← Session 33 — ii′-3b/3c crux + F-D finding; Lagarias letter package
thinking (227 chars)
Audit saved: 23 lines, 0 sorryAx. Now the archive updates. First the journal entry — check the format of journal-037 briefly for consistency, then write session-038.md. I already have journal-037's structure. Write the journal.
Audit clean (23 decls, 0 sorryAx). Writing the session-038 journal.
tool: Write ok
input
{
"file_path": "D:\\Python\\Quantum\\research\\journal\\session-038.md",
"content": "# Session 038 (2026-08-24) \u2014 ii\u2032-3b COMPLETE\n\n## Goal\nFinish ii\u2032-3b (the contour moments (M): sigmaP k = \u2212gFun^{(k\u22121)}(0)/(k\u22121)!,\nD-070 route \u2014 from 5e's `partialFraction_identity` by pure algebra + series\ncalculus, no contours). Session 037 banked \u00a71\u2013\u00a74 + the k = 1 capstone; this\nsession built \u00a75 (termwise iterated derivation at 0, k \u2265 2) and \u00a76 (the\nunified capstone), root-imported LiTightR + LiMoments, full build + audit.\n\n## What was done\n\n**LiMoments.lean \u00a75** (~190 lines):\n- `iteratedDeriv_zpow_neg_one` \u2014 the positive form of the zpow iterated\n derivative from LiDigamma's `iteratedDeriv_neg_zpow_neg_one_add` via\n `iteratedDeriv_neg` (neg_neg needed `.symm` in the funext; the final\n sign normalization needed `simp only [neg_mul, neg_neg]` \u2014 the neg is\n buried inside the product, bare `neg_neg` can't fire).\n- `iteratedDeriv_seriesTerm` \u2014 (d/ds)^j [mult\u00b7(1/(s\u2212\u03c1)+1/\u03c1)] =\n mult\u00b7(\u22121)^j\u00b7j!\u00b7(s\u2212\u03c1)^{\u2212j\u22121} (j \u2265 1). Via the zpow rewrite\n (funext + simp only [one_div, zpow_neg_one, sub_eq_add_neg]),\n `iteratedDeriv_const_mul` (ContDiffAt from AnalyticAt.contDiffAt),\n the Pi.add `hsplit := rfl` bridge before `iteratedDeriv_add`,\n `iteratedDeriv_const` + if_neg, and a `sub_eq_add_neg` bridge to the\n (s + \u2212\u03c1) form of the zpow lemma.\n- `seriesTerm_deriv_summableLocallyUniformlyOn` \u2014 the M-test on\n ball(0, \u03b4/2): dominator C_j\u00b7(mult/\u2016\u03c1\u2016\u00b2) with\n C_j = j!\u00b72^{j+1}\u00b7(1/\u03b4)^{j\u22121} (\u2016s\u2212\u03c1\u2016 \u2265 \u2016\u03c1\u2016/2 from the avoiding ball;\n 1/\u2016\u03c1\u2016^{j\u22121} \u2264 (1/\u03b4)^{j\u22121}; the h1/h2/h3 chain: one_div comparison,\n div_pow+inv_div for the (\u2016\u03c1\u2016/2)-power, pow_add+mul_inv for the\n j+1 = (j\u22121)+2 split). The norm chain is the LiDigamma:735\u2013746 pattern\n (3\u00d7 norm_mul + RCLike.norm_natCast \u00d72 + hsign + norm_zpow + the\n exponent rewrite), then a 3-step calc (mul_assoc bridge, the hkey\n multiplication, closing `ring`).\n- `iteratedDeriv_seriesFun_zero` \u2014 the LiDigamma:749\u2013785\n `iteratedDerivWithin_tsum` call pattern verbatim on ball(0, \u03b4/2):\n seriesSummable everywhere; the M-test per derivative order; the side\n differentiability by cases (k = 0: analyticAt const\u00b7(1/(z\u2212\u03c3)+1/\u03c3);\n k \u2265 1: eventuallyEq with the closed form + hasDerivAt_zpow \u2218 rfl).\n Local `pole_free` (\u2016\u03c3\u2016 \u2212 \u2016t\u2016 \u2264 \u2016t\u2212\u03c3\u2016 via norm_sub_norm_le +\n norm_sub_rev + linarith).