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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: 2026-08-19 | Session 011 COMPLETE (task (a): Lean proof\ntier (i) COMPLETE \u2014 chain_rule_sqrt_shift, sInfty_lower_bound,\nmarginTilde_convex all PROVED with clean axiom audits; ~1100 lines, 10\ncommits; user machine crashed mid-session, zero work lost).\n\n## CURRENT POSITION\n\u2714 PHASE 0, 1, 4 COMPLETE. PHASE 3 (Track C): 3.1\u20133.8 CLOSED (R-004,\nfull tag). PHASE 2 (Track B): mapped to exhaustion at current\ntechnology (2.6\u20132.13). PHASE 5: 5.3 \u2714, 5.4 \u2714, 5.2 \u2714 (live);\n5.1 skeleton \u2714 + **proof tier (i) COMPLETE (session 011)**.\n\n**Theorem status (unchanged by session 011's Lean work):**\n- T-1 (R-004): [PROVED-CONDITIONAL(computational RH-to-T\u2080;\n  computational finite verification)]. D-056: A = 10.5, B\u2080 = 48;\n  E-028: 26\u00d7 slack, N\u2080 = 80 000, margin(N\u2081) = 2.458e26; D-057\n  convexity PROVED (E-029) \u2014 and now FORMALIZED IN LEAN (tier i).\n- T-2 (R-003 + D-041): factorization + (\u2605) \u27fa (1.12) [PROVED modulo\n  Phase-5 formalities]; (1.12) \u27f9 spec(D) \u2282 \u211d [PROVED via Suzuki + D1];\n  \u21d0 [SKELETON L3/L4].\n- T-3 (valley, D-049 + D-058): [PROVED-CONDITIONAL(RH)].\n\n**Paper:** research/paper/draft.tex \u2014 complete draft, 12 pp, MiKTeX\ncompiles clean; every claim audited (D-060). No figures yet.\n\n**Lean:** research/lean/NguyenRH1/ \u2014 sorryAx remains ONLY on:\nlambda_pos_finite_height (tier ii), R003_exact_factorization (tier iv),\n4 valley statements (tier iii). Tier (i) done: chain_rule_sqrt_shift,\nsInfty_lower_bound (Bernoulli + \u03b3-shifted harmonic bounds, parity\nalgebra, no decimal estimates), marginTilde_convex (full D-057:\n8-block \u03c8 table with signs, IIMaj exponential bound \u2264 1.316 < 2 via\nfactor monotonicity, assembly via convexOn_of_deriv2_nonneg).\nAll proved declarations: PrintAxioms = 3 standard axioms only.\n\n## ACTIVE PLAN (next stage)\n1. Tier (ii): traced contour bound inside lambda_pos_finite_height\n   (explicit N(T)/S(T)/\u03b6\u2032/\u03b6 bounds \u2014 big).\n2. Optional: E-023b (acb box cover for M\u2080 \u2014 removes the last\n   grid-verified constant in R-004).\n3. Optional: E-021 n = 10\u2074 rerun (cheap via caches).\n4. Optional: paper figures/tables from numerics/data CSVs.\nDeprioritized: a=13+ push; adversary-ceiling LP; T4b; \u03bb-channel\n(G-004); \u03b8-channel (dead, E-024). Live research opening: symbol-space\nroute on (\u2605) (D-046 revival condition (ii)).\n\n## NEXT ACTION\nSession 012: user picks \u2014 (a) Lean tier (ii)\n(lambda_pos_finite_height contour bounds); (b) E-023b acb M\u2080 upgrade;\n(c) paper figures; (d) (\u2605) symbol-space research opening.\n\n## COMPLETED (Sessions 001\u2013010)\n- [x] Phase 0, Phase 1 (Track A \u2192 monitoring mode, D-013).\n- [x] 2.6 V3 root-cause + repair (E-016b/c, D-025).\n- [x] 2.7 R-003 exact factorization (D-026, E-017/D-027, ledger #5).\n- [x] 2.8 a=12 no transition (E-018/D-028, backend v2, E-019/D-029).