← Session 28 — ii′-5e: partial-fraction identity (zero series + F entire)
thinking (913 chars)
Build GREEN (8766 jobs). Now the axiom audit. Declarations in LiFEntire:
- Fexpr, badPoint
- analyticAt_digamma, analyticAt_digamma_div_two
- zeta_zero_classification
- logDeriv_zeta_sub_mult_div_eventually
- logDeriv_zeta_eq_logDeriv_zetaA_sub, Fexpr_eventually_one
- digammaSeriesPart, add_nat_add_one_ne_zero_of_mem_ball, digammaSeriesPart_analyticOn, digamma_eq_seriesPart_near_zero, Fexpr_eventually_zero
- riemannZeta_neg_two_mul, integerComplement_of_mem_ball_neg_natCast, add_nat_add_one_ne_zero_of_mem_ball_neg, digammaSeriesPartSub, digammaSeriesPartSub_analyticOn, digammaSeriesPart_eq_sub_add_single, Hsub, digamma_eq_neg_inv_add_Hsub, Hsub_analyticAt, Fexpr_eventually_neg_two_mul
- Fexpr_eventually_nontrivial
- Fexpr_analyticAt_of_not_bad, exists_ball_good_of_not_bad
- Gentire, gentire_eq_Fexpr, gentire_eventually_eq_witness, gentire_analyticAt_and_eq
Write the audit to Scratch.lean, run, save.
Build GREEN (8766 jobs). Axiom audit now.
tool: Write ok
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\Scratch.lean",
"content": "/- Session 029 axiom audit: LiFEntire.lean (ii\u2032-5e-iv COMPLETE). -/\nimport Mathlib\nimport NguyenRH1.LiFEntire\n\nopen NguyenRH1\n\n#print axioms Fexpr\n#print axioms badPoint\n#print axioms analyticAt_digamma\n#print axioms analyticAt_digamma_div_two\n#print axioms zeta_zero_classification\n#print axioms logDeriv_zeta_sub_mult_div_eventually\n#print axioms logDeriv_zeta_eq_logDeriv_zetaA_sub\n#print axioms Fexpr_eventually_one\n#print axioms digammaSeriesPart\n#print axioms add_nat_add_one_ne_zero_of_mem_ball\n#print axioms digammaSeriesPart_analyticOn\n#print axioms digamma_eq_seriesPart_near_zero\n#print axioms Fexpr_eventually_zero\n#print axioms riemannZeta_neg_two_mul\n#print axioms integerComplement_of_mem_ball_neg_natCast\n#print axioms add_nat_add_one_ne_zero_of_mem_ball_neg\n#print axioms digammaSeriesPartSub\n#print axioms digammaSeriesPartSub_analyticOn\n#print axioms digammaSeriesPart_eq_sub_add_single\n#print axioms Hsub\n#print axioms digamma_eq_neg_inv_add_Hsub\n#print axioms Hsub_analyticAt\n#print axioms Fexpr_eventually_neg_two_mul\n#print axioms Fexpr_eventually_nontrivial\n#print axioms Fexpr_analyticAt_of_not_bad\n#print axioms exists_ball_good_of_not_bad\n#print axioms Gentire\n#print axioms gentire_eq_Fexpr\n#print axioms gentire_eventually_eq_witness\n#print axioms gentire_analyticAt_and_eq\n"
}
result 2026-08-23 16:43:25Z → 2026-08-23 16:43:25Z
{
"type": "update",
"filePath": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\Scratch.lean",
"content": "/- Session 029 axiom audit: LiFEntire.lean (ii\u2032-5e-iv COMPLETE). -/\nimport Mathlib\nimport NguyenRH1.LiFEntire\n\nopen NguyenRH1\n\n#print axioms Fexpr\n#print axioms badPoint\n#print axioms analyticAt_digamma\n#print axioms analyticAt_digamma_div_two\n#print axioms zeta_zero_classification\n#print axioms logDeriv_zeta_sub_mult_div_eventually\n#print axioms logDeriv_zeta_eq_logDeriv_zetaA_sub\n#print axioms Fexpr_eventually_one\n#print axioms digammaSeriesPart\n#print axioms add_nat_add_one_ne_zero_of_mem_ball\n#print axioms digammaSeriesPart_analyticOn\n#print axioms digamma_eq_seriesPart_near_zero\n#print axioms Fexpr_eventually_zero\n#print axioms riemannZeta_neg_two_mul\n#print axioms