← Session 29 — ii′-5e-v: circle bound (far-tail + series bounds)
Now NGUYEN.md (checklist + session log) and db.
tool: Edit
input
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"replace_all": false,
"file_path": "D:\\Python\\Quantum\\NGUYEN.md",
"old_string": " 8766 jobs. **5e-v-b COMPLETE (sessions 030\u2013032)**:\n LiCircleBound.lean (~2867 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 and **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): the threshold lemma\n gapCircle_threshold (416\u00b7\u0108\u2080 \u2264 4k+5/2) + the zero-free circle,\n the count brick sum_zeroMult_le_of_im_band, the generic\n dyadic_family_le (Finset.sum_fiberwise_of_maps_to), five shell\n bounds (low/inlo/inhi/crit/up incl. the \u03b3-gap arc analysis:\n strip arcs |t\u2212\u03b3| \u2265 1/(32\u0108\u2080), near-axis \u221a13\u22121) + the far tail\n (91\u00b7A\u2080\u00b7log R). Remaining: 5e-v-c logDeriv/elem assembly \u27f9\n \u2016Fexpr\u2016 \u2264 C(log R)\u00b3 \u2192 5e-v-d Schwarz squeeze \u27f9 capstone \u2203 B.",
"new_string": " 8766 jobs. **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."
}
raw content_json (database row)
[{"type":"text","text":"Now NGUYEN.md (checklist + session log) and db."},{"type":"tool_use","id":"Edit_249","name":"Edit","input":{"replace_all":false,"file_path":"D:\\Python\\Quantum\\NGUYEN.md","old_string":" 8766 jobs. **5e-v-b COMPLETE (sessions 030–032)**:\n LiCircleBound.lean (~2867 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 and **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): the threshold lemma\n gapCircle_threshold (416·Ĉ₀ ≤ 4k+5/2) + the zero-free circle,\n the count brick sum_zeroMult_le_of_im_band, the generic\n dyadic_family_le (Finset.sum_fiberwise_of_maps_to), five shell\n bounds (low/inlo/inhi/crit/up incl. the γ-gap arc analysis:\n strip arcs |t−γ| ≥ 1/(32Ĉ₀), near-axis √13−1) + the far tail\n (91·A₀·log R). Remaining: 5e-v-c logDeriv/elem assembly ⟹\n ‖Fexpr‖ ≤ C(log R)³ → 5e-v-d Schwarz squeeze ⟹ capstone ∃ B.","new_string":" 8766 jobs. **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."},"extra_content":null}]