[{"type":"thinking","thinking":"The timeout is at the doc-comment/lemma start (820:0) — the elaboration of the statement's `whnf`. The statement has `iteratedDerivWithin j (fun s : ℂ => seriesTerm s ρ) (Metric.ball 0 (δ / 2))` — the `δ / 2` where δ : ℝ — fine. Hmm, whnf timeout at statement elaboration... Actually the error position 820:0 might be where the previous declaration ended or where elaboration of THIS lemma began; whnf timeouts during `apply` at line 829 could be reported at declaration start.\n\nPossible culprit: `apply SummableLocallyUniformlyOn_of_locally_bounded Metric.isOpen_ball` — unification of the goal `SummableLocallyUniformlyOn (fun ρ => iteratedDerivWithin ...) (ball)` with the lemma's conclusion `SummableLocallyUniformlyOn f s` — should be fast.\n\nAlternatively the timeout is during type-checking the STATEMENT: `SummableLocallyUniformlyOn` for functions into ℂ requires [NormedAddCommGroup F] [CompleteSpace F] — typeclass search fine.\n\nHmm, whnf specifically: maybe unifying `Metric.ball (0 : ℂ) (δ / 2)` — `0` here: `Metric.ball 0` — the 0 : ℂ inferred from family codomain? The family: ρ → (ℂ → ℂ)? iteratedDerivWithin j (fun s : ℂ => ...) (ball 0 (δ/2)) : ℂ → ℂ. And SummableLocallyUniformlyOn {f : α → β → F} — β = ℂ, F = ℂ. The `0` in `Metric.ball 0 (δ/2)` needs to be (0 : ℂ) — I wrote `Metric.ball 0 (δ / 2)` without ascription; inference from expected type should work.\n\nLet me get more diagnostics — run with diagnostics on a copy? Quicker: check where exactly it times out by bisecting: put `set_option maxHeartbeats 400000 in` before the lemma and see if it goes through, or first test just the statement:\n\nActually the error says maxHeartbeats 200000 reached at whnf. Let me try doubling first — if it passes at 400k, fine (banked pattern: iimaj_bracket_bound needed 800000; set_option goes BEFORE the doc comment).\n\nBut whnf timeout in a statement usually indicates an elaboration loop — e.g. `SummableLocallyUniformlyOn_of_locally_bounded` unification triggering defeq unfolding of `iteratedDerivWithin` massively. Hmm, but the error is at 820:0 which is the doc comment start — declaration-level errors are reported at the declaration's start. So the timeout could be anywhere in the proof.\n\nLet me try maxHeartbeats 800000 first.","signature":""},{"type":"text","text":"Timeout at `whnf` in the new lemma. Trying a heartbeat bump first (banked pattern from session 011)."},{"type":"tool_use","id":"Edit_40","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiMoments.lean","old_string":"/-- The k-th derivative family (k ≥ 1) is summable locally uniformly on\nball(0, δ/2) (the M-test; dominator C_j·mult/‖ρ‖² via ‖s−ρ‖ ≥ ‖ρ‖/2 and\n1/‖ρ‖^{j−1} ≤ (1/δ)^{j−1}). -/\nlemma seriesTerm_deriv_summableLocallyUniformlyOn {j : ℕ} (hj : 1 ≤ j)","new_string":"set_option maxHeartbeats 800000 in\n/-- The k-th derivative family (k ≥ 1) is summable locally uniformly on\nball(0, δ/2) (the M-test; dominator C_j·mult/‖ρ‖² via ‖s−ρ‖ ≥ ‖ρ‖/2 and\n1/‖ρ‖^{j−1} ≤ (1/δ)^{j−1}). -/\nlemma seriesTerm_deriv_summableLocallyUniformlyOn {j : ℕ} (hj : 1 ≤ j)"},"extra_content":null}]