[{"type":"thinking","thinking":"Two failures:\n1. **Line 475** (Bn_FAlt_80000_ge): the LOWER bound proof `274000 ≤ Bn FAlt 80000` uses hbrlo with C0hat: `110.3498 ≤ (2/3)·C0hat + ...`. The new Bn has Z2hat in that bracket — hbrlo's form mismatches (the goal's bracket has Z2hat). And 4·FAlt vs 2·FAlt (the goal shows `4 * FAlt` — that's already the new form; the proof's linarith uses hterm2 with C0hat form). Fix: hbrlo with Z2hat lower bound: Z2hat ≥ 0.6·5.6 + 0.886·(log log lower?) + 2.7. The lower bounds: log(T+2) ≥ 5.6, loglog(T+2) ≥ 0 (hloglogT2nn : 0 ≤ loglog). Z2hat ≥ 0.6·5.6 + 0 + 2.7 = 6.06. (2/3)·6.06 + 10.5·5.6 + 48 = 4.04 + 58.8 + 48 = 110.84. hbrlo : 110.84 ≤ (2/3)·Z2hat + ... — then hterm2 : 4·283·110.84 ≤ 4T·[...] and 4·FAlt ≥ 0 (hFAlt0) and hterm4 (Ĥ lower) — the total lower: 0 + 4·283·110.84 + 53.408 + 2·55.5978·(7·191.85+3.3) + 0 + 1 = 125,470 + 53.4 + 198,037 + 1 ≈ 323,561 ≥ 274,000 ✓ huge slack. linarith will close with hterm2 (C0hat→Z2hat form), hterm4, hFAlt0, hII.\n\nActually the goal displayed: `4 * FAlt + 4·T·(Z2-bracket) + 40·1.3352 + 2(e⁴+1)(7Ĥ+3.3) + IIMaj + 1 < 274000 ⊢ False` — the negated form (the proof does by_contra? no — it's `274000 ≤ Bn`: linarith with the haves). The failing part: hterm2's bracket is the C0hat form but the goal's bracket is Z2hat — rewrite hbrlo/hterm2 with Z2hat.\n\n2. **Line 597** (Bn_FAlt_100000_ge presumably — similar). Same fix.\n\nLet me find those _ge proofs and patch them.","signature":""},{"type":"text","text":"The two `_ge` (lower-bound) proofs also use the C0hat bracket. Patching them to Z2hat lower bounds."},{"type":"tool_use","id":"Read_224","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiBasePoints.lean","offset":430,"limit":48},"extra_content":null}]