← Session 30 — ii′-5e squeeze capstone + 5f perimeter repair
thinking (157 chars)
Now update NGUYEN.md §5 checklist (the ii′-5e entry) and add the session-034 entry to §8.6 session log. Let me look at the current ii′-5e entry in NGUYEN.md.
Now NGUYEN.md: the ii′-5e checklist entry + the session log.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\NGUYEN.md",
"old_string": " **5e-v-b + 5e-v-c COMPLETE (sessions 030\u2013033)**:\n LiCircleBound.lean (~3928 lines) \u2014 count bridges (A0count from\n Zeta23's RvM local count, mult-weighted, all t, unconditional),\n the Dirichlet bound \u2016\u03b6\u2032/\u03b6\u2016 \u2264 dirichletC2 (re \u2265 2),\n tsum_split_finset, lowZeroConst, the far-tail bound\n zero_tail_inv_sq_le (\u03a3_{|\u03b3|>X} m/(1+\u03b3\u00b2) \u2264 16\u00b7A\u2080\u00b7log X/X,\n X \u2265 200 \u2014 the dyadic fiber machine + ENNReal.tsum_fiberwise),\n **the series circle bound seriesFun_norm_le_gapCircle**\n (\u2016seriesFun s\u2016 \u2264 2\u00b7lowZeroConst + 2900\u00b7A\u2080\u00b7\u0108\u2080(4k+9/2)\u00b7(log R)\u00b2\n on the \u03b3-gap circle, k \u2265 4000), and **the Fexpr circle bound\n Fexpr_circle_le** (\u2016Fexpr s\u2016 \u2264 2\u00b7lowZeroConst + dirichletC2 +\n 400000\u00b7A\u2080\u00b7\u0108\u2080(R+2)\u00b7(log R)\u00b2): three-region logDeriv assembly\n (Dirichlet / 5c+5d capstones + the near sum via gapCircle_sep /\n FE + \u0393R bracket), digamma_circle_le (uniform \u03c8 bound, left\n near-axis via the \u2124-clearance), and\n **logDeriv_Gamma\u211d_eq_of_not_neg_nat** (the (G) formula at any\n non-pole point incl. s = \u2212R \u2014 direct logDeriv_mul, no\n continuity). Remaining: 5e-v-d Schwarz squeeze \u27f9 capstone \u2203 B.",
"new_string": " **5e-v-b + 5e-v-c COMPLETE (sessions 030\u2013033)**:\n LiCircleBound.lean (~3928 lines) \u2014 count bridges (A0count from\n Zeta23's RvM local count, mult-weighted, all t, unconditional),\n the Dirichlet bound \u2016\u03b6\u2032/\u03b6\u2016 \u2264 dirichletC2 (re \u2265 2),\n tsum_split_finset, lowZeroConst, the far-tail bound\n zero_tail_inv_sq_le (\u03a3_{|\u03b3|>X} m/(1+\u03b3\u00b2) \u2264 16\u00b7A\u2080\u00b7log X/X,\n X \u2265 200 \u2014 the dyadic fiber machine + ENNReal.tsum_fiberwise),\n **the series circle bound seriesFun_norm_le_gapCircle**\n (\u2016seriesFun s\u2016 \u2264 2\u00b7lowZeroConst + 2900\u00b7A\u2080\u00b7\u0108\u2080(4k+9/2)\u00b7(log R)\u00b2\n on the \u03b3-gap circle, k \u2265 4000), and **the Fexpr circle bound\n Fexpr_circle_le** (\u2016Fexpr s\u2016 \u2264 2\u00b7lowZeroConst + dirichletC2 +\n 400000\u00b7A\u2080\u00b7\u0108\u2080(R+2)\u00b7(log R)\u00b2): three-region logDeriv assembly\n (Dirichlet / 5c+5d capstones + the near sum via gapCircle_sep /\n FE + \u0393R bracket), digamma_circle_le (uniform \u03c8 bound, left\n near-axis via the \u2124-clearance), and\n **logDeriv_Gamma\u211d_eq_of_not_neg_nat** (the (G) formula at any\n non-pole point incl. s = \u2212R \u2014 direct logDeriv_mul, no\n continuity). **5e-v-d COMPLETE (session 034) \u2014 ii\u2032-5e DONE**:\n LiSqueeze.lean (~330 lines, 5 decls audited clean; LiCircleBound\n + LiSqueeze root-imported) \u2014 the Schwarz squeeze\n (`gentire_const`: max-modulus + ball-form Schwarz on the \u03b3-gap\n circles, growth (log R)\u00b3/R \u2192 0 via Q := R^{1/4} \u27f9 Gentire \u2261\n Gentire 0 =: B) and **THE CAPSTONE `partialFraction_identity`\n (hZC : ZeroCountProp)**: \u2203 B : \u2102, \u03b6\u2032/\u03b6(s) = B + seriesFun s \u2212\n 1/s \u2212 1/(s\u22121) + \u00bdlog \u03c0 \u2212 \u00bd\u03c8(s/2) off the excluded set \u2014 the\n partial-fraction identity Lean-proved modulo ONLY the declared\n perimeter. Remaining: 5f (tight constants 10.5/48 from D-056's\n two-point analysis of the identity)."