\n- [x] 1.6 \u03be\u2032-world saturated (E-020b/D-030); 1.7 T4b closed (D-031).\n- [x] 3.3 \u2192 G-003; 3.4 (Suzuki line spawned); 3.5 design (D-032/D-033).\n- [x] (\u2605) design (D-034/D-035); new tasks 2.9/2.10/2.11.\n- [x] 3.6 D-036 explicit contour constants (session 006 cont.9).\n- [x] 3.7 E-021 (session 007): S_\u221e exact + c\u2080, |S_f| curve, A/B\u2080\n      measured; 6-bug saga documented.\n- [x] Session 008: regroup; R7 resources atlas registered; 3.8\n      COMPLETE (D-037, E-023, R-004 ledger #6); 2.10 COMPLETE\n      (E-022/E-022b + D-040, valley observable); 2.9-D1 COMPLETE\n      (D-041); 2.11 COMPLETE (D-038); 2.12 COMPLETE (E-024 + D-042,\n      \u03b8-independence); 2.13 COMPLETE (E-025 + D-043, discretization\n      floor; quadratic locking correction).\n- [x] Session 009: PHASE 4 COMPLETE (D-052/D-053/D-054, E-027 + D-055,\n      repairs 4.5a\u2013d: D-056\u2013D-059; R-004 tag restored).\n- [x] Session 010: 5.3 paper draft complete; 5.4 honesty audit (D-060);\n      5.1/5.2 skeleton stage (D-061).\n- [x] Session 011: Lean proof tier (i) COMPLETE \u2014 sInfty_lower_bound,\n      marginTilde_convex, chain_rule_sqrt_shift PROVED (journal-011;\n      10 commits; D-061 \u00a75 updated).\n\n## OPEN CONJECTURES / THREADS\n- (\u2605) (R-003): central conjectural target (task 2.9).\n- Q-S1 (D-019 \u00a73): L\u00b2\u2192uniform lifting. Q-S2: \u210b(T_a) de Branges (2.4).\n  \u03b8(a) theory: must explain both metrics (D-028 F3) + z\u2081\u00b7a\u22484.5 law.\n- Q6 (D-001); Q14 Gutzwiller (Phase 2); T2 Christoffel/CMS (D-006).\nCLOSED: T1, T3, T4, T4b (D-031), T5 (\u2192G-001), 3.4a/b/c, 3.3 (\u2192G-003),\n2.8 (D-029), 1.6 (D-030), 1.7 (D-031), 3.5-design (D-033), (\u2605)-design\n(D-035), 3.6 (D-036), 3.7 (E-021), 3.8 (D-037/R-004), 5.3, 5.4,\n5.1-tier-(i).\n\n## BLOCKERS\n(none)\n\n## HANDOFF NOTES\n- db.py add-derivation/log-experiment use INSERT OR REPLACE keyed by\n  id \u2014 a mistyped re-register OVERWRITES the row.\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n  list. add-derivation signature: positional id, --title --task\n  --status --file (NO --date flag). Session registration via direct\n  sqlite3 insert (journal_file column).\n- venv: ./.venv/Scripts/python.exe. git: git -c user.name=\"NGUYEN-RH-1\"\n  -c user.email=\"research@local\" commit (config NOT modified).\n- LONG RUNS: DETACHED + sandbox DISABLED + log file; poll. For lake:\n  SINGLE command per detached spawn; short PrintAxioms in foreground.\n- LEAN: elan 4.2.3 at ~/.elan/bin (export PATH per shell); toolchain\n  v4.33.0-rc2; zeta-23-lean fully built (9010 jobs) + cache ~7 GB;\n  NguyenRH1 at research/lean/NguyenRH1 with path requires. Iterate\n  single-file with `lake env lean NguyenRH1/LiSkeleton.lean` from the\n  package dir (elan errors \"no default toolchain\" outside it).