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  "file_path": "D:\\Python\\Quantum\\STATE.md",
  "content": "# STATE.md \u2014 NGUYEN-RH-1 RESUME POINT\n# \u2b50 READ THIS FIRST at the start of every session.\nLast updated: 2026-08-18 | Session: 005 (stopped mid-A3-root-cause; user break)\n\n## CURRENT POSITION\n\u2714 PHASE 0 COMPLETE. \u2714 PHASE 1 COMPLETE (Track A monitoring mode).\nPHASE 3 (Track C): 3.1 mapped, 3.2 arithmetic side DONE to n=2000\n(E-011/R-001), 3.3 CLOSED (D-021 \u2192 G-003, E-012), 3.4a/b/c COMPLETE.\nSuzuki line: Q-S3c ATTACKED (E-016, D-024 \u2014 partial): Herglotz \u03c1_W at\n\u03b8=\u03c0 vs \u03c1_F; V1/V2/V4 pass, **V3 (zero-Poisson reconstruction) fails\nrel ~0.3 \u2014 root cause open**. Findings: \u03b8=\u03c0 zeros REAL; z\u2081(\u03c0)\u00b7a \u2248 4.5\nstiff law (NOT rigid half-shift); no \u03b8=\u03c0 zero in (0,\u03c0/a); raw-L2\n\u03b8=\u03c0\u2248\u03b8=0 (plateau-dominated; need small-y-weighted metric).\n\n## ACTIVE PLAN (user-approved 2026-08-18): do ALL queued items one by one\nOrder: A3 \u2192 A1 \u2192 A2 \u2192 C \u2192 B; D runs in background.\n  A3 = Q-S3c Herglotz diagnostic \u2014 IN PROGRESS (V3 root cause)\n  A1 = Q-S3a analytic v\u00b1 \u2192 A_\u221e^{-1}e^{\u00b1\u00b7} convergence\n  A2 = Q-S3b prime-sum backend redesign \u2192 a ~ 12\u201314\n  C  = \u03be\u2032-world bandwidth-one ceiling (LawN256 analogue)\n  B  = T4b scoping (node mechanism on \u03be\u207d\u1d4f\u207e)\n  D  = E-015 Li n\u22643000 detached run\n\n## IN PROGRESS\n- **E-015 (item D) RUNNING detached, PID 23300** (n_max=3000, dps=1450;\n  ETA ~1.5\u20132 h from 2026-08-18 launch; log:\n  research/numerics/data/E-015-run.log). If machine was shut down:\n  rerun `./.venv/Scripts/python.exe research/numerics/scripts/\n  E-015-li-coefficients-n3000.py --force` DETACHED WITH SANDBOX\n  DISABLED (sandbox blocks multiprocessing DuplicateHandle \u2014 WinError 5;\n  session-005 lesson). After completion: db.py log-experiment E-015\n  (registration deferred \u2014 CSV didn't exist at session end).\n\n## NEXT ACTION\n1. Root-cause E-016 V3 (D-024 \u00a74): three candidates \u2014 (a) Im \u03ba \u2260 0\n   (measure directly: Im(W\u2032/W)(0)); (b) low-zero bookkeeping (count 381\n   vs lattice 382 at a=4); (c) large-z zero-finder float64 noise in\n   recon (test: recon with zeros \u2264 60 + EM tail from 60; if y=20\n   mismatch changes materially, (c) confirmed).\n2. Then resume order: A1 \u2192 A2 \u2192 C \u2192 B; collect/register E-015.\n\n## COMPLETED (Session 005)\n- [x] E-015 created (E-011 method, n_max=3000, own output files) +\n      launched detached\n- [x] E-016 created + run: Herglotz fine structure \u03b8=\u03c0 vs F\n      (V1/V2/V4 pass; V3 fail recorded honestly in JSON)\n- [x] D-024 analysis (partial); E-016 + D-024 registered in research.db\n- [x] Bring-up bugs fixed in E-016: hat-derivative factor h; \u03be(1)=\u00bd\n      removable pole; flint NaN at s=1; zero-finder replaced by exact\n      real-gauge brentq (c=1 \u27f9 W pure imaginary on \u211d at \u03b8=\u03c0)\n\n## OPEN CONJECTURES / THREADS\n- Q-S1 (D-019 \u00a73): L\u00b2\u2192uniform lifting for Cor 1.6 (Phase 4 candidate).\n- Q-S2: \u210b(T_a) as de Branges-type space (Phase 2.4 link, alive).\n- Q-S3: \u03b8(a) identification \u2014 \u03b8=\u03c0 candidate (D-023); Q-S3c attacked\n  (D-024): stiff z\u2081\u00b7a\u22484.5 law at \u03b8=\u03c0 is a NEW constraint any \u03b8(a)\n  theory must explain; density-collapse transition must start at a\u226b10;\n  Q-S3a/b queued.\n- Q6 uncertainty \u2194 bandwidth-one ceiling bridge (D-001); Q14 Gutzwiller\n  (Phase 2); T2 Christoffel/CMS (D-006); T4b higher derivatives (D-022\n  \u00a75); \u03be\u2032-world ceiling (LawN256 analogue).