[{"type":"text","text":"Now the ψ-row literals in the convexity proof."},{"type":"tool_use","id":"Bash_205","name":"Bash","input":{"command":"cd D:/Python/Quantum && python - << 'EOF'\np = 'research/lean/NguyenRH1/NguyenRH1/LiSkeleton.lean'\nsrc = open(p, encoding='utf-8').read()\nsubs = [\n  # vF literal: mFblock coefficient -2 -> -4\n  (\"\"\"    have vF : deriv (deriv (mFblock F)) n =\n        (-2) * (psiOf F (Real.sqrt n + 1) / (4 * n)) := by\n      unfold mFblock\n      rw [deriv2_const_mul (-2) (hdd hCDFc) (hev hCDFc),\"\"\",\n   \"\"\"    have vF : deriv (deriv (mFblock F)) n =\n        (-4) * (psiOf F (Real.sqrt n + 1) / (4 * n)) := by\n      unfold mFblock\n      rw [deriv2_const_mul (-4) (hdd hCDFc) (hev hCDFc),\"\"\"),\n  # vTL1 literal\n  (\"\"\"    have vTL1 : deriv (deriv mTL1b) n = (-((8/3)*0.433 + 42)) *\"\"\",\n   \"\"\"    have vTL1 : deriv (deriv mTL1b) n = (-((8/3)*0.6 + 42)) *\"\"\"),\n  # vId literal\n  (\"\"\"    have vId : deriv (deriv mIdb) n = (-((8/3)*2.9 + 192)) *\n        (psiOf id (Real.sqrt n + 1) / (4 * n)) := by\n      unfold mIdb\n      have hCDidc : ContDiffOn ℝ 2 (fun m => id (Real.sqrt m + 1)) (Set.Ioi 20) :=\n        contDiffOn_id.comp contDiffOn_sqrt_shift (Set.mapsTo_univ _ _)\n      rw [show (fun m => -(8/3*2.9 + 192) * (Real.sqrt m + 1)) =\n          (fun m => -(8/3*2.9 + 192) * id (Real.sqrt m + 1)) from rfl,\"\"\",\n   \"\"\"    have vId : deriv (deriv mIdb) n = (-((8/3)*2.7 + 192)) *\n        (psiOf id (Real.sqrt n + 1) / (4 * n)) := by\n      unfold mIdb\n      have hCDidc : ContDiffOn ℝ 2 (fun m => id (Real.sqrt m + 1)) (Set.Ioi 20) :=\n        contDiffOn_id.comp contDiffOn_sqrt_shift (Set.mapsTo_univ _ _)\n      rw [show (fun m => -(8/3*2.7 + 192) * (Real.sqrt m + 1)) =\n          (fun m => -(8/3*2.7 + 192) * id (Real.sqrt m + 1)) from rfl,\"\"\"),\n  # hnn1 literal\n  (\"\"\"    have hnn1 : (0 : ℝ) ≤ -2 * (psiOf F (Real.sqrt n + 1) / (4 * n)) :=\"\"\",\n   \"\"\"    have hnn1 : (0 : ℝ) ≤ -4 * (psiOf F (Real.sqrt n + 1) / (4 * n)) :=\"\"\"),\n  # hnn2 literal\n  (\"\"\"    have hnn2 : (0 : ℝ) ≤ (-((8/3)*0.433 + 42)) *\"\"\",\n   \"\"\"    have hnn2 : (0 : ℝ) ≤ (-((8/3)*0.6 + 42)) *\"\"\"),\n  # hnn4 literal\n  (\"\"\"    have hnn4 : (0 : ℝ) ≤ (-((8/3)*2.9 + 192)) *\"\"\",\n   \"\"\"    have hnn4 : (0 : ℝ) ≤ (-((8/3)*2.7 + 192)) *\"\"\"),\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","description":"Update ψ-row literals in convexity proof"},"extra_content":null}]