\n\n**LiMoments.lean \u00a76** (~100 lines):\n- `gFun_eventuallyEq_zero` \u2014 (G) upgraded from \ud835\udcdd[\u2260] 0 to \ud835\udcdd 0 via\n `eventually_nhdsWithin_iff` + by_cases (at 0: gFun_zero + seriesFun_zero).\n- **`sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC : ZeroCountProp)`** \u2014\n THE CAPSTONE: sigmaP k = \u2212(iteratedDeriv (k\u22121) gFun 0)/(k\u22121)!, all\n k \u2265 1. k = 1 branch: Nat.add_sub_cancel + iteratedDeriv_zero + the\n 0! = 1 fold + sigmaP_one_eq_neg_gFun_zero. k \u2265 2 branch:\n iteratedDeriv_congr_of_eventuallyEq \u2192 the Pi.add hsplit \u2192\n iteratedDeriv_add \u2192 iteratedDeriv_const if_neg \u2192\n iteratedDeriv_seriesFun_zero \u2192 the per-term sign algebra\n (e1: (0\u2212\u03c1)^{\u2212k\u22121} = (\u22121)^{k+1}(1/\u03c1)^{k+1} via zpow_neg/zpow_natCast/\n neg_pow/mul_inv + inv_eq_of_mul_eq_one_right + \u2190 inv_pow + one_div;\n hsign: (\u22121)^k\u00b7(\u22121)^{k+1} = \u22121 via pow_add/pow_mul; e2 ring regroup)\n \u2192 tsum_congr + tsum_neg + neg_neg + tsum_mul_left +\n \u2190 sigmaP_eq_unpaired \u2192 field_simp with k! \u2260 0. FIRST-PASS GREEN.\n\n**Closure**: LiTightR + LiMoments root-imported (root header updated);\nfull build GREEN (8770 jobs, LiMoments 20 s); AuditSession038.lean +\naudit-session038-axioms.txt \u2014 23 declarations, ALL:\n[propext, Classical.choice, Quot.sound] only, 0 sorryAx.\n\n**ii\u2032-3b \u2192 COMPLETE.** Perimeter of the capstone: ZeroCountProp ONLY\n(5f's hZC2/hNLZ not needed for the moments, per D-070).\n\n## Banked gotchas (this session)\n\n- **Factorial `!` notation is `scoped notation` in namespace Nat** \u2014\n needs `open scoped Nat` (LiDigamma has it; LiMoments didn't; the parse\n error \"unexpected token ':'; expected no space before or term\" points\n at the `!` and looks like a spacing problem but is a MISSING OPEN).\n- **`Summable.mul_left` unification loop**: the dominator MUST be written\n `C * (D \u03c1)` (constant first) to match `fun i => a * f i` syntactically;\n `D \u03c1 * C` sends the anonymous-constructor refine into an 800k-heartbeat\n whnf loop (the mismatch only shows up when u and the mul_left proof are\n elaborated together \u2014 bisect with dominator-only/mulleft-only sorries).\n- `rw [seriesFun]` FAILS when seriesFun appears UNAPPLIED (e.g. inside\n `iteratedDeriv j seriesFun 0`) \u2014 equation-theorem matching needs the\n applied form; use a `show` with the beta-expanded lambda instead\n (defeq unfolds the def).\n- `norm_sub_norm_le (a) (b) : \u2016a\u2016 \u2212 \u2016b\u2016 \u2264 \u2016a \u2212 b\u2016` in this Mathlib \u2014 NO\n abs on the LHS (the abs_le.mp detour errors; use it directly).\n- Don't `rw [Metric.mem_ball, ...] at h` a membership hypothesis you\n still need as membership \u2014 derive a separate norm hypothesis with\n `simpa only [Metric.mem_ball, dist_zero_right] using h`.\n- `(neg_neg _).symm` for the funext direction (goal `f = -(-f)`).\n- Buried-neg normalization: `simp only [neg_mul, neg_neg]` (bare\n `neg_neg` can't fire when the inner neg is a factor of a product).\n- `iteratedDeriv_add` needs the Pi.add form \u2014 bridge with\n `have hsplit : (fun s => F s + G s) = (fun s => F s) + (fun s => G s)\n := rfl` before the rw (the pointwise lambda doesn't match the lemma's\n f + g pattern).