\n- LEAN 4 gotchas (session 011, hard-won \u2014 full list in journal-011):\n  HasDerivAt.add_const adds to VALUE (use .comp for precomposition);\n  Pi.mul_apply/Pi.add_apply/Pi.sub_apply simp after .mul/.add/.sub;\n  convert leaves instance side-goals \u2192 `first | rfl | ring`;\n  field_simp often closes goals (trailing ring errors);\n  Finset.sum_image takes Set.InjOn, map = g, summand = f;\n  deriv^[2] \u2260 deriv (deriv \u00b7) syntactically (show bridges);\n  subtype coercions (m : \u211d) vs (m.1 : \u211d) can explode isDefEq \u2014 pin\n  families explicitly; -a*b vs -(a*b) breaks Real.exp_neg rewrites;\n  check norm_num digit-bounds by hand (two tight ones failed);\n  set_option maxHeartbeats goes BEFORE the doc comment;\n  iimaj_bracket_bound needs maxHeartbeats 800000.\n- flint for ALL \u03b6/Stieltjes >16 digits; mp.zetazero safe; mpmath\n  complex-\u03b6 OK to ~1e-10; mpmath zeta (integer+Hurwitz)\n  UNTRUSTWORTHY beyond ~57 digits at any dps.\n- PRECISION RULES (session 007): (1) mp.mp.dps = X BEFORE every\n  mp.mpf(string) parse; (2) long decimal constants as STRINGS;\n  (3) float64 zero ordinates insufficient for \u03c3_m; (4) Li binomial\n  truncation boundary error ~C(n,M)\u00b714^{\u2212M} peaks at M = n/15.\n- prime_backend_v2: blockwise \u039b to e\u00b2\u2074, cache E-019-backend-cache.npz;\n  monkeypatch E16.prime_sum_vec + E16._BUILD.clear().\n- Winding diagnostic: \u22654000 pts/edge near real zeros.\n- E-016/E-016b FROZEN; correct machinery: E-016c, E-017/E-018.\n- \u03b3-locking claim protocol: D-029 \u00a73.\n- Lagarias paper math/0404394 (research/paper/): \u00a75\u20136 read in full.\n- research/resources/: 43-note RH-equivalence atlas = R7.\n- E-021 caches: E-021-zeta-cache.json, E-021-zeros100-hi-cache.json,\n  E-021-zeros-cache.npy (4624 zeros float64 \u2014 P1 use ONLY).\n- E-023: E-023-assembly.csv + .json (M\u2080, N\u2080, N\u2081, margins).\n- E-027: detector stress test; zeros cache E-027-zeros-cache.npy;\n  rerun 16 s with cache (--force).\n- PAPER: build with pdflatex+bibtex in research/paper/ (MiKTeX);\n  draft.pdf is gitignored. Audit rule (D-060 \u00a75): any edit to\n  draft.tex re-opens the audit for the edited lines.\n"
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  "content": "# STATE.md \u2014 NGUYEN-RH-1 RESUME POINT\n# \u2b50 READ THIS FIRST at the start of every session.\nLast updated: 2026-08-19 | Session 011 COMPLETE (task (a): Lean proof\ntier (i) COMPLETE \u2014 chain_rule_sqrt_shift, sInfty_lower_bound,\nmarginTilde_convex all PROVED with clean axiom audits; ~1100 lines, 10\ncommits; user machine crashed mid-session, zero work lost).\n\n## CURRENT POSITION\n\u2714 PHASE 0, 1, 4 COMPLETE. PHASE 3 (Track C): 3.1\u20133.8 CLOSED (R-004,\nfull tag). PHASE 2 (Track B): mapped to exhaustion at current\ntechnology (2.6\u20132.13). PHASE 5: 5.3 \u2714, 5.4 \u2714, 5.2 \u2714 (live);\n5.1 skeleton \u2714 + **proof tier (i) COMPLETE (session 011)**.\n\n**Theorem status (unchanged by session 011's Lean work):**\n- T-1 (R-004): [PROVED-CONDITIONAL(computational RH-to-T\u2080;\n  computational finite verification)]. D-056: A = 10.5, B\u2080 = 48;\n  E-028: 26\u00d7 slack, N\u2080 = 80 000, margin(N\u2081) = 2.458e26; D-057\n  convexity PROVED (E-029) \u2014 and now FORMALIZED IN LEAN (tier i).\n- T-2 (R-003 + D-041): factorization + (\u2605) \u27fa (1.12) [PROVED modulo\n  Phase-5 formalities]; (1.12) \u27f9 spec(D) \u2282 \u211d [PROVED via Suzuki + D1];\n  \u21d0 [SKELETON L3/L4].