\n- 3.2 next: E-015 (n\u22643000) in flight; then asymptotic attack; optional\n  Arb ball-arithmetic certification.\nCLOSED: T1 (D-010/E-004), T3 (D-009), T4 (D-022), T5 (\u2192G-001),\n3.4a (D-016), 3.3 (\u2192G-003).\n\n## BLOCKERS\n(none \u2014 E-016 V3 is an open problem, not a blocker; other items proceed)\n\n## HANDOFF NOTES\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n  list (no --session flag on add-derivation; log-experiment REQUIRES the\n  CSV to exist \u2014 sha256'd at registration).\n- venv interpreter: ./.venv/Scripts/python.exe (NOT ./venv/...).\n- git commits need: git -c user.name=\"NGUYEN-RH-1\" -c\n  user.email=\"research@local\" commit (config must NOT be modified).\n- Break prompt rule active: ask before long runs, especially near 5:00 PM.\n- Hardware: Ryzen 9 7945HX 16c/32t, 64GB RAM, RTX 4090 Laptop 16GB.\n- venv packages: pypdf, sympy 1.14, mpmath 1.3, numpy 2.5.2, scipy 1.18,\n  flint (python-flint; use for ALL zeta/Stieltjes \u2014 mpmath's are broken\n  beyond ~16 digits in this env; mp.zetazero is safe; real-axis mp.zeta\n  at dps 40 verified to 8.8e-17 vs flint at s=1.5/10.5/20.5 \u2014 E-016).\n- LONG RUNS: CLI kills Bash tasks at ~2 min default (10 min max). Launch\n  DETACHED (session-004 pattern) **with sandbox DISABLED** (session-005:\n  sandboxed detached launch dies \u2014 multiprocessing spawn DuplicateHandle\n  WinError 5), then poll the log file.\n- flint.acb.stieltjes(k) scales ~k\u00b3 (28s @ k=2000, 3530 bits); full\n  0..3000 sweep ETA ~1.5\u20132 h on 14 Pool workers.\n- E-009b eigensolver floor: eigenvalues < ~1e-11 at h=5e-3 are at/below\n  backward-error noise \u2014 quote as upper bounds only.\n- E-010/E-016 build cache pattern: (a,h) builds reused; sieve to e^20\n  covers a \u2264 10 (~15s).\n- E-016: at \u03b8=\u03c0 the exact real gauge is g(z) = z Im Vp \u2212 Re Vp\n  (c=\u221a(n\u208a/n\u208b)=1 exactly by mirror symmetry) \u2014 brentq on sign changes;\n  do NOT use |W|-minima+polish (noisy at large z).\n"
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  "filePath": "D:\\Python\\Quantum\\research\\journal\\session-014.md",
  "content": "# Session 014 \u2014 2026-08-21 \u2014 Tier ii\u2032 launched: design + two discoveries\n\n## Directive\nUser chose option (a): do tier ii\u2032 (close SfBoundProp in Lean) BEFORE\nsubmission, with Paper A frozen and submittable at all times. Freeze\nprotocol in force: no edits to paperA.tex/paperB.tex/draft.tex/\nreferences.bib until ii\u2032-7; no edits to existing Lean proofs except the\nliCoeff correctness fix (below, flagged); commit at every sub-stage.\n\n## Work done (sub-stage ii\u2032-0: design \u2192 D-064)\n1. Baseline verified clean (git: only untracked LaTeX artifacts).\n2. Two parallel inventory agents surveyed: (i) vendored residue/\n   meromorphic API; (ii) Zeta23 zero infrastructure + NguyenRH1 defs +\n   Mathlib zeta/digamma/Jensen/Borel\u2013Carath\u00e9odory surface.\n3. Read liCoeff/Sf/perimeter defs, D-036, D-056, D-037 (full), and the\n   primary source (Lagarias math/0404394 \u00a74\u20136, archived PDF).\n4. Axiom-checked all planned Zeta23 dependencies LIVE: zero_sum_inv_sq,\n   zeta_local_zero_count, zeta_reflect_zero, zeta_mult_reflect,\n   RectangleIntegral'_eq_sumResiduesIn, ResidueMult, logDerivResidue,\n   riemannZetaLogDerivResidue \u2014 ALL 3 standard axioms only.\n5. Settled the exact identity chain NUMERICALLY (dps 40\u201350, mpmath +\n   E-021 zero cache; see D-064 \u00a73 table).\n6. Wrote D-064 (design doc: discoveries, routes R1\u2013R5, lemma graph,\n   revised sub-stage map ii\u2032-1a..7). Registered in index.md + db.\n\n## DISCOVERY 1 \u2014 liCoeff encoding defect (correctness, not cosmetic)\n`liCoeff` (LiSkeleton.lean:39) is an unordered tsum whose family is NOT\nSummable for any n \u2265 1 (summand ~ n/|\u03b3|, \u03a3 mult/|\u03c1| = \u221e by RvM).