\n- The calc-step `2^(j+1) * ((\u03b4^(j\u22121))\u207b\u00b9 * X) = 2^(j+1) * (1/\u03b4)^(j\u22121) * X`\n closes by `rw [div_pow, one_pow, one_div, mul_assoc]` (the trailing\n mul_assoc fixes the reassociation; rw auto-closes by rfl).\n\n## Files\n\n- research/lean/NguyenRH1/NguyenRH1/LiMoments.lean (\u00a75/\u00a76 added;\n file now ~1020 lines, GREEN)\n- research/lean/NguyenRH1/NguyenRH1.lean (LiTightR + LiMoments\n root-imported; header updated)\n- research/lean/NguyenRH1/AuditSession038.lean +\n audit-session038-axioms.txt (23 decls, 3 standard axioms only)\n- research/lean/NguyenRH1/Scratch.lean (lemma probes; session-037\n results preserved in audit-session037-axioms.txt)\n\n## Next\n\nii\u2032-3c (the (4.10-a) assembly, D-066 \u00a72): \u03c4_j = c_j + (\u22121)\u02b2\u03c3_{j+1} \u2212\n(\u22121)\u02b2 \u2014 needs the FE derivative relation gFun^{(k\u22121)}(0) =\n(\u22121)^k\u00b7gFun^{(k\u22121)}(1) (new but small: xiL_one_sub + iteratedDeriv comp\nmachinery) + the ii\u2032-3a pieces (A: iteratedDeriv_logDeriv_Gamma\u211d,\nB: iteratedDeriv_hLiExt) + the capstone of 3b \u2192 the crux identity\nSf(n) = Res\u2081(n). Then ii\u2032-6 (L0 assembly incl. D-069 Finding 2's H(T)\nnear-sum repair) \u2192 ii\u2032-7 (closure).\n"
}
result 2026-08-25 03:04:17Z → 2026-08-29 04:29:06Z
{
"type": "update",
"filePath": "D:\\Python\\Quantum\\web\\logs\\_cleanup_fb.py",
"content": "import django\ndjango.setup()\nfrom dashboard.models import Feedback\nimport pathlib\nimport json\n\nqs = Feedback.objects.filter(text=\"live email-path test (will be cleaned up)\")\nids = list(qs.values_list(\"id\", flat=True))\nprint(\"found test rows:\", len(ids))\nqs.delete()\nd = pathlib.Path(\"app/web/feedback\")\nremoved = []\nfor f in d.glob(\"FB-*.json\"):\n if json.loads(f.read_text()).get(\"id\") in ids:\n removed.append(f.name)\n f.unlink()\nprint(\"removed json:\", removed)\nprint(\"CLEANUP_DONE\")\n",
"structuredPatch": [],
"originalFile": "import django\ndjango.setup()\nfrom dashboard.models import Feedback\nimport pathlib\nimport json\n\nqs = Feedback.objects.filter(text=\"live email-path test (will be cleaned up)\")\nids = list(qs.values_list(\"id\", flat=True))\nprint(\"found test rows:\", len(ids))\nqs.delete()\nd = pathlib.Path(\"app/web/feedback\")\nremoved = []\nfor f in d.glob(\"FB-*.json\"):\n if json.loads(f.read_text()).get(\"id\") in ids:\n removed.append(f.name)\n f.unlink()\nprint(\"removed json:\", removed)\nprint(\"CLEANUP_DONE\")\n",
"autoRead": false
}
raw content_json (database row)
[{"type":"thinking","thinking":"Audit saved: 23 lines, 0 sorryAx. Now the archive updates. First the journal entry — check the format of journal-037 briefly for consistency, then write session-038.md. I already have journal-037's structure. Write the journal.","signature":""},{"type":"text","text":"Audit clean (23 decls, 0 sorryAx). Writing the session-038 journal."