[{"type":"thinking","thinking":"Now update STATE.md (§8.4 step 4: LAST with NEXT ACTION). Rewrite the relevant sections.","signature":""},{"type":"text","text":"Now STATE.md (updated last, per protocol)."},{"type":"tool_use","id":"Write_54","name":"Write","input":{"file_path":"D:\\Python\\Quantum\\STATE.md","content":"# STATE.md — NGUYEN-RH-1 RESUME POINT\n# ⭐ READ THIS FIRST at the start of every session.\nLast updated: 2026-08-17 | Session: 004 (fork 2 E-011 complete; killed-session recovery)\n\n## CURRENT POSITION\n✔ PHASE 0 COMPLETE. ✔ PHASE 1 COMPLETE (Track A monitoring mode).\nPHASE 3 (Track C) UNDERWAY: 3.1 mapped (D-014, E-006/007, D-015/017),\n3.2 arithmetic side DONE to n=2000 (E-011/R-001), 3.4a/b/c COMPLETE.\nSuzuki line: g + A_a Galerkin + W-function machinery ALL VALIDATED\n(E-009/E-010); next Suzuki problem = Q-S3 (choice of theta(a), D-020 §4).\n\n## COMPLETED (Session 004)\n- [x] Recovered killed session: E-011 orphaned mid-edit (failing data from\n      OLD script revision). Root-caused: wrong hardcoded λ₁ constant\n      (digit 22+) + mp.dps getter typo; old run had 53-bit contamination\n- [x] Paper archive reorg (papers → research/paper/, reference texts\n      added); committed b04e50a\n- [x] E-010 extended re-run verified + re-registered (a≤8, λ=−1, h_conv\n      to 2.5e-3; all 4 checks pass)\n- [x] E-011 n_max=2000 ALL CHECKS PASS: λ₁ err 4.31e-102; V2 worst ratio\n      0.125 (n≤116 vs E-008); λ_n>0 ∀n≤2000; V5 rel dev 6.67e-705;\n      λ₂₀₀₀=5351.7595, refined asymptotic ratio 1.00216 → R-001\n- [x] Detached-run machinery established for long jobs (see HANDOFF)\n\n## IN PROGRESS\n(none — clean stop; fork 2 of 4 done)\n\n## NEXT ACTION\nFORK RULE (§8.4a) in progress — forks 1 (E-010) and 2 (E-011) DONE.\nRemaining forks:\n  3. 3.3: de Bruijn–Newman heat flow vs 2/3-density.\n  4. T4: ξ′-analogue (cheap secondary Track A target).\nAfter all forks: gather thoughts with user. NEW Suzuki-side option\n(opened by D-020, not a fork obligation): Q-S3 attack — least-squares\nread-off of θ(a), φ(a,z) from Cor 1.6 target; check Suzuki §7–8 and\nKim et al. (2607.24830) for canonical extension choices.\n\n## OPEN CONJECTURES / THREADS\n- Q-S1 (D-019 §3): L²→uniform lifting for Cor 1.6 (Phase 4 candidate).\n- Q-S2: ℋ(T_a) as de Branges-type space (Phase 2.4 link, alive).\n- Q-S3: θ(a) identification — THE Suzuki-line crux (D-020 §4).\n- Q6 uncertainty ↔ bandwidth-one ceiling bridge (D-001); Q14 Gutzwiller\n  (Phase 2); T2 Christoffel/CMS (D-006); T4 ξ′-analogue.\n- 3.2 next: push Li n past 2000 (detached runs) or asymptotic attack;\n  optional hardening: Arb ball-arithmetic λ_n certification.\nCLOSED: T1 (D-010/E-004), T3 (D-009), T5 (→G-001), 3.4a (D-016).\n\n## BLOCKERS\n(none)\n\n## HANDOFF NOTES\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n  list (no --session flag on add-derivation).\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 — mpmath's are broken\n  beyond ~16 digits in this env; mp.zetazero is safe).\n- LONG RUNS: CLI kills Bash tasks at ~2 min default (10 min max). For\n  longer jobs launch DETACHED:\n    subprocess.Popen([sys.executable, script, args...], stdout=logfile,\n      stderr=subprocess.STDOUT,\n      creationflags=0x00000008 | 0x00000200)  # DETACHED_PROCESS | NEW_GROUP\n  then poll the log file. (Session-004 lesson.)\n- flint.acb.stieltjes(k) scales ~k³ (28s @ k=2000, 3530 bits); full\n  0..2000 sweep ≈ 12.5 min on 14 Pool workers.\n- E-009b eigensolver floor: eigenvalues < ~1e-11 at h=5e-3 are at/below\n  backward-error noise — quote as upper bounds only.\n- E-010 build cache pattern: (a,h) builds reused across (λ,θ); sieve to\n  e^14 covers a ≤ 7.\n"},"extra_content":null}]