\nTherefore liCoeff n = 0 (junk), making `LiVerifiedUpTo` FALSE and\n`SfBoundProp` FALSE as encoded (at n = 10\u2075: |Sf| \u2265 432 501 > 347 000\n\u2265 Bn by the certified LiBasePoints bounds). The session-012 theorems\nare vacuously true; the session-013 audit could not see this (it checks\naxioms, not hypothesis truth). Paper A's mathematics is unaffected \u2014\npure encoding defect. FIX DESIGNED (D-064 \u00a71): paired symmetric form\n(manifestly real, absolutely summable via pair bound |pair| \u2264\nC(n)\u00b7mult/|\u03c1|\u00b2 + Zeta23's proved `zero_sum_inv_sq`). Scheduled as\nsub-stage ii\u2032-1a (first executable item).\n\n## DISCOVERY 2 \u2014 the crux identity is Sf = Res\u2081 EXACTLY\nThe D-036/D-037 bookkeeping, settled against Lagarias's paper and\nverified numerically:\n- **Sf(n) := S_\u221e(n) + 1 \u2212 \u03bb_n = Res\u2081(n) = \u03a3_{j=1}^n C(n,j)\u00b7c_{j\u22121}**\n  (c_k = Laurent coefficients of \u2212\u03b6\u2032/\u03b6 at 1). Follows from Lagarias\n  (4.10) [\u03c4_j = \u03b7_j + (\u22121)\u02b2\u03c3_{j+1} \u2212 (\u22121)\u02b2\u03b4] summed binomially.\n  Verified: (4.10) at j=0 exact to 15 digits (\u03bb\u2081 = 0.02309570896612103);\n  crux consequence \u03bb\u2082 = 0.09234573523 matches E-015's certified\n  0.09234573522804667 exactly.\n- **Residue theorem**: sides(T) = \u03bb_n(T) + triv + Res\u2081(n), verified to\n  2e-21 (n=2) by direct contour integration.\n- **Assembly is TAIL-FREE**: |Sf| \u2264 |\u03bb_n(T)| + |sides| + |triv| \u2264\n  2N(T) + [side pieces] + 1 = B(n) \u2014 no tail term anywhere (the crux\n  absorbs it). This is why D-037's B(n) has none.\n- The w=1 pole (order n+1) residue computation reduces to a Leibniz\n  rule: (w\u22121)^{n+1}J = [w\u207f \u2212 (w\u22121)\u207f]h(w), h = (w\u22121)(\u2212\u03b6\u2032/\u03b6) analytic \u2014\n  Res = \u03a3_j C(n,j)c_{j\u22121} confirmed algebraically.\n- SIDE EFFECT: D-037's line-63 compressed identity needs an erratum\n  pointer to D-064 (correct reading: Sf = Res\u2081 = sides \u2212 \u03bb_n(T) \u2212 triv).\n\n## Inventory highlights (why tier ii\u2032 is feasible)\n- Rectangle residue theorem EXISTS (vendored FromPNTPlus\n  `RectangleIntegral'_eq_sumResiduesIn`, axiom-clean) \u2014 needs the\n  simple-pole scaffold extended to finite order (bounded, R1).\n- `logDerivResidue`, `ResidueMult`, `riemannZetaLogDerivResidue`\n  vendored and clean.\n- Mathlib HAS Borel\u2013Carath\u00e9odory, Jensen's formula, digamma,\n  HadamardThreeLines, MeromorphicAt/Order/NormalForm/FactorizedRational.\n- Zeta23 HAS proved \u03a3 mult/(1+\u2016\u03b3_\u03c1\u2016\u00b2) < \u221e (zero_sum_inv_sq), local\n  zero count, RvM, reflect/conj symmetry, window finiteness.\n- Mathlib has NO Weierstrass/Hadamard factorization; FromPNTPlus\n  StrongPNTPrefix has the local Blaschke/Borel toolkit.\n\n## Route decisions (D-064 \u00a74)\nR1 build higher-order residue machinery (1\u20132 sess); R2 crux via (4.10)\n\u2014 investigate zeta-23 EF reuse (\u03b22) first, Hadamard fallback (\u03b21)\n(2\u20134 sess, the long pole); R3 R-bound via LOCAL route\n(Borel\u2013Carath\u00e9odory/Jensen/Blaschke \u2014 machinery exists) (2\u20133 sess);\nR4 the old \"w=1 \u2194 S_\u221e\" monster is KILLED by Discovery 2 (factors into\nR1's Leibniz computation + R2's (4.10)); R5 perimeter unchanged.\n\n## State at stop\nD-064 complete; sub-stage map ii\u2032-1a..7 (total ~9\u201316 sessions).\nNEXT: ii\u2032-1a (liCoeff pairing fix + summability). Paper A untouched\n(compiles at session-013 state; submission-ready fallback intact \u2014\nD-064 \u00a78).\n",
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