\n- T-3 (valley, D-049 + D-058): [PROVED-CONDITIONAL(RH)].\n\n**Paper:** research/paper/draft.tex \u2014 complete draft, 12 pp, MiKTeX\ncompiles clean; every claim audited (D-060). No figures yet.\n\n**Lean:** research/lean/NguyenRH1/ \u2014 sorryAx remains ONLY on:\nlambda_pos_finite_height (tier ii), R003_exact_factorization (tier iv),\n4 valley statements (tier iii). Tier (i) done: chain_rule_sqrt_shift,\nsInfty_lower_bound (Bernoulli + \u03b3-shifted harmonic bounds, parity\nalgebra, no decimal estimates), marginTilde_convex (full D-057:\n8-block \u03c8 table with signs, IIMaj exponential bound \u2264 1.316 < 2 via\nfactor monotonicity, assembly via convexOn_of_deriv2_nonneg).\nAll proved declarations: PrintAxioms = 3 standard axioms only.\n\n## ACTIVE PLAN (next stage)\n1. Tier (ii): traced contour bound inside lambda_pos_finite_height\n   (explicit N(T)/S(T)/\u03b6\u2032/\u03b6 bounds \u2014 big).\n2. Optional: E-023b (acb box cover for M\u2080 \u2014 removes the last\n   grid-verified constant in R-004).\n3. Optional: E-021 n = 10\u2074 rerun (cheap via caches).\n4. Optional: paper figures/tables from numerics/data CSVs.\nDeprioritized: a=13+ push; adversary-ceiling LP; T4b; \u03bb-channel\n(G-004); \u03b8-channel (dead, E-024). Live research opening: symbol-space\nroute on (\u2605) (D-046 revival condition (ii)).\n\n## NEXT ACTION\nSession 012: user picks \u2014 (a) Lean tier (ii)\n(lambda_pos_finite_height contour bounds); (b) E-023b acb M\u2080 upgrade;\n(c) paper figures; (d) (\u2605) symbol-space research opening.\n\n## COMPLETED (Sessions 001\u2013010)\n- [x] Phase 0, Phase 1 (Track A \u2192 monitoring mode, D-013).\n- [x] 2.6 V3 root-cause + repair (E-016b/c, D-025).\n- [x] 2.7 R-003 exact factorization (D-026, E-017/D-027, ledger #5).\n- [x] 2.8 a=12 no transition (E-018/D-028, backend v2, E-019/D-029).\n- [x] 1.6 \u03be\u2032-world saturated (E-020b/D-030); 1.7 T4b closed (D-031).\n- [x] 3.3 \u2192 G-003; 3.4 (Suzuki line spawned); 3.5 design (D-032/D-033).\n- [x] (\u2605) design (D-034/D-035); new tasks 2.9/2.10/2.11.\n- [x] 3.6 D-036 explicit contour constants (session 006 cont.9).\n- [x] 3.7 E-021 (session 007): S_\u221e exact + c\u2080, |S_f| curve, A/B\u2080\n      measured; 6-bug saga documented.\n- [x] Session 008: regroup; R7 resources atlas registered; 3.8\n      COMPLETE (D-037, E-023, R-004 ledger #6); 2.10 COMPLETE\n      (E-022/E-022b + D-040, valley observable); 2.9-D1 COMPLETE\n      (D-041); 2.11 COMPLETE (D-038); 2.12 COMPLETE (E-024 + D-042,\n      \u03b8-independence); 2.13 COMPLETE (E-025 + D-043, discretization\n      floor; quadratic locking correction).\n- [x] Session 009: PHASE 4 COMPLETE (D-052/D-053/D-054, E-027 + D-055,\n      repairs 4.5a\u2013d: D-056\u2013D-059; R-004 tag restored).\n- [x] Session 010: 5.3 paper draft complete; 5.4 honesty audit (D-060);\n      5.1/5.2 skeleton stage (D-061).\n- [x] Session 011: Lean proof tier (i) COMPLETE \u2014 sInfty_lower_bound,\n      marginTilde_convex, chain_rule_sqrt_shift PROVED (journal-011;\n      10 commits; D-061 \u00a75 updated).