[{"type":"thinking","thinking":"The timeout at 3156 is at the `ring` after the choreography — and there's a suspicious thing: line 3156's doc comment for farGLeftMaj_combo_summable — \"kernel unknown constant farGLeftMaj_combo_summable\" — wait, now I see: the file at 3156-3163 has farGLeftMaj_combo_summable defined. The kernel error says unknown constant — meaning when the elaborator reached farGLeftMaj_shift_summable's reference, combo_summable wasn't in the env — because its own elaboration FAILED?? no — the combo_summable's proof is a term `(((...).add ...).add ...).mul_left _` — maybe ITS elaboration timed out (line 3174 timeout is at farGLeftMaj_summable?).\n\nRoot suspicion: the `ring` at 3154 and similar heavy tactics on these big literal expressions are timing out because of the giant real-number terms with Real.log atoms — ring's preprocessing shouldn't be THAT slow. Something else: maybe `rw [hD, h9, mul_add, mul_add, add_div, add_div, mul_add]` produced a goal where `ring` must unify huge polynomials with the ↑ℓ atoms — fine — but 200k heartbeats is a lot.\n\nWait — maybe the actual problem is elsewhere: the timeouts at whnf/isDefEq — these smell like the elaborator is trying to unify something expensive — possibly the `from rfl` beta-bridges (the huge show-terms with the nested fun-lambdas) or the `by positivity` calls on giant expressions (positivity on (10 + ↑(ℓ+14))² — fine).\n\nHold on — line 3147: `by positivity : (0 : ℝ) ≤ (10 + ((ℓ + 14 : ℕ) : ℝ)) ^ 2` — fine. Line 3149: rw [hcast] at the GOAL — hcast : ↑(ℓ+14) = ↑ℓ+14 — but the goal after the two applies is `C0hat (↑(ℓ+14) + 1) ≤ 0.433·(log ↑(ℓ+14) + 0.1942) + ...` — rw [hcast] rewrites ↑(ℓ+14) → ↑ℓ+14 ✓ then exact h1 — h1 was already hcast-rewritten at 3146 ✓ fine.\n\nThe timeouts might be CUMULATIVE — the file is now ~3300 lines and each compile re-elaborates everything, but `lake env lean` on one file should handle that (it's been fine up to ~3000 lines).\n\nLet me try increasing maxHeartbeats for the specific lemmas, or better — restructure to avoid the expensive ring entirely: replace the `ring` in shift_le's le_of_eq with an explicit small-step proof:\n\ngoal (after rw [hD, h9]): \n`4.5 * (c0 + 0.433·log X + 0.886·loglog X) / D² = 4.5 * (c0·(1/D²) + 0.433·log X/D² + 0.886·loglog X/D²)`\nwhere X = ↑ℓ+14, D = X+10.\n\nDo it WITHOUT ring:\n```\n    rw [hD, h9]\n    rw [show (4.5 : ℝ) * (0.433 * 0.1942 + 0.886 * 0.0736 + 2.9 + 0.433 * Real.log X' + 0.886 * Real.log X'')\n        = (4.5 * (0.433 * 0.1942 + 0.886 * 0.0736 + 2.9)) + 4.5 * (0.433 * Real.log X') + 4.5 * (0.886 * Real.log X'') from by ring]\n    rw [add_div, add_div]\n    congr 1\n    · rw [show (4.5 * (0.433 * 0.1942 + 0.886 * 0.0736 + 2.9)) / D² = 4.5 * ((0.433 * 0.1942 + 0.886 * 0.0736 + 2.9) * (1 / D²)) from by ring]\n    · rw [show (4.5 * (0.433 * Real.log X')) / D² = 4.5 * (0.433 * (Real.log X' / D²)) from by ring]\n    · rw [show (4.5 * (0.886 * Real.log X'')) / D² = 4.5 * (0.886 * (Real.log X'' / D²)) from by ring]\n```\nEach small rw has a tiny `by ring` — those should be fast. Hmm — but `by ring` on each still uses ring. The expressions are much smaller though.\n\nActually — let me reconsider WHY ring times out here. `ring` on ℝ with atoms log X, loglog X, D², (D²)⁻¹: the polynomial is degree-2 in D with ~10 atoms — ring should be instant. The isDefEq timeout is suspicious of something pathological — maybe ring tries to unfold Real.log or the casts?! Or — the issue is the goal after the choreography is NOT what I think (maybe the rewrites produced something ring can't close and it flails). Let me test the choreography's output interactively: replace `ring` with `id` and inspect... can't easily. ALTERNATIVE: use `abel`? or `linear_combination` (used heavily in this project — it's their house tool for such equalities!). linear_combination normalizes too. Or just bump maxHeartbeats on these two lemmas: `set_option maxHeartbeats 800000 in lemma ...` — the project does this elsewhere (iimaj_bracket_bound needs 800000). Pragmatic: bump to 800000 for farGLeftMaj_shift_le and farGLeftMaj_series_le.\n\nLet me try the maxHeartbeats bump first (cheapest).","signature":""},{"type":"text","text":"The timeouts look like heartbeat exhaustion on the heavy algebra. Bumping maxHeartbeats on the two offenders (the project does this elsewhere)."},{"type":"tool_use","id":"Bash_196","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1 && python - <<'EOF'\np = 'NguyenRH1/LiTightR.lean'\nsrc = open(p, encoding='utf-8').read()\nsrc = src.replace(\"\"\"/-- The pointwise majorant bound for the shifted farGLeftMaj. -/\nlemma farGLeftMaj_shift_le (ℓ : ℕ) :\"\"\", \"\"\"/-- The pointwise majorant bound for the shifted farGLeftMaj. -/\nset_option maxHeartbeats 800000 in\nlemma farGLeftMaj_shift_le (ℓ : ℕ) :\"\"\")\nsrc = src.replace(\"\"\"/-- **The left-tail series bound**. -/\nlemma farGLeftMaj_series_le :\"\"\", \"\"\"/-- **The left-tail series bound**. -/\nset_option maxHeartbeats 800000 in\nlemma farGLeftMaj_series_le :\"\"\")\nopen(p, 'w', encoding='utf-8').write(src)\nprint(\"done\")\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiTightR.lean 2>&1 | head -30","description":"Bump maxHeartbeats and recompile","timeout":420000},"extra_content":null}]