integerComplement_of_mem_ball_neg_natCast\n#print axioms add_nat_add_one_ne_zero_of_mem_ball_neg\n#print axioms digammaSeriesPartSub\n#print axioms digammaSeriesPartSub_analyticOn\n#print axioms digammaSeriesPart_eq_sub_add_single\n#print axioms Hsub\n#print axioms digamma_eq_neg_inv_add_Hsub\n#print axioms Hsub_analyticAt\n#print axioms Fexpr_eventually_neg_two_mul\n#print axioms Fexpr_eventually_nontrivial\n#print axioms Fexpr_analyticAt_of_not_bad\n#print axioms exists_ball_good_of_not_bad\n#print axioms Gentire\n#print axioms gentire_eq_Fexpr\n#print axioms gentire_eventually_eq_witness\n#print axioms gentire_analyticAt_and_eq\n",
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"lines": [
"-/- Session 028 axiom audit: LiSeries.lean (ii\u2032-5e-iii COMPLETE). -/",
"+/- Session 029 axiom audit: LiFEntire.lean (ii\u2032-5e-iv COMPLETE). -/",
" import Mathlib",
"-import NguyenRH1.LiSeries",
"+import NguyenRH1.LiFEntire",
" ",
" open NguyenRH1",
" ",
"-#print axioms seriesTerm",
"-#print axioms seriesFun",
"-#print axioms one_add_normSq_gammaOf_le",
"-#print axioms one_div_sub_add_one_div",
"-#print axioms seriesTerm_norm_le",
"-#print axioms finite_subtype_norm_lt",
"-#print axioms seriesTerm_summable_majorant",
"-#print axioms seriesSummable",
"-#print axioms exists_ball_avoid_nontrivialZeros",
"-#print axioms seriesFun_analyticAt",
"-#print axioms seriesFun_analyticOnNhd",
"-#print axioms nontrivialZero_isolated",
"-#print axioms seriesTermSub",
"-#print axioms seriesFunSub",
"-#print axioms seriesTermSub_norm_le",
"-#print axioms seriesTermSub_summable",
"-#print axioms single_summable",
"-#print axioms seriesFun_eq_sub_add",
"-#print axioms seriesFun_sub_term",
"-#print axioms seriesFunSub_analyticAt",
"-#print axioms seriesFun_sub_self_term_analyticAt",
"-#print axioms seriesFun_sub_polar_analyticAt",
"+#print axioms Fexpr",
"+#print axioms badPoint",
"+#print axioms analyticAt_digamma",
"+#print axioms analyticAt_digamma_div_two",
"+#print axioms zeta_zero_classification",
"+#print axioms logDeriv_zeta_sub_mult_div_eventually",
"+#print axioms logDeriv_zeta_eq_logDeriv_zetaA_sub",
"+#print axioms Fexpr_eventually_one",
"+#print axioms digammaSeriesPart",
"+#print axioms add_nat_add_one_ne_zero_of_mem_ball",
"+#print axioms digammaSeriesPart_analyticOn",
"+#print axioms digamma_eq_seriesPart_near_zero",
"+#print axioms Fexpr_eventually_zero",
"+#print axioms riemannZeta_neg_two_mul",
"+#print axioms integerComplement_of_mem_ball_neg_natCast",
"+#print axioms add_nat_add_one_ne_zero_of_mem_ball_neg",
"+#print axioms digammaSeriesPartSub",
"+#print axioms digammaSeriesPartSub_analyticOn",
"+#print axioms digammaSeriesPart_eq_sub_add_single",
"+#print axioms Hsub",
"+#print axioms digamma_eq_neg_inv_add_Hsub",
"+#print axioms Hsub_analyticAt",
"+#print axioms Fexpr_eventually_neg_two_mul",
"+#print axioms Fexpr_eventually_nontrivial",
"+#print axioms Fexpr_analyticAt_of_not_bad",
"+#print axioms exists_ball_good_of_not_bad",
"+#print axioms Gentire",
"+#print axioms gentire_eq_Fexpr",
"+#print axioms gentire_eventually_eq_witness",
"+#print axioms gentire_analyticAt_and_eq",
" "
]
}
],