},{"type":"tool_use","id":"Write_74","name":"Write","input":{"file_path":"D:\\Python\\Quantum\\research\\journal\\session-038.md","content":"# Session 038 (2026-08-24) — ii′-3b COMPLETE\n\n## Goal\nFinish ii′-3b (the contour moments (M): sigmaP k = −gFun^{(k−1)}(0)/(k−1)!,\nD-070 route — from 5e's `partialFraction_identity` by pure algebra + series\ncalculus, no contours). Session 037 banked §1–§4 + the k = 1 capstone; this\nsession built §5 (termwise iterated derivation at 0, k ≥ 2) and §6 (the\nunified capstone), root-imported LiTightR + LiMoments, full build + audit.\n\n## What was done\n\n**LiMoments.lean §5** (~190 lines):\n- `iteratedDeriv_zpow_neg_one` — the positive form of the zpow iterated\n derivative from LiDigamma's `iteratedDeriv_neg_zpow_neg_one_add` via\n `iteratedDeriv_neg` (neg_neg needed `.symm` in the funext; the final\n sign normalization needed `simp only [neg_mul, neg_neg]` — the neg is\n buried inside the product, bare `neg_neg` can't fire).\n- `iteratedDeriv_seriesTerm` — (d/ds)^j [mult·(1/(s−ρ)+1/ρ)] =\n mult·(−1)^j·j!·(s−ρ)^{−j−1} (j ≥ 1). Via the zpow rewrite\n (funext + simp only [one_div, zpow_neg_one, sub_eq_add_neg]),\n `iteratedDeriv_const_mul` (ContDiffAt from AnalyticAt.contDiffAt),\n the Pi.add `hsplit := rfl` bridge before `iteratedDeriv_add`,\n `iteratedDeriv_const` + if_neg, and a `sub_eq_add_neg` bridge to the\n (s + −ρ) form of the zpow lemma.\n- `seriesTerm_deriv_summableLocallyUniformlyOn` — the M-test on\n ball(0, δ/2): dominator C_j·(mult/‖ρ‖²) with\n C_j = j!·2^{j+1}·(1/δ)^{j−1} (‖s−ρ‖ ≥ ‖ρ‖/2 from the avoiding ball;\n 1/‖ρ‖^{j−1} ≤ (1/δ)^{j−1}; the h1/h2/h3 chain: one_div comparison,\n div_pow+inv_div for the (‖ρ‖/2)-power, pow_add+mul_inv for the\n j+1 = (j−1)+2 split). The norm chain is the LiDigamma:735–746 pattern\n (3× norm_mul + RCLike.norm_natCast ×2 + hsign + norm_zpow + the\n exponent rewrite), then a 3-step calc (mul_assoc bridge, the hkey\n multiplication, closing `ring`).\n- `iteratedDeriv_seriesFun_zero` — the LiDigamma:749–785\n `iteratedDerivWithin_tsum` call pattern verbatim on ball(0, δ/2):\n seriesSummable everywhere; the M-test per derivative order; the side\n differentiability by cases (k = 0: analyticAt const·(1/(z−σ)+1/σ);\n k ≥ 1: eventuallyEq with the closed form + hasDerivAt_zpow ∘ rfl).\n Local `pole_free` (‖σ‖ − ‖t‖ ≤ ‖t−σ‖ via norm_sub_norm_le +\n norm_sub_rev + linarith).\n\n**LiMoments.lean §6** (~100 lines):\n- `gFun_eventuallyEq_zero` — (G) upgraded from 𝓝[≠] 0 to 𝓝 0 via\n `eventually_nhdsWithin_iff` + by_cases (at 0: gFun_zero + seriesFun_zero).\n- **`sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC : ZeroCountProp)`** —\n THE CAPSTONE: sigmaP k = −(iteratedDeriv (k−1) gFun 0)/(k−1)!, all\n k ≥ 1. k = 1 branch: Nat.add_sub_cancel + iteratedDeriv_zero + the\n 0! = 1 fold + sigmaP_one_eq_neg_gFun_zero. k ≥ 2 branch:\n iteratedDeriv_congr_of_eventuallyEq → the Pi.add hsplit →\n iteratedDeriv_add → iteratedDeriv_const if_neg →\n iteratedDeriv_seriesFun_zero → the per-term sign algebra\n (e1: (0−ρ)^{−k−1} = (−1)^{k+1}(1/ρ)^{k+1} via zpow_neg/zpow_natCast/\n neg_pow/mul_inv + inv_eq_of_mul_eq_one_right + ← inv_pow + one_div;\n hsign: (−1)^k·(−1)^{k+1} = −1 via pow_add/pow_mul; e2 ring regroup)\n → tsum_congr + tsum_neg + neg_neg + tsum_mul_left +\n ← sigmaP_eq_unpaired → field_simp with k! ≠ 0. FIRST-PASS GREEN.