[{"type":"thinking","thinking":"Wait — line 585-600 shows my Z2 edits already applied to the _le proof... but the error at line 597 is `linarith [h1, h2]` INSIDE hbr of the _le proof! The hbr at line 592-597 uses hZ2 (≤ 7.7483) and hlogT2 (≤ 5.8): (2/3)·7.7483 + 10.5·5.8 + 48 = 5.16553 + 60.9 + 48 = 114.0655 ✓ the arithmetic should work: linarith [h1 : (2/3)·Z2hat ≤ (2/3)·7.7483, h2 : 10.5·log ≤ 10.5·5.8]. (2/3)·7.7483 = 5.165533...; 10.5·5.8 = 60.9; total 114.06553 ≤ 114.0655?? 5.16553+60.9+48 = 114.06553 > 114.0655! OFF BY 0.00003 — my certified constant 114.0655 is too tight! (2/3)·7.7483 = 5.1655333; +60.9 = 66.0655; +48 = 114.065533 > 114.0655. Arithmetic slip in my head: 0.6·5.8 = 3.48; 0.886·1.77 = 1.56822; +2.7: Z2 ≤ 7.74822, I certified 7.7483 ✓ fine. (2/3)·7.7483 = 5.16553̄. 10.5·5.8 = 60.9. Sum: 5.16553̄+60.9+48 = 114.06553̄ — exceeds 114.0655 by 3.3×10⁻⁵. Fix: hbr ≤ 114.0656 (and recompute the total: 4·318·114.0656 = 145,091.5; total ≈ 348,196 ≤ 350,000 ✓ still fine).\n\nAlso the first error at line 475 (80000_ge) needs the Z2hat-lower fix, and there's presumably a 100000_ge proof further down with the same issue — wait, no: the 597 error is in the _le proof (hbr's linarith). And 475 is in 80000_ge. Is there a 100000_ge? Let me check — the grep showed only Bn_FAlt_80000_ge among _ge. And the 80000_ge's hbrlo uses C0hat — must convert to Z2hat-lower.\n\nLet me fix:\n1. 80000_ge: hbrlo with Z2hat: Z2hat ≥ 0.6·5.6 + 0 + 2.7 = 6.06; hbrlo : 110.84 ≤ (2/3)·Z2hat + ... (4.04+58.8+48 = 110.84); hterm2 : 4·283·110.84.\n2. 100000_le hbr: 114.0655 → 114.0656; hterm2's bound 4·318·114.0656.","signature":""},{"type":"text","text":"Two fixes: the `_ge` proof's bracket needs the Z2hat lower bound, and my hbr constant is off by 3×10⁻⁵ (rounding)."},{"type":"tool_use","id":"Bash_226","name":"Bash","input":{"command":"cd D:/Python/Quantum && python - << 'EOF'\np = 'research/lean/NguyenRH1/NguyenRH1/LiBasePoints.lean'\nsrc = open(p, encoding='utf-8').read()\nsubs = [\n# 80000_ge: C0hat bracket -> Z2hat lower (0.6*5.6 + 0 + 2.7 = 6.06; (2/3)*6.06 + 58.8 + 48 = 110.84)\n(\"\"\"  have hbrlo : (110.3498 : ℝ) ≤ (2 / 3 : ℝ) * C0hat (Real.sqrt 80000 + 1) +\n      10.5 * Real.log (Real.sqrt 80000 + 1 + 2) + 48 := by\n    have h1 := mul_le_mul_of_nonneg_left hC0lo (by norm_num : (0 : ℝ) ≤ 2 / 3)\n    have h2 := mul_le_mul_of_nonneg_left hlogT2ge (by norm_num : (0 : ℝ) ≤ 10.5)\n    linarith [h1, h2]\n  have hterm2 : (4 * 283 * 110.3498 : ℝ) ≤ 4 * (Real.sqrt 80000 + 1) *\n      ((2 / 3) * C0hat (Real.sqrt 80000 + 1) +\n        10.5 * Real.log (Real.sqrt 80000 + 1 + 2) + 48) := by\"\"\",\n \"\"\"  -- Z₂ T ≥ 6.06 (0.6·5.6 + 0 + 2.7; log log ≥ 0; the corrected count, D-071)\n  have hZ2lo : (6.06 : ℝ) ≤ Z2hat (Real.sqrt 80000 + 1) := by\n    unfold Z2hat\n    linarith [hlogT2ge, hloglogT2nn]\n  have hbrlo : (110.84 : ℝ) ≤ (2 / 3 : ℝ) * Z2hat (Real.sqrt 80000 + 1) +\n      10.5 * Real.log (Real.sqrt 80000 + 1 + 2) + 48 := by\n    have h1 := mul_le_mul_of_nonneg_left hZ2lo (by norm_num : (0 : ℝ) ≤ 2 / 3)\n    have h2 := mul_le_mul_of_nonneg_left hlogT2ge (by norm_num : (0 : ℝ) ≤ 10.5)\n    linarith [h1, h2]\n  have hterm2 : (4 * 283 * 110.84 : ℝ) ≤ 4 * (Real.sqrt 80000 + 1) *\n      ((2 / 3) * Z2hat (Real.sqrt 80000 + 1) +\n        10.5 * Real.log (Real.sqrt 80000 + 1 + 2) + 48) := by\"\"\"),\n# 100000_le hbr: 114.0655 -> 114.0656 (the exact (2/3)*7.7483 + 60.9 + 48 = 114.06553)\n(\"\"\"  have hbr : (2 / 3 : ℝ) * Z2hat (Real.sqrt 100000 + 1) +\n      10.5 * Real.log (Real.sqrt 100000 + 1 + 2) + 48 ≤ 114.0655 := by\"\"\",\n \"\"\"  have hbr : (2 / 3 : ℝ) * Z2hat (Real.sqrt 100000 + 1) +\n      10.5 * Real.log (Real.sqrt 100000 + 1 + 2) + 48 ≤ 114.0656 := by\"\"\"),\n(\"\"\"  have hterm2 : 4 * (Real.sqrt 100000 + 1) * ((2 / 3) * Z2hat (Real.sqrt 100000 + 1) +\n      10.5 * Real.log (Real.sqrt 100000 + 1 + 2) + 48) ≤ 4 * 318 * 114.0655 := by\"\"\",\n \"\"\"  have hterm2 : 4 * (Real.sqrt 100000 + 1) * ((2 / 3) * Z2hat (Real.sqrt 100000 + 1) +\n      10.5 * Real.log (Real.sqrt 100000 + 1 + 2) + 48) ≤ 4 * 318 * 114.0656 := by\"\"\"),\n]\ncount = 0\nfor old, new in subs:\n    if old in src:\n        src = src.replace(old, new)\n        count += 1\n    else:\n        print('MISS:', old[:70].replace('\\n',' | '))\nopen(p, 'w', encoding='utf-8').write(src)\nprint(f'{count}/{len(subs)} substitutions applied')\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && cd D:/Python/Quantum/research/lean/NguyenRH1 && lake env lean NguyenRH1/LiBasePoints.lean 2>&1 | head -25","description":"Fix _ge bracket + rounding, rebuild LiBasePoints","timeout":600000},"extra_content":null}]