + zeroDisc_isNontrivial;\n scaledZeta + F(0) = 1 (zeta_lower_bound_two); the\n multiplicity-invariance chain; scaledZeta_jensen_count\n (ZerosBound, \u2264 log((9/4)|t|\u00b2)/log(33/32)); R-gap via the\n \u00d710-rescaled midpoint pigeonhole (R_c \u2208 [2.3, 2.4], clearance\n gapD = 1/(50(k+1))); g = Cf r_c F analytic + nonvanishing\n (Zeta23 Cf/ZeroFactorization); |g| \u2264 (9/4)|t|\u00b2\u00b7gapD^{\u2212M_c} on the\n ball; LogOfAnalyticFunction + BorelCaratheodoryDeriv (450\u00b7M);\n logDeriv chain + affine push-forward + near/extras split.\n **Capstone: logDeriv_riemannZeta_sub_nearZeros_le** \u2014 the LOOSE\n R-bound \u2016\u03b6\u2032/\u03b6(s) \u2212 \u03a3_{|\u03b3\u2212t|<1} m/(s\u2212\u03c1)\u2016 \u2264 100000\u00b7(log|t|)\u00b2 on\n \u03c3 \u2208 [1/2, 7/2], |t| \u2265 10, \u03b6 s \u2260 0 (no perimeter hypothesis \u2014\n Jensen count input). Build GREEN (8753 jobs); 32 decls audited:\n 3 standard axioms only. Next: 5d (FE-reflection + left digamma)."
}
raw content_json (database row)
[{"type":"thinking","thinking":"Also update the gotchas line in STATE.md's handoff to point at journal-024, and update NGUYEN.md's Phase 5B checklist (the ii′-5c entry). Let me also add a short line to the Lean gotchas section in STATE.md — actually the NEXT ACTION already references journal-024 gotchas. Let me add the session-024 entry to the NGUYEN.md §8.6 session log and update the ii′-5c checklist line in §5 Phase 5B.","signature":""},{"type":"text","text":"Now the NGUYEN.md checklist updates."},{"type":"tool_use","id":"Edit_125","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\NGUYEN.md","old_string":" plan: loose disc bound as the GROWTH INPUT for the\n partial-fraction identity (5e), tight constants from D-056's\n analysis of the identity (5f). **ii′-5c HALF (session 023)**:\n LiDisc.lean — zeroDiscFinset + zeroDisc_isNontrivial; scaledZeta\n (unit-disc scaling) + F(0) = 1 via Zeta23 zeta_lower_bound_two\n (‖ζ(2+it)‖ ≥ 1/3, no μ-series build); the multiplicity-invariance\n chain (analyticOrderNatAt_riemannZeta_affine/const_mul/\n scaledZeta); scaledZeta_jensen_count (ZerosBound, ≤\n log((9/4)|t|²)/log(33/32)). Next: 5c back half (R-gap, g, BC).","new_string":" plan: loose disc bound as the GROWTH INPUT for the\n partial-fraction identity (5e), tight constants from D-056's\n analysis of the identity (5f). **ii′-5c COMPLETE (sessions\n 023–024)**: LiDisc.lean — zeroDiscFinset + zeroDisc_isNontrivial;\n scaledZeta + F(0) = 1 (zeta_lower_bound_two); the\n multiplicity-invariance chain; scaledZeta_jensen_count\n (ZerosBound, ≤ log((9/4)|t|²)/log(33/32)); R-gap via the\n ×10-rescaled midpoint pigeonhole (R_c ∈ [2.3, 2.4], clearance\n gapD = 1/(50(k+1))); g = Cf r_c F analytic + nonvanishing\n (Zeta23 Cf/ZeroFactorization); |g| ≤ (9/4)|t|²·gapD^{−M_c} on the\n ball; LogOfAnalyticFunction + BorelCaratheodoryDeriv (450·M);\n logDeriv chain + affine push-forward + near/extras split.\n **Capstone: logDeriv_riemannZeta_sub_nearZeros_le** — the LOOSE\n R-bound ‖ζ′/ζ(s) − Σ_{|γ−t|<1} m/(s−ρ)‖ ≤ 100000·(log|t|)² on\n σ ∈ [1/2, 7/2], |t| ≥ 10, ζ s ≠ 0 (no perimeter hypothesis —\n Jensen count input). Build GREEN (8753 jobs); 32 decls audited:\n 3 standard axioms only. Next: 5d (FE-reflection + left digamma)."},"extra_content":null}]