[{"type":"thinking","thinking":"The timeouts are at 1612 (`nlinarith [hsqrt316, he]`), 1614 (`linarith [h2, hlog1]`), 1616 (hA' line or 1617's nlinarith). Line 1612's nlinarith: goal `Real.exp 1 ≤ Real.sqrt (n:ℝ) + 1` — from hsqrt316 (316 ≤ √n) and he (e ≤ 2.7182818286): e ≤ 2.72 ≤ 317 ≤ √n+1 ✓ — nlinarith TIMED OUT?? — that's a trivial linear fact! Why would nlinarith timeout there... — unless the isDefEq timeout is from `rw [Real.le_log_iff_exp_le ht2]` producing a goal whose form makes nlinarith choke. The goal after rw: `Real.exp 1 ≤ Real.sqrt (n:ℝ) + 1` — atoms: exp 1, √n — linear ✓ — hmm — isDefEq timeout at 1612:48 — col 48 — the `he` argument position?? — the `he := Real.exp_one_lt_d9.le` — its type: exp 1 ≤ 2.7182818286 — hmm.\n\nHmm — wait — 1612:48 is the isDefEq timeout, 1614:6 tactic-execution timeout, 1616:4 tactic-execution timeout. The FIRST timeout (1612 isDefEq) might poison the rest (cascade). The isDefEq timeout could be nlinarith's preprocessing trying to unify something... — nlinarith calls ring_nf which does isDefEq checks — on WHAT here? The goal `exp 1 ≤ √↑n + 1` — tiny. UNLESS the context is HUGE (dozens of haves with big types — nlinarith's hypothesis collection... — nlinarith only uses the listed haves + context?? — nlinarith uses the LISTED haves AND tries products of hypotheses from the context?? — no — nlinarith [list] uses list + nothing else? — actually nlinarith ALSO considers hypotheses in the local context (all of them!) for products — with the huge context (hsf, hnormRect?? no — this is hFAlt's inner h1 — the context at that point has ~20 haves, some with massive types (hTwide, hHhat... no — this is inside hFAlt at line 1606 — the context has hnR..hTwide, hTle, hsf, hbridge(the calc!), hVl, hVr, hH, hnorm, htri, hpinch, he13, h2πpos, h2πle, he13', hIIMaj0, hDLR0, hC0T0, hHhat0, hX0, hsqrt0, hlogT1 — the bridge calc has a huge type — nlinarith's atomization of all context hypotheses could explode on those big types!!\n\nActually — the isDefEq timeout at 1612 — nlinarith [hsqrt316, he] — with the giant context — nlinarith's preprocessing (ring_nf on all context hyps for atom collection?) — nlinarith considers pairwise products of context hypotheses too!! With huge types that explodes.\n\nFIX: use `linarith` (not nlinarith) for these trivially-linear goals — linarith also scans context but is much cheaper... — actually linarith also preprocesses context. Hmm — the safest: make the tiny sub-proofs use explicit `have`-chains with linarith and FEW facts, or restructure hFAlt to have smaller context. But hFAlt's context is genuinely big.\n\nHmm — wait — actually — is the timeout REALLY context-size? The pinch (with a smaller context) worked... — the pinch's nlinarith calls also had ~15 haves in context but smaller types. The hFAlt region's context includes hsf (huge), hbridge (huge calc), hH, hnorm, htri — massive types.\n\nStandard fix: `clear` the irrelevant hypotheses before the expensive nlinarith calls, OR use `linarith only [list]` — `linarith only [h1, h2]` restricts linarith to the listed haves + local variables (NO context scan!) ✓ — use `linarith only [...]` for the small steps. Or nlinarith only [...]? — does nlinarith support `only`? — yes: `nlinarith only [h1, h2]`.\n\nLet me apply `only` to the nlinarith/linarith calls in the big-context regions (hFAlt, hX, hHhat, and the final assembly — the final nlinarith has an explicit list of ~20 haves — nlinarith scans context TOO on top of the list?? — the docs: nlinarith [h1, h2] uses the listed haves AND the local context hypotheses. With the giant context + 20 listed, that's a lot of products. Use `nlinarith only [the list]` for the final too.)