← Session 29 — ii′-5e-v: circle bound (far-tail + series bounds)
thinking (387 chars)
`Real.pi_lt_d2 : π < 3.15` exists (d2-style naming). And `Real.pi_gt_three : 3 < π`. Fix: Real.pi_lt_315 → Real.pi_lt_d2 (two places: digamma_right_le and digamma_circle_le, both `Real.pi ≤ 45` bounds — actually with pi_lt_d2 : π < 3.15 I get π < 3.15 ≤ 45 ✓).
Now apply all the fixes: pi name, hdist's abs split, himsq's sq_abs, hRmin rewrite, hre_neg rewrite, hlt rewrite, h4 rewrite.
`Real.pi_lt_d2 : π < 3.15`. Now applying the full fix set to c-ii.
tool: Bash
input
{
"command": "cd \"D:/Python/Quantum/research/lean/NguyenRH1\" && python - << 'PYEOF'\np = 'NguyenRH1/LiCircleBound.lean'\nsrc = open(p, encoding='utf-8').read()\nsrc = src.replace('Real.pi_lt_315', 'Real.pi_lt_d2')\n# fix hdist abs split in digamma_right_le\nsrc = src.replace(''' rw [h2] at h1\n have h3 : (0 : \u211d) \u2264 (m : \u211d) := Nat.cast_nonneg _\n linarith [hwre, h1, h3]\n have h1 := norm_digamma_le_of_dist_nat (show (0 : \u211d) < 1 by norm_num)''', ''' rw [h2] at h1\n have h3 : (0 : \u211d) \u2264 (m : \u211d) := Nat.cast_nonneg _\n have h4 : |w.re + (m : \u211d)| = w.re + (m : \u211d) := abs_of_nonneg (by linarith [hwre, h3])\n linarith [hwre, h1, h3, h4]\n have h1 := norm_digamma_le_of_dist_nat (show (0 : \u211d) < 1 by norm_num)''')\n# fix hre/him2 simp calls\nsrc = src.replace(\"have hre : (s / 2).re = s.re / 2 := by simp [Complex.div_re, Complex.ofNat_re]\",\n \"have hre : (s / 2).re = s.re / 2 := by simp [Complex.div_re]\")\nsrc = src.replace(\"have him2 : (s / 2).im = s.im / 2 := by simp [Complex.div_im, Complex.ofNat_im]\",\n \"have him2 : (s / 2).im = s.im / 2 := by simp [Complex.div_im]\")\n# fix himsq\nsrc = src.replace(''' have himsq : s.im ^ 2 < 100 := by nlinarith [him10, abs_nonneg s.im]''',\n ''' have himsq : s.im ^ 2 < 100 := by\n have h1 : s.im ^ 2 = |s.im| ^ 2 := (sq_abs s.im).symm\n rw [h1]\n nlinarith [him10, abs_nonneg s.im]''')\nopen(p, 'w', encoding='utf-8').write(src)\nPYEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiCircleBound.lean 2>&1 | head -30",
"description": "Apply first round of c-ii fixes",
"timeout": 300000
}
raw content_json (database row)
[{"type":"thinking","thinking":"`Real.pi_lt_d2 : π < 3.15` exists (d2-style naming). And `Real.pi_gt_three : 3 < π`. Fix: Real.pi_lt_315 → Real.pi_lt_d2 (two places: digamma_right_le and digamma_circle_le, both `Real.pi ≤ 45` bounds — actually with pi_lt_d2 : π < 3.15 I get π < 3.15 ≤ 45 ✓).\n\nNow apply all the fixes: pi name, hdist's abs split, himsq's sq_abs, hRmin rewrite, hre_neg rewrite, hlt rewrite, h4 rewrite.","signature":""},{"type":"text","text":"`Real.pi_lt_d2 : π < 3.15`. Now applying the full fix set to c-ii."},{"type":"tool_use","id":"Bash_184","name":"Bash","input":{"command":"cd \"D:/Python/Quantum/research/lean/NguyenRH1\" && python - << 'PYEOF'\np = 'NguyenRH1/LiCircleBound.lean'\nsrc = open(p, encoding='utf-8').read()\nsrc = src.replace('Real.pi_lt_315', 'Real.pi_lt_d2')\n# fix hdist abs split in digamma_right_le\nsrc = src.replace(''' rw [h2] at h1\n have h3 : (0 : ℝ) ≤ (m : ℝ) := Nat.cast_nonneg _\n linarith [hwre, h1, h3]\n have h1 := norm_digamma_le_of_dist_nat (show (0 : ℝ) < 1 by norm_num)''', ''' rw [h2] at h1\n have h3 : (0 : ℝ) ≤ (m : ℝ) := Nat.cast_nonneg _\n have h4 : |w.re + (m : ℝ)| = w.re + (m : ℝ) := abs_of_nonneg (by linarith [hwre, h3])\n linarith [hwre, h1, h3, h4]\n have h1 := norm_digamma_le_of_dist_nat (show (0 : ℝ) < 1 by norm_num)''')\n# fix hre/him2 simp calls\nsrc = src.replace(\"have hre : (s / 2).re = s.re / 2 := by simp [Complex.div_re, Complex.ofNat_re]\",\n \"have hre : (s / 2).re = s.re / 2 := by simp [Complex.div_re]\")\nsrc = src.replace(\"have him2 : (s / 2).im = s.im / 2 := by simp [Complex.div_im, Complex.ofNat_im]\",\n \"have him2 : (s / 2).im = s.im / 2 := by simp [Complex.div_im]\")\n# fix himsq\nsrc = src.replace(''' have himsq : s.im ^ 2 < 100 := by nlinarith [him10, abs_nonneg s.im]''',\n ''' have himsq : s.im ^ 2 < 100 := by\n have h1 : s.im ^ 2 = |s.im| ^ 2 := (sq_abs s.im).symm\n rw [h1]\n nlinarith [him10, abs_nonneg s.im]''')\nopen(p, 'w', encoding='utf-8').write(src)\nPYEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiCircleBound.lean 2>&1 | head -30","description":"Apply first round of c-ii fixes","timeout":300000},"extra_content":null}]