"originalFile": "/- Session 028 axiom audit: LiSeries.lean (ii\u2032-5e-iii COMPLETE). -/\nimport Mathlib\nimport NguyenRH1.LiSeries\n\nopen NguyenRH1\n\n#print axioms seriesTerm\n#print axioms seriesFun\n#print axioms one_add_normSq_gammaOf_le\n#print axioms one_div_sub_add_one_div\n#print axioms seriesTerm_norm_le\n#print axioms finite_subtype_norm_lt\n#print axioms seriesTerm_summable_majorant\n#print axioms seriesSummable\n#print axioms exists_ball_avoid_nontrivialZeros\n#print axioms seriesFun_analyticAt\n#print axioms seriesFun_analyticOnNhd\n#print axioms nontrivialZero_isolated\n#print axioms seriesTermSub\n#print axioms seriesFunSub\n#print axioms seriesTermSub_norm_le\n#print axioms seriesTermSub_summable\n#print axioms single_summable\n#print axioms seriesFun_eq_sub_add\n#print axioms seriesFun_sub_term\n#print axioms seriesFunSub_analyticAt\n#print axioms seriesFun_sub_self_term_analyticAt\n#print axioms seriesFun_sub_polar_analyticAt\n",
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raw content_json (database row)
[{"type":"thinking","thinking":"Build GREEN (8766 jobs). Now the axiom audit. Declarations in LiFEntire:\n- Fexpr, badPoint\n- analyticAt_digamma, analyticAt_digamma_div_two\n- zeta_zero_classification\n- logDeriv_zeta_sub_mult_div_eventually\n- logDeriv_zeta_eq_logDeriv_zetaA_sub, Fexpr_eventually_one\n- digammaSeriesPart, add_nat_add_one_ne_zero_of_mem_ball, digammaSeriesPart_analyticOn, digamma_eq_seriesPart_near_zero, Fexpr_eventually_zero\n- riemannZeta_neg_two_mul, integerComplement_of_mem_ball_neg_natCast, add_nat_add_one_ne_zero_of_mem_ball_neg, digammaSeriesPartSub, digammaSeriesPartSub_analyticOn, digammaSeriesPart_eq_sub_add_single, Hsub, digamma_eq_neg_inv_add_Hsub, Hsub_analyticAt, Fexpr_eventually_neg_two_mul\n- Fexpr_eventually_nontrivial\n- Fexpr_analyticAt_of_not_bad, exists_ball_good_of_not_bad\n- Gentire, gentire_eq_Fexpr, gentire_eventually_eq_witness, gentire_analyticAt_and_eq\n\nWrite the audit to Scratch.lean, run, save.","signature":""},{"type":"text","text":"Build GREEN (8766 jobs). Axiom audit now."},{"type":"tool_use","id":"Write_222","name":"Write","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\Scratch.lean","content":"/- Session 029 axiom audit: LiFEntire.lean (ii′-5e-iv COMPLETE). -/\nimport Mathlib\nimport NguyenRH1.LiFEntire\n\nopen NguyenRH1\n\n#print axioms Fexpr\n#print axioms badPoint\n#print axioms analyticAt_digamma\n#print axioms analyticAt_digamma_div_two\n#print axioms zeta_zero_classification\n#print axioms logDeriv_zeta_sub_mult_div_eventually\n#print axioms logDeriv_zeta_eq_logDeriv_zetaA_sub\n#print axioms Fexpr_eventually_one\n#print axioms digammaSeriesPart\n#print axioms add_nat_add_one_ne_zero_of_mem_ball\n#print axioms digammaSeriesPart_analyticOn\n#print axioms digamma_eq_seriesPart_near_zero\n#print axioms Fexpr_eventually_zero\n#print axioms riemannZeta_neg_two_mul\n#print axioms integerComplement_of_mem_ball_neg_natCast\n#print axioms add_nat_add_one_ne_zero_of_mem_ball_neg\n#print axioms digammaSeriesPartSub\n#print axioms digammaSeriesPartSub_analyticOn\n#print axioms digammaSeriesPart_eq_sub_add_single\n#print axioms Hsub\n#print axioms digamma_eq_neg_inv_add_Hsub\n#print axioms Hsub_analyticAt\n#print axioms Fexpr_eventually_neg_two_mul\n#print axioms Fexpr_eventually_nontrivial\n#print axioms Fexpr_analyticAt_of_not_bad\n#print axioms exists_ball_good_of_not_bad\n#print axioms Gentire\n#print axioms gentire_eq_Fexpr\n#print axioms gentire_eventually_eq_witness\n#print axioms gentire_analyticAt_and_eq\n"},"extra_content":null}]