\n\n## OPEN CONJECTURES / THREADS\n- (\u2605) (R-003): central conjectural target (task 2.9).\n- Q-S1 (D-019 \u00a73): L\u00b2\u2192uniform lifting. Q-S2: \u210b(T_a) de Branges (2.4).\n  \u03b8(a) theory: must explain both metrics (D-028 F3) + z\u2081\u00b7a\u22484.5 law.\n- Q6 (D-001); Q14 Gutzwiller (Phase 2); T2 Christoffel/CMS (D-006).\nCLOSED: T1, T3, T4, T4b (D-031), T5 (\u2192G-001), 3.4a/b/c, 3.3 (\u2192G-003),\n2.8 (D-029), 1.6 (D-030), 1.7 (D-031), 3.5-design (D-033), (\u2605)-design\n(D-035), 3.6 (D-036), 3.7 (E-021), 3.8 (D-037/R-004), 5.3, 5.4,\n5.1-tier-(i).\n\n## BLOCKERS\n(none)\n\n## HANDOFF NOTES\n- db.py add-derivation/log-experiment use INSERT OR REPLACE keyed by\n  id \u2014 a mistyped re-register OVERWRITES the row.\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n  list. add-derivation signature: positional id, --title --task\n  --status --file (NO --date flag). Session registration via direct\n  sqlite3 insert (journal_file column).\n- venv: ./.venv/Scripts/python.exe. git: git -c user.name=\"NGUYEN-RH-1\"\n  -c user.email=\"research@local\" commit (config NOT modified).\n- LONG RUNS: DETACHED + sandbox DISABLED + log file; poll. For lake:\n  SINGLE command per detached spawn; short PrintAxioms in foreground.\n- LEAN: elan 4.2.3 at ~/.elan/bin (export PATH per shell); toolchain\n  v4.33.0-rc2; zeta-23-lean fully built (9010 jobs) + cache ~7 GB;\n  NguyenRH1 at research/lean/NguyenRH1 with path requires. Iterate\n  single-file with `lake env lean NguyenRH1/LiSkeleton.lean` from the\n  package dir (elan errors \"no default toolchain\" outside it).\n- LEAN 4 gotchas (session 011, hard-won \u2014 full list in journal-011):\n  HasDerivAt.add_const adds to VALUE (use .comp for precomposition);\n  Pi.mul_apply/Pi.add_apply/Pi.sub_apply simp after .mul/.add/.sub;\n  convert leaves instance side-goals \u2192 `first | rfl | ring`;\n  field_simp often closes goals (trailing ring errors);\n  Finset.sum_image takes Set.InjOn, map = g, summand = f;\n  deriv^[2] \u2260 deriv (deriv \u00b7) syntactically (show bridges);\n  subtype coercions (m : \u211d) vs (m.1 : \u211d) can explode isDefEq \u2014 pin\n  families explicitly; -a*b vs -(a*b) breaks Real.exp_neg rewrites;\n  check norm_num digit-bounds by hand (two tight ones failed);\n  set_option maxHeartbeats goes BEFORE the doc comment;\n  iimaj_bracket_bound needs maxHeartbeats 800000.\n- flint for ALL \u03b6/Stieltjes >16 digits; mp.zetazero safe; mpmath\n  complex-\u03b6 OK to ~1e-10; mpmath zeta (integer+Hurwitz)\n  UNTRUSTWORTHY beyond ~57 digits at any dps.\n- PRECISION RULES (session 007): (1) mp.mp.dps = X BEFORE every\n  mp.mpf(string) parse; (2) long decimal constants as STRINGS;\n  (3) float64 zero ordinates insufficient for \u03c3_m; (4) Li binomial\n  truncation boundary error ~C(n,M)\u00b714^{\u2212M} peaks at M = n/15.\n- prime_backend_v2: blockwise \u039b to e\u00b2\u2074, cache E-019-backend-cache.npz;\n  monkeypatch E16.prime_sum_vec + E16._BUILD.clear().\n- Winding diagnostic: \u22654000 pts/edge near real zeros.