}
raw content_json (database row)
[{"type":"thinking","thinking":"Now update NGUYEN.md §5 checklist (the ii′-5e entry) and add the session-034 entry to §8.6 session log. Let me look at the current ii′-5e entry in NGUYEN.md.","signature":""},{"type":"text","text":"Now NGUYEN.md: the ii′-5e checklist entry + the session log."},{"type":"tool_use","id":"Edit_54","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\NGUYEN.md","old_string":" **5e-v-b + 5e-v-c COMPLETE (sessions 030–033)**:\n LiCircleBound.lean (~3928 lines) — count bridges (A0count from\n Zeta23's RvM local count, mult-weighted, all t, unconditional),\n the Dirichlet bound ‖ζ′/ζ‖ ≤ dirichletC2 (re ≥ 2),\n tsum_split_finset, lowZeroConst, the far-tail bound\n zero_tail_inv_sq_le (Σ_{|γ|>X} m/(1+γ²) ≤ 16·A₀·log X/X,\n X ≥ 200 — the dyadic fiber machine + ENNReal.tsum_fiberwise),\n **the series circle bound seriesFun_norm_le_gapCircle**\n (‖seriesFun s‖ ≤ 2·lowZeroConst + 2900·A₀·Ĉ₀(4k+9/2)·(log R)²\n on the γ-gap circle, k ≥ 4000), and **the Fexpr circle bound\n Fexpr_circle_le** (‖Fexpr s‖ ≤ 2·lowZeroConst + dirichletC2 +\n 400000·A₀·Ĉ₀(R+2)·(log R)²): three-region logDeriv assembly\n (Dirichlet / 5c+5d capstones + the near sum via gapCircle_sep /\n FE + ΓR bracket), digamma_circle_le (uniform ψ bound, left\n near-axis via the ℤ-clearance), and\n **logDeriv_Gammaℝ_eq_of_not_neg_nat** (the (G) formula at any\n non-pole point incl. s = −R — direct logDeriv_mul, no\n continuity). Remaining: 5e-v-d Schwarz squeeze ⟹ capstone ∃ B.","new_string":" **5e-v-b + 5e-v-c COMPLETE (sessions 030–033)**:\n LiCircleBound.lean (~3928 lines) — count bridges (A0count from\n Zeta23's RvM local count, mult-weighted, all t, unconditional),\n the Dirichlet bound ‖ζ′/ζ‖ ≤ dirichletC2 (re ≥ 2),\n tsum_split_finset, lowZeroConst, the far-tail bound\n zero_tail_inv_sq_le (Σ_{|γ|>X} m/(1+γ²) ≤ 16·A₀·log X/X,\n X ≥ 200 — the dyadic fiber machine + ENNReal.tsum_fiberwise),\n **the series circle bound seriesFun_norm_le_gapCircle**\n (‖seriesFun s‖ ≤ 2·lowZeroConst + 2900·A₀·Ĉ₀(4k+9/2)·(log R)²\n on the γ-gap circle, k ≥ 4000), and **the Fexpr circle bound\n Fexpr_circle_le** (‖Fexpr s‖ ≤ 2·lowZeroConst + dirichletC2 +\n 400000·A₀·Ĉ₀(R+2)·(log R)²): three-region logDeriv assembly\n (Dirichlet / 5c+5d capstones + the near sum via gapCircle_sep /\n FE + ΓR bracket), digamma_circle_le (uniform ψ bound, left\n near-axis via the ℤ-clearance), and\n **logDeriv_Gammaℝ_eq_of_not_neg_nat** (the (G) formula at any\n non-pole point incl. s = −R — direct logDeriv_mul, no\n continuity). **5e-v-d COMPLETE (session 034) — ii′-5e DONE**:\n LiSqueeze.lean (~330 lines, 5 decls audited clean; LiCircleBound\n + LiSqueeze root-imported) — the Schwarz squeeze\n (`gentire_const`: max-modulus + ball-form Schwarz on the γ-gap\n circles, growth (log R)³/R → 0 via Q := R^{1/4} ⟹ Gentire ≡\n Gentire 0 =: B) and **THE CAPSTONE `partialFraction_identity`\n (hZC : ZeroCountProp)**: ∃ B : ℂ, ζ′/ζ(s) = B + seriesFun s −\n 1/s − 1/(s−1) + ½log π − ½ψ(s/2) off the excluded set — the\n partial-fraction identity Lean-proved modulo ONLY the declared\n perimeter. Remaining: 5f (tight constants 10.5/48 from D-056's\n two-point analysis of the identity)."},"extra_content":null}]