\n\nHmm — but wait — the final assembly NEEDS the context variables (T, n are variables, fine) but not the other haves. `nlinarith only [hsf, hnormRect, hVl', hVr', hH', hbridge, hIIMajAbs, hHhatAbs, hDLRAbs, hXAbs, hPinchAbs, hFAlt, hX, hHhat, hIIMaj0, hDLR0, hHhat0, hX0]` ✓.\n\nAlso 1614: `linarith [h2, hlog1]` — goal `Real.log (Real.log T) ≤ Real.log (Real.log (√n+1))` — wait no — line 1614 is inside hC: after the `apply Real.log_le_log ...`, the remaining goal: `Real.log T ≤ Real.log (√n+1)` — with h2 := hB (exactly that!) — `linarith [h2, hlog1]` — should be `exact h2`!! — the goal after apply Real.log_le_log (pos) is `Real.log T ≤ Real.log (√n+1)` — h2 : Real.log T ≤ Real.log (√n+1) ✓ exact h2. But I wrote linarith — which scanned the context and timed out. Change to `exact h2`.\n\nAnd 1612's nlinarith → `nlinarith only [hsqrt316, he]` — or better a plain linarith only. Hmm — the goal `Real.exp 1 ≤ √↑n + 1` — from he : exp 1 ≤ 2.7182818286 and hsqrt316 : 316 ≤ √n: e ≤ 2.72 ≤ 317 ✓ — `linarith only [hsqrt316, he]`.\n\nAnd 1616-1617: `have hA' := mul_le_mul_of_nonneg_left hA hconst; nlinarith [hA', hB, hC]` — the nlinarith at 1617 → `nlinarith only [hA', hB, hC]` — hmm — does it need Real.pi? — the goal: (1/2π)·(T·log T) + 0.137·log T + 0.443·loglog T + const ≤ (1/2π)·(T'·log T') + 0.137·log T' + 0.443·loglog T' + const ✓ from hA' hB hC ✓ linarith only [hA', hB, hC] ✓ linear ✓ use linarith only.\n\nAlso — the `Real.exp_one_lt_d9.le` fix (issue 3): change `have h4 : Real.exp 1 ≤ 2.7183 := Real.exp_one_lt_d9.le` to the correct bound.\n\nWait — actually — hmm — `norm_num at h4 ⊢` with h4 : exp 1 ≤ 2.7182818286 — norm_num at ⊢ computes (1.4)^3 → 2.744 — goal `exp 1 ≤ 2.744` — then linarith [h4] — e ≤ 2.7183 ≤ 2.744 ✓ — with `linarith only [h4]`. And norm_num at h4 — leave (norm_num on h4's 2.7182818286 — harmless). Actually — simplify: `have h4 : Real.exp 1 ≤ 2.7182818286 := Real.exp_one_lt_d9.le; norm_num1 at ⊢; linarith only [h4]` — hmm — norm_num1 at ⊢ computes 1.4^3 = 2.744 ✓.\n\nAlso — issue 1 (1338): remove `one_mul` from the rw — `rw [div_le_iff₀ (Real.exp_pos 1)]; nlinarith [Real.exp_one_gt_d9]` — hmm — also potential context-scan (in C0hat_le_self the context is small ✓ fine).\n\nAlso — the `norm_num at h4 ⊢` pattern in h2's block (he13's h1): `have h2 : (Real.exp (1/3))^3 ≤ (1.4)^3 := by have h3 := ...; rw [h3]; have h4 : Real.exp 1 ≤ 2.7182818286 := Real.exp_one_lt_d9.le; norm_num at h4 ⊢; linarith [h4]` — the linarith [h4] with small context (inside he13's block — context is large again!) — `linarith only [h4]`.\n\nAnd issue 2: pinch_horizontal's hTn1 → _hTn1.\n\nAnd issue 4 (1565): he13' fix (the div form).\n\nAnd issue 5 (1603): Real.log_nonneg (1 ≤ T) fix.\n\nLet me also preemptively add `only` to the other large-context nlinarith/linarith calls in sfBoundProp's body (hFAlt's hA/hB/hC steps, hX's steps, hHhat, hBn?, hIIMajAbs rings (ring doesn't scan context ✓ fine), hHhatAbs/hDLRAbs/hXAbs (rwa — fine), the final nlinarith). Let me be systematic: in sfBoundProp, replace every `nlinarith [list]` and `linarith [list]` in the big-context zone with `nlinarith only [list]` / `linarith only [list]` where the goal is genuinely linear in the listed atoms.\n\nWhich ones:\n- hTle's `linarith [hTn1]` — small context? — at that point context is moderate — but let me add only everywhere downstream of the bridge calc (the context bloats after hsf/hbridge).\n- hFAlt block: all its linarith/nlinarith → only-versions.\n- hX block: nlinarith [hZ, hlog] → nlinarith only [hZ, hlog]; nlinarith [hlogT1] → only; nlinarith [h4] → only.