\n- E-016/E-016b FROZEN; correct machinery: E-016c, E-017/E-018.\n- \u03b3-locking claim protocol: D-029 \u00a73.\n- Lagarias paper math/0404394 (research/paper/): \u00a75\u20136 read in full.\n- research/resources/: 43-note RH-equivalence atlas = R7.\n- E-021 caches: E-021-zeta-cache.json, E-021-zeros100-hi-cache.json,\n  E-021-zeros-cache.npy (4624 zeros float64 \u2014 P1 use ONLY).\n- E-023: E-023-assembly.csv + .json (M\u2080, N\u2080, N\u2081, margins).\n- E-027: detector stress test; zeros cache E-027-zeros-cache.npy;\n  rerun 16 s with cache (--force).\n- PAPER: build with pdflatex+bibtex in research/paper/ (MiKTeX);\n  draft.pdf is gitignored. Audit rule (D-060 \u00a75): any edit to\n  draft.tex re-opens the audit for the edited lines.\n",
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        " # STATE.md \u2014 NGUYEN-RH-1 RESUME POINT",
        " # \u2b50 READ THIS FIRST at the start of every session.",
        "-Last updated: 2026-08-19 | Session 010 COMPLETE (Phase 5: 5.3 paper",
        "-draft complete + 5.4 honesty audit complete (D-060) + 5.1/5.2 Lean at",
        "-skeleton stage (D-061): toolchain installed, zeta-23-lean full build",
        "-green, live axiom audit passed, NguyenRH1 package compiling).",
        "+Last updated: 2026-08-19 | Session 011 COMPLETE (task (a): Lean proof",
        "+tier (i) COMPLETE \u2014 chain_rule_sqrt_shift, sInfty_lower_bound,",
        "+marginTilde_convex all PROVED with clean axiom audits; ~1100 lines, 10",
        "+commits; user machine crashed mid-session, zero work lost).",
        " ",
        " ## CURRENT POSITION",
        " \u2714 PHASE 0, 1, 4 COMPLETE. PHASE 3 (Track C): 3.1\u20133.8 CLOSED (R-004,",
        " full tag). PHASE 2 (Track B): mapped to exhaustion at current",
        "-technology (2.6\u20132.13). PHASE 5: 5.3 \u2714, 5.4 \u2714, 5.1/5.2 skeleton \u2714",
        "-(proof tiers remain).",
        "+technology (2.6\u20132.13). PHASE 5: 5.3 \u2714, 5.4 \u2714, 5.2 \u2714 (live);",
        "+5.1 skeleton \u2714 + **proof tier (i) COMPLETE (session 011)**.",
        " ",
        "-**Theorem status (post-repair, post-audit \u2014 unchanged by audit):**",
        "+**Theorem status (unchanged by session 011's Lean work):**",
        " - T-1 (R-004): [PROVED-CONDITIONAL(computational RH-to-T\u2080;",
        "-  computational finite verification)]. D-056: A = 10.5, B\u2080 = 48",
        "-  (honest C\u2080 with log log term); digamma |r| \u2264 1.2/|w|\u00b2 proved.",
        "-  E-028: 26\u00d7 slack, N\u2080 = 80 000, overlap 6.25\u00d7, margin(N\u2081) =",
        "-  2.458e26. D-057: convexity PROVED (E-029). Remaining tagged inputs:",
        "-  Platt\u2013Trudgian (interval arithmetic), Misguich\u2013Voros (literature),",
        "-  M\u2080 grid+Lipschitz (E-023; E-023b acb upgrade optional).",
        "+  computational finite verification)]. D-056: A = 10.5, B\u2080 = 48;",
        "+  E-028: 26\u00d7 slack, N\u2080 = 80 000, margin(N\u2081) = 2.458e26; D-057",
        "+  convexity PROVED (E-029) \u2014 and now FORMALIZED IN LEAN (tier i).",
