← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)
thinking (1068 chars)
Now check the IIMaj_deriv2_lt consumer (line 2388's hIIM in marginTilde_convex) — it uses `IIMaj_deriv2_lt` which I just renamed to `IIMaj_deriv2_lt_three` with a different bound (1/(3n) instead of 1/(2n)). The marginTilde_convex's final linarith: `linarith [hIIM, hnn1..hnn9]` with hIIM : IIMaj″ < 1/(2n) and the goal 0 ≤ 1/(2n) + nonnegs + (−1)·IIMaj″. If I rename, the consumer breaks — but the ii′-6-a2 Bn redefinition will rewrite marginTilde_convex's mIIM handling anyway (coefficient 1.5). For now, update the consumer to IIMaj_deriv2_lt_three so the CURRENT build stays green before the a2 edits... — wait, the current marginTilde_convex with the OLD mIIM (−1) uses `1/(2n) − IIMaj″ > 0` ⟸ IIMaj″ < 1/(2n) — with the lt_three bound (1/(3n)) that's STRONGER ✓ still works (1/(2n) − 1/(3n) > 0 ✓). So updating the consumer to IIMaj_deriv2_lt_three keeps the current proof working ✓.
Also update the doc comment at 1498-1501 (the ≤ 1.316 < 2 mention — should say ≤ 1.3155 < 4/3).
Let me update the consumer + the doc comment's tail, then build-check LiSkeleton.
Updating the convexity consumer to the strengthened lemma and the doc tail, then build-checking.
tool: Read ok
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean",
"offset": 1496,
"limit": 10
}
result 2026-08-26 10:56:40Z → 2026-08-26 10:56:40Z
{
"type": "text",
"file": {
"filePath": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean",
"content": "\nset_option maxHeartbeats 800000 in\n/-- [PROVED session 011; strengthened to 4/3 session 040 for the\nD-074 dog-leg's 1.5\u00b7IIMaj charge] The B\u0303\u2084 bracket bound (D-057 \u00a73):\nfor s \u2265 \u221a20,\n\u03c8\u0303\u2033(s) \u2212 \u03c8\u0303\u2032(s)/s < 2. Factor-monotone argument: the bound splits as\n4.56\u00b7[(s+1)/s]\u00b7[(b\u00b2s+b)e^{\u2212as}]\u00b7[1+e^{\u2212s/2}], three positive decreasing\nfactors; at s = \u221a20 the product is \u2264 1.316 < 2. -/\ntheorem iimaj_bracket_bound {s : \u211d} (hs : Real.sqrt 20 \u2264 s) :\n 4.56 * (2 * (-iimA * Real.exp (-iimA * s) - iimB * Real.exp (-iimB * s)) +",
"numLines": 10,
"startLine": 1496,
"totalLines": 2797
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raw content_json (database row)
[{"type":"thinking","thinking":"Now check the IIMaj_deriv2_lt consumer (line 2388's hIIM in marginTilde_convex) — it uses `IIMaj_deriv2_lt` which I just renamed to `IIMaj_deriv2_lt_three` with a different bound (1/(3n) instead of 1/(2n)). The marginTilde_convex's final linarith: `linarith [hIIM, hnn1..hnn9]` with hIIM : IIMaj″ < 1/(2n) and the goal 0 ≤ 1/(2n) + nonnegs + (−1)·IIMaj″. If I rename, the consumer breaks — but the ii′-6-a2 Bn redefinition will rewrite marginTilde_convex's mIIM handling anyway (coefficient 1.5). For now, update the consumer to IIMaj_deriv2_lt_three so the CURRENT build stays green before the a2 edits... — wait, the current marginTilde_convex with the OLD mIIM (−1) uses `1/(2n) − IIMaj″ > 0` ⟸ IIMaj″ < 1/(2n) — with the lt_three bound (1/(3n)) that's STRONGER ✓ still works (1/(2n) − 1/(3n) > 0 ✓). So updating the consumer to IIMaj_deriv2_lt_three keeps the current proof working ✓.\n\nAlso update the doc comment at 1498-1501 (the ≤ 1.316 < 2 mention — should say ≤ 1.3155 < 4/3).\n\nLet me update the consumer + the doc comment's tail, then build-check LiSkeleton.","signature":""},{"type":"text","text":"Updating the convexity consumer to the strengthened lemma and the doc tail, then build-checking."},{"type":"tool_use","id":"Read_540","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean","offset":1496,"limit":10},"extra_content":null}]