\n\n**Closure**: LiTightR + LiMoments root-imported (root header updated);\nfull build GREEN (8770 jobs, LiMoments 20 s); AuditSession038.lean +\naudit-session038-axioms.txt — 23 declarations, ALL:\n[propext, Classical.choice, Quot.sound] only, 0 sorryAx.\n\n**ii′-3b → COMPLETE.** Perimeter of the capstone: ZeroCountProp ONLY\n(5f's hZC2/hNLZ not needed for the moments, per D-070).\n\n## Banked gotchas (this session)\n\n- **Factorial `!` notation is `scoped notation` in namespace Nat** —\n needs `open scoped Nat` (LiDigamma has it; LiMoments didn't; the parse\n error \"unexpected token ':'; expected no space before or term\" points\n at the `!` and looks like a spacing problem but is a MISSING OPEN).\n- **`Summable.mul_left` unification loop**: the dominator MUST be written\n `C * (D ρ)` (constant first) to match `fun i => a * f i` syntactically;\n `D ρ * C` sends the anonymous-constructor refine into an 800k-heartbeat\n whnf loop (the mismatch only shows up when u and the mul_left proof are\n elaborated together — bisect with dominator-only/mulleft-only sorries).\n- `rw [seriesFun]` FAILS when seriesFun appears UNAPPLIED (e.g. inside\n `iteratedDeriv j seriesFun 0`) — equation-theorem matching needs the\n applied form; use a `show` with the beta-expanded lambda instead\n (defeq unfolds the def).\n- `norm_sub_norm_le (a) (b) : ‖a‖ − ‖b‖ ≤ ‖a − b‖` in this Mathlib — NO\n abs on the LHS (the abs_le.mp detour errors; use it directly).\n- Don't `rw [Metric.mem_ball, ...] at h` a membership hypothesis you\n still need as membership — derive a separate norm hypothesis with\n `simpa only [Metric.mem_ball, dist_zero_right] using h`.\n- `(neg_neg _).symm` for the funext direction (goal `f = -(-f)`).\n- Buried-neg normalization: `simp only [neg_mul, neg_neg]` (bare\n `neg_neg` can't fire when the inner neg is a factor of a product).\n- `iteratedDeriv_add` needs the Pi.add form — bridge with\n `have hsplit : (fun s => F s + G s) = (fun s => F s) + (fun s => G s)\n := rfl` before the rw (the pointwise lambda doesn't match the lemma's\n f + g pattern).\n- The calc-step `2^(j+1) * ((δ^(j−1))⁻¹ * X) = 2^(j+1) * (1/δ)^(j−1) * X`\n closes by `rw [div_pow, one_pow, one_div, mul_assoc]` (the trailing\n mul_assoc fixes the reassociation; rw auto-closes by rfl).\n\n## Files\n\n- research/lean/NguyenRH1/NguyenRH1/LiMoments.lean (§5/§6 added;\n file now ~1020 lines, GREEN)\n- research/lean/NguyenRH1/NguyenRH1.lean (LiTightR + LiMoments\n root-imported; header updated)\n- research/lean/NguyenRH1/AuditSession038.lean +\n audit-session038-axioms.txt (23 decls, 3 standard axioms only)\n- research/lean/NguyenRH1/Scratch.lean (lemma probes; session-037\n results preserved in audit-session037-axioms.txt)\n\n## Next\n\nii′-3c (the (4.10-a) assembly, D-066 §2): τ_j = c_j + (−1)ʲσ_{j+1} −\n(−1)ʲ — needs the FE derivative relation gFun^{(k−1)}(0) =\n(−1)^k·gFun^{(k−1)}(1) (new but small: xiL_one_sub + iteratedDeriv comp\nmachinery) + the ii′-3a pieces (A: iteratedDeriv_logDeriv_Gammaℝ,\nB: iteratedDeriv_hLiExt) + the capstone of 3b → the crux identity\nSf(n) = Res₁(n). Then ii′-6 (L0 assembly incl. D-069 Finding 2's H(T)\nnear-sum repair) → ii′-7 (closure).\n"},"extra_content":null}]