\n- hHhat: nlinarith [hC2, hlog] → only.\n- hHhat0's nlinarith [hC0T0.le, hL1] → only (context large).\n- hX0's nlinarith [hT0.le] → hmm — hX0's goal: 0 ≤ 4T·X(T) + 40·1.3352 — from h1 (Z2hat ≥ 0), h2 (log ≥ 0), T ≥ 0: 4·T·X ≥ 0 — NONLINEAR (T·X product!) — nlinarith only [hT0.le, h1, h2] — needs the product T·X ≥ 0 — nlinarith pairwise ✓.\n- he13's nlinarith [h1, h5] → nlinarith only [h1, h5].\n- hlogT1's nlinarith [hTn, hsqrt316, he] → only.\n- hFAlt's hlog1's nlinarith [hTn, hsqrt316, he] → only.\n- Final: nlinarith only [big list].\n- Also hTle's linarith [hTn1] → linarith only [hTn1] (safe).\n- The hX0 in the hX-block (hX0'): nlinarith [hlogT1] → only.\n- Also `hC0T0`'s linarith — small — skip (before the bloat).\n- hHhat0's nlinarith [hC0T0.le, hL1] → only.\n\nHmm — also the `nlinarith [hsqrt316, hTn]` for hT1 (early, small context — fine).\n\nAlso — WAIT — potential problem: `linarith only [list]` does NOT use local hypotheses outside the list — so I must make sure every needed fact is IN the list. Let me carefully re-audit each goal I'm changing... — I'll do the edits surgically.\n\nAlso — h4's in hX's block: `nlinarith [h4]` — goal 4·T·X ≤ 4·T'·X' from h4 : T·X ≤ T'·X' — mul by 4 — linear ✓ `nlinarith only [h4]` — hmm — 4·(T·X) vs 4·T·X — association ✓ linarith normalizes ✓.\n\nLet me now write all the edits. First the six errors:\n1. 1338: remove `, one_mul` from the rw chain.\n2. 1363: hTn1 → _hTn1 in pinch_horizontal.\n3. 1552: h4's ascription → 2.7182818286.\n4. 1565: he13' restructure (div form) + hIIMajAbs calc form.\n5. 1603: Real.log_nonneg arg fix.\n6. timeouts: `only` everywhere in the big zone.","signature":""},{"type":"text","text":"Timeouts are context-scan blowups — `linarith only`/`nlinarith only` needed throughout the big zone. Applying all fixes."},{"type":"tool_use","id":"Edit_174","name":"Edit","input":{"replace_all":false,"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSideBounds.lean","old_string":"  have hinv : (1 : ℝ) / Real.exp 1 ≤ 0.36789 := by\n    rw [div_le_iff₀ (Real.exp_pos 1), one_mul]\n    nlinarith [Real.exp_one_gt_d9]","new_string":"  have hinv : (1 : ℝ) / Real.exp 1 ≤ 0.36789 := by\n    rw [div_le_iff₀ (Real.exp_pos 1)]\n    nlinarith [Real.exp_one_gt_d9]"},"extra_content":null},{"type":"tool_use","id":"Edit_175","name":"Edit","input":{"replace_all":false,"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSideBounds.lean","old_string":"theorem pinch_horizontal {n : ℕ} (hn : 100000 ≤ n) {T : ℝ}\n    (hTn : Real.sqrt (n : ℝ) ≤ T) (hTn1 : T ≤ Real.sqrt (n : ℝ) + 1) :","new_string":"theorem pinch_horizontal {n : ℕ} (hn : 100000 ≤ n) {T : ℝ}\n    (hTn : Real.sqrt (n : ℝ) ≤ T) (_hTn1 : T ≤ Real.sqrt (n : ℝ) + 1) :"},"extra_content":null},{"type":"tool_use","id":"Edit_176","name":"Edit","input":{"replace_all":false,"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSideBounds.lean","old_string":"        rw [h3]\n        have h4 : Real.exp 1 ≤ 2.7183 := Real.exp_one_lt_d9.le\n        norm_num at h4 ⊢\n        linarith [h4]\n      exact le_of_pow_le_pow_left₀ (by norm_num : (3 : ℕ) ≠ 0) (by norm_num : (0 : ℝ) ≤ 1.4) h2\n    have h5 : (3 : ℝ) ≤ Real.pi := Real.pi_gt_three.le\n    nlinarith [h1, h5]","new_string":"        rw [h3]\n        have h4 : Real.exp 1 ≤ 2.7182818286 := Real.exp_one_lt_d9.le\n        norm_num1 at ⊢\n        linarith only [h4]\n      exact le_of_pow_le_pow_left₀ (by norm_num : (3 : ℕ) ≠ 0) (by norm_num : (0 : ℝ) ≤ 1.4) h2\n    have h5 : (3 : ℝ) ≤ Real.pi := Real.pi_gt_three.le\n    nlinarith only [h1, h5]"},"extra_content":null}]