[{"type":"thinking","thinking":"Now I need to look at the referenced lemmas from other files to get the exact names/signatures:\n1. `iteratedDeriv_neg_zpow_neg_one_add` from LiDigamma\n2. `seriesTerm`, `seriesFun` definitions from LiSeries\n3. `exists_ball_avoid_nontrivialZeros` from LiSeries\n4. The `iteratedDerivWithin_tsum` pattern in LiDigamma (lines 735–785)\n5. `iteratedDeriv_congr_of_eventuallyEq` (LiDigamma:568)\n6. `iteratedDeriv_const_mul` (Lemmas.lean:368 — probably in Zeta23)\n7. `SummableLocallyUniformlyOn_of_locally_bounded` signature\n\nLet me grep these.","signature":""},{"type":"text","text":"Now let me gather the exact signatures of the referenced machinery."},{"type":"tool_use","id":"Grep_6","name":"Grep","input":{"pattern":"iteratedDeriv_neg_zpow_neg_one_add|theorem iteratedDerivWithin_tsum|lemma iteratedDerivWithin_tsum|SummableLocallyUniformlyOn_of_locally_bounded|iteratedDeriv_congr_of_eventuallyEq|iteratedDeriv_const_mul|theorem iteratedDeriv_neg|lemma iteratedDeriv_neg","path":"D:\\Python\\Quantum\\research\\lean","output_mode":"content","-n":true,"head_limit":40},"extra_content":null},{"type":"tool_use","id":"Grep_7","name":"Grep","input":{"pattern":"def seriesTerm|def seriesFun|noncomputable def seriesFun|exists_ball_avoid_nontrivialZeros|def sigmaP|def sigmaSlice|theorem seriesSummable|seriesFun_analyticAt","path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1","output_mode":"content","-n":true,"head_limit":40},"extra_content":null}]