        " - T-2 (R-003 + D-041): factorization + (\u2605) \u27fa (1.12) [PROVED modulo",
        "-  Phase-5 formalities, itemized D-059]; (1.12) \u27f9 spec(D) \u2282 \u211d [PROVED",
        "-  via Suzuki + D1]; \u21d0 [SKELETON L3/L4]. **The paper now states this",
        "-  split explicitly (5.4 audit correction).**",
        "-- T-3 (valley theorem, D-049 + D-058): upper bounds",
        "-  [PROVED-CONDITIONAL(RH)] with K(\u03b3,\u03b3) \u2264 1/m_\u03b3; floors/profile B1\u2032/B3\u2032",
        "-  [PROVED-CONDITIONAL(RH)] (isolated zeros clean rate; general form",
        "-  with Gram constant + annulus count E(\u03b3,a)); detector three levels",
        "-  (E-027/D-055): bare immediate / pencil magnitude / carrier \u03c0/(2a)",
        "-  exact (crossings measured within 0.02%\u20132.3%).",
        "+  Phase-5 formalities]; (1.12) \u27f9 spec(D) \u2282 \u211d [PROVED via Suzuki + D1];",
        "+  \u21d0 [SKELETON L3/L4].",
        "+- T-3 (valley, D-049 + D-058): [PROVED-CONDITIONAL(RH)].",
        " ",
        " **Paper:** research/paper/draft.tex \u2014 complete draft, 12 pp, MiKTeX",
        "-compiles clean; every claim audited (D-060). Numerics appendix +",
        "-obstruction analysis included. No figures yet (CSVs available).",
        "+compiles clean; every claim audited (D-060). No figures yet.",
        " ",
        "-**Lean:** research/lean/NguyenRH1/ \u2014 9 skeleton theorems compile",
        "-(sorryAx-marked); inherited zeta-23-lean fully built + live-audited",
        "-(D-061). elan at ~/.elan/bin (PATH export needed per shell).",
        "+**Lean:** research/lean/NguyenRH1/ \u2014 sorryAx remains ONLY on:",
        "+lambda_pos_finite_height (tier ii), R003_exact_factorization (tier iv),",
        "+4 valley statements (tier iii). Tier (i) done: chain_rule_sqrt_shift,",
        "+sInfty_lower_bound (Bernoulli + \u03b3-shifted harmonic bounds, parity",
        "+algebra, no decimal estimates), marginTilde_convex (full D-057:",
        "+8-block \u03c8 table with signs, IIMaj exponential bound \u2264 1.316 < 2 via",
        "+factor monotonicity, assembly via convexOn_of_deriv2_nonneg).",
        "+All proved declarations: PrintAxioms = 3 standard axioms only.",
        " ",
        " ## ACTIVE PLAN (next stage)",
        "-1. Prove the elementary Lean tier: sInfty_lower_bound,",
        "-   marginTilde_convex (11-block table), chain_rule_sqrt_shift",
        "-   (D-061 \u00a75 tier (i)).",
        "+1. Tier (ii): traced contour bound inside lambda_pos_finite_height",
        "+   (explicit N(T)/S(T)/\u03b6\u2032/\u03b6 bounds \u2014 big).",
        " 2. Optional: E-023b (acb box cover for M\u2080 \u2014 removes the last",
        "    grid-verified constant in R-004).",
        "-3. Optional: E-021 n = 10\u2074 rerun (cheap via caches; needs zeta-cache",
        "-   filename bump).",
        "+3. Optional: E-021 n = 10\u2074 rerun (cheap via caches).",
        " 4. Optional: paper figures/tables from numerics/data CSVs.",
        " Deprioritized: a=13+ push; adversary-ceiling LP; T4b; \u03bb-channel",
        " (G-004); \u03b8-channel (dead, E-024). Live research opening: symbol-space",
        " route on (\u2605) (D-046 revival condition (ii)).",
        " ",
        " ## NEXT ACTION",
        "-Session 011: user picks \u2014 (a) Lean proof tier (i) (sInfty_lower_bound",
        "-first: Bernoulli + harmonic bounds, positivity-friendly); (b) E-023b",
        "-acb M\u2080 upgrade; (c) paper figures; (d) new research on the (\u2605)",
        "-symbol-space opening.",
        "+Session 012: user picks \u2014 (a) Lean tier (ii)",
        "+(lambda_pos_finite_height contour bounds); (b) E-023b acb M\u2080 upgrade;",
        "+(c) paper figures; (d) (\u2605) symbol-space research opening.",
        " ",
        "-## COMPLETED (Sessions 001\u2013009)",
        "+## COMPLETED (Sessions 001\u2013010)",
        " - [x] Phase 0, Phase 1 (Track A \u2192 monitoring mode, D-013).",
        " - [x] 2.6 V3 root-cause + repair (E-016b/c, D-025).",
        " - [x] 2.7 R-003 exact factorization (D-026, E-017/D-027, ledger #5)."
      ]
    },
    {
      "oldStart": 76,
      "oldLines": 6,
      "newStart": 68,
      "newLines": 11,
      "lines": [
        "       floor; quadratic locking correction).",
        " - [x] Session 009: PHASE 4 COMPLETE (D-052/D-053/D-054, E-027 + D-055,",
        "       repairs 4.5a\u2013d: D-056\u2013D-059; R-004 tag restored).",
        "+- [x] Session 010: 5.3 paper draft complete; 5.4 honesty audit (D-060);",
        "+      5.1/5.2 skeleton stage (D-061).",
        "+- [x] Session 011: Lean proof tier (i) COMPLETE \u2014 sInfty_lower_bound,",
        "+      marginTilde_convex, chain_rule_sqrt_shift PROVED (journal-011;",
        "+      10 commits; D-061 \u00a75 updated).",
        " ",
        " ## OPEN CONJECTURES / THREADS",
        " - (\u2605) (R-003): central conjectural target (task 2.9)."
      ]
    },
    {
      "oldStart": 84,
      "oldLines": 16,
      "newStart": 81,
      "newLines": 15,
      "lines": [
        " - Q6 (D-001); Q14 Gutzwiller (Phase 2); T2 Christoffel/CMS (D-006).",
        " CLOSED: T1, T3, T4, T4b (D-031), T5 (\u2192G-001), 3.4a/b/c, 3.3 (\u2192G-003),",
        " 2.8 (D-029), 1.6 (D-030), 1.7 (D-031), 3.5-design (D-033), (\u2605)-design",
        "-(D-035), 3.6 (D-036), 3.7 (E-021), 3.8 (D-037/R-004), 5.3, 5.4.",
        "+(D-035), 3.6 (D-036), 3.7 (E-021), 3.8 (D-037/R-004), 5.3, 5.4,",
        "+5.1-tier-(i).",
        " ",
        " ## BLOCKERS",
        " (none)",
        " ",
        " ## HANDOFF NOTES",
        " - db.py add-derivation/log-experiment use INSERT OR REPLACE keyed by",
        "-  id \u2014 a mistyped re-register OVERWRITES the row (session 009:",
        "-  restored a clobbered D-052 row; session 010: deliberately re-keyed",
        "-  D-056 with corrected title).",
        "+  id \u2014 a mistyped re-register OVERWRITES the row.",
        " - db.py: init, log-experiment, add-result, add-derivation, add-graveyard,",
        "   list. add-derivation signature: positional id, --title --task",
        "   --status --file (NO --date flag). Session registration via direct"
      ]
    },