← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)
thinking (92 chars)
All 26 declarations audit clean. Commit DL-5 with the D-074 log + NGUYEN.md + STATE updates.
All 26 audit clean. Committing DL-5.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\derivations\\D-074-dogleg-repair.md",
"old_string": "- 2026-08-25 (session 040): **DL-4 COMPLETE** \u2014 the far-right\n vertical drop in LiDogLeg.lean (+~160 lines; full build GREEN 8773\n jobs; audit: 23 decls, 3 standard axioms only, 0 sorryAx):",
"new_string": "- 2026-08-25 (session 040): **DL-5 COMPLETE** \u2014 the total\n right-horizontal bound in LiDogLeg.lean (+~210 lines; full build\n GREEN 8773 jobs; audit: 26 decls, 3 standard axioms only, 0\n sorryAx): **`hIntegral_Jlag_low_le_dogLegUpper`** (for n \u2265 16,\n T \u2208 [\u221an, \u221an+1], U = (3/2)T: \u2016HIntegral (Jlag n) 3 (2\u221an) T\u2016 \u2264\n ((\u221an+1)/2)(e^{5/2}+1)/2 + 8.38 + IIMaj/2 \u2014 the exact identity +\n the three piece bounds, U\u2212T = T/2 accounting),\n **`hIntegral_Jlag_low_neg_norm_le_dogLegUpper`** (the lower side by\n conjugation: Jlag_conj + `intervalIntegral.intervalIntegral_conj` \u2014\n the interval conj lemma is namespaced intervalIntegral.*), and\n `dogLegUpper_two_sides`. The full dog-leg is now PROVED in Lean\n with NO perimeter and NO assumption above T_cut. Banked: the\n `\u2191(\u2212T)\u00b7I` vs `\u2212(\u2191T)\u00b7I` cast-form discipline (rw needs the EXACT\n cast form `((-T : \u211d) : \u2102)`); intervalIntegral.intervalIntegral_conj\n for the interval-level conj map (the plain integral_conj pattern\n does not see through the interval wrapper); integral_congr goals\n are beta-redexes (dsimp/show first). Next: ii\u2032-6-a2 (the Bn\n dog-leg redefinition at the E-034-validated constants:\n DogLegRight(n) = ((\u221an+1)/2)(e^{5/2}+1)/2 + 8.38 + IIMaj(n)/2 per\n side, \u00d72 sides \u2014 margins 13 160/88 911/2.458e26 at 8e4/10\u2075/N\u2081).\n- 2026-08-25 (session 040): **DL-4 COMPLETE** \u2014 the far-right\n vertical drop in LiDogLeg.lean (+~160 lines; full build GREEN 8773\n jobs; audit: 23 decls, 3 standard axioms only, 0 sorryAx):"
}
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\NGUYEN.md",
"old_string": " \u2192 DL-5 (total right-horizontal bound + lower side by conjugation).",
"new_string": " \u2192 DL-5 COMPLETE (session 040, LiDogLeg.lean +~210 lines, build\n 8773, audit clean): **hIntegral_Jlag_low_le_dogLegUpper** +\n **hIntegral_Jlag_low_neg_norm_le_dogLegUpper** (both \u2264\n ((\u221an+1)/2)(e^{5/2}+1)/2 + 8.38 + IIMaj/2 for T \u2208 [\u221an, \u221an+1],\n U = (3/2)T) + dogLegUpper_two_sides \u2014 the full dog-leg PROVED\n in Lean, no perimeter, nothing above T_cut."
}
raw content_json (database row)
[{"type":"thinking","thinking":"All 26 declarations audit clean. Commit DL-5 with the D-074 log + NGUYEN.md + STATE updates.","signature":""},{"type":"text","text":"All 26 audit clean. Committing DL-5."},{"type":"tool_use","id":"Edit_413","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\derivations\\D-074-dogleg-repair.md","old_string":"- 2026-08-25 (session 040): **DL-4 COMPLETE** — the far-right\n vertical drop in LiDogLeg.lean (+~160 lines; full build GREEN 8773\n jobs; audit: 23 decls, 3 standard axioms only, 0 sorryAx):","new_string":"- 2026-08-25 (session 040): **DL-5 COMPLETE** — the total\n right-horizontal bound in LiDogLeg.lean (+~210 lines; full build\n GREEN 8773 jobs; audit: 26 decls, 3 standard axioms only, 0\n sorryAx): **`hIntegral_Jlag_low_le_dogLegUpper`** (for n ≥ 16,\n T ∈ [√n, √n+1], U = (3/2)T: ‖HIntegral (Jlag n) 3 (2√n) T‖ ≤\n ((√n+1)/2)(e^{5/2}+1)/2 + 8.38 + IIMaj/2 — the exact identity +\n the three piece bounds, U−T = T/2 accounting),\n **`hIntegral_Jlag_low_neg_norm_le_dogLegUpper`** (the lower side by\n conjugation: Jlag_conj + `intervalIntegral.intervalIntegral_conj` —\n the interval conj lemma is namespaced intervalIntegral.*), and\n `dogLegUpper_two_sides`. The full dog-leg is now PROVED in Lean\n with NO perimeter and NO assumption above T_cut. Banked: the\n `↑(−T)·I` vs `−(↑T)·I` cast-form discipline (rw needs the EXACT\n cast form `((-T : ℝ) : ℂ)`); intervalIntegral.intervalIntegral_conj\n for the interval-level conj map (the plain integral_conj pattern\n does not see through the interval wrapper); integral_congr goals\n are beta-redexes (dsimp/show first). Next: ii′-6-a2 (the Bn\n dog-leg redefinition at the E-034-validated constants:\n DogLegRight(n) = ((√n+1)/2)(e^{5/2}+1)/2 + 8.38 + IIMaj(n)/2 per\n side, ×2 sides — margins 13 160/88 911/2.458e26 at 8e4/10⁵/N₁).\n- 2026-08-25 (session 040): **DL-4 COMPLETE** — the far-right\n vertical drop in LiDogLeg.lean (+~160 lines; full build GREEN 8773\n jobs; audit: 23 decls, 3 standard axioms only, 0 sorryAx):"},"extra_content":null},{"type":"tool_use","id":"Edit_414","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\NGUYEN.md","old_string":" → DL-5 (total right-horizontal bound + lower side by conjugation).","new_string":" → DL-5 COMPLETE (session 040, LiDogLeg.lean +~210 lines, build\n 8773, audit clean): **hIntegral_Jlag_low_le_dogLegUpper** +\n **hIntegral_Jlag_low_neg_norm_le_dogLegUpper** (both ≤\n ((√n+1)/2)(e^{5/2}+1)/2 + 8.38 + IIMaj/2 for T ∈ [√n, √n+1],\n U = (3/2)T) + dogLegUpper_two_sides — the full dog-leg PROVED\n in Lean, no perimeter, nothing above T_cut."},"extra_content":null}]