← Session 18 — Lean tier (ii): finite-height proof + certified base points
thinking (1099 chars)
Line 452: hbrlo in Bn_FAlt_80000_ge: goal `110.34987 ≤ (2/3)·C0hat + 10.5·log + 48` with h1 : (2/3)·5.3248 ≤ (2/3)·C0hat and h2 : 10.5·5.6 ≤ 10.5·log. Sum: (2/3)·5.3248 + 10.5·5.6 + 48 = 3.54987 + 58.8 + 48 = 110.34987. linarith should close: it needs to see (2/3)*5.3248 = 3.54987 — rational arithmetic ✓. Hmm, why did it fail? (2/3)·5.3248: 2/3 is not exactly representable... in ℝ it's 2·3⁻¹ — linarith handles rational division EXACTLY: (2/3)·5.3248 = 10.6496/3 = 3.5498666... And 110.34987 vs 3.5498667+58.8+48 = 110.3498667 — 110.3498667 < 110.34987!! MY CONSTANT IS WRONG: 3.5498667 ≠ 3.54987. (2/3)·5.3248 = 3.549866... I wrote 110.34987 but the true sum is 110.3498666... So 110.34987 ≤ ... is FALSE (barely, by 3×10⁻⁶). My arithmetic slip: (2/3)·5.3248 = 3.54986667, sum = 110.34986667. Target should be 110.3498 (round DOWN for the lower bound). Use 110.3498: then term2 lower = 4·283·110.3498 = 1132·110.3498 = 124916.2 (1132·110.3498 = 124916.19...). Bn lower total: 124916.19 + 53.408 + 149697.1 + 1 = 274667.7 ≥ 274000 ✓ unchanged.
Fix: 110.34987 → 110.3498 in both hbrlo and hterm2.
Arithmetic slip: (2/3)·5.3248 = 3.549866..., so the lower-bound constant must round *down* to 110.3498, not 110.34987.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/research/lean/NguyenRH1/NguyenRH1 && sed -i 's/110\\.34987/110.3498/g' LiBasePoints.lean && grep -n \"110.3498\" LiBasePoints.lean",
"description": "Fix the lower-bound constant"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Line 452: hbrlo in Bn_FAlt_80000_ge: goal `110.34987 ≤ (2/3)·C0hat + 10.5·log + 48` with h1 : (2/3)·5.3248 ≤ (2/3)·C0hat and h2 : 10.5·5.6 ≤ 10.5·log. Sum: (2/3)·5.3248 + 10.5·5.6 + 48 = 3.54987 + 58.8 + 48 = 110.34987. linarith should close: it needs to see (2/3)*5.3248 = 3.54987 — rational arithmetic ✓. Hmm, why did it fail? (2/3)·5.3248: 2/3 is not exactly representable... in ℝ it's 2·3⁻¹ — linarith handles rational division EXACTLY: (2/3)·5.3248 = 10.6496/3 = 3.5498666... And 110.34987 vs 3.5498667+58.8+48 = 110.3498667 — 110.3498667 < 110.34987!! MY CONSTANT IS WRONG: 3.5498667 ≠ 3.54987. (2/3)·5.3248 = 3.549866... I wrote 110.34987 but the true sum is 110.3498666... So 110.34987 ≤ ... is FALSE (barely, by 3×10⁻⁶). My arithmetic slip: (2/3)·5.3248 = 3.54986667, sum = 110.34986667. Target should be 110.3498 (round DOWN for the lower bound). Use 110.3498: then term2 lower = 4·283·110.3498 = 1132·110.3498 = 124916.2 (1132·110.3498 = 124916.19...). Bn lower total: 124916.19 + 53.408 + 149697.1 + 1 = 274667.7 ≥ 274000 ✓ unchanged.\n\nFix: 110.34987 → 110.3498 in both hbrlo and hterm2.","signature":""},{"type":"text","text":"Arithmetic slip: (2/3)·5.3248 = 3.549866..., so the lower-bound constant must round *down* to 110.3498, not 110.34987."},{"type":"tool_use","id":"Bash_168","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1/NguyenRH1 && sed -i 's/110\\.34987/110.3498/g' LiBasePoints.lean && grep -n \"110.3498\" LiBasePoints.lean","description":"Fix the lower-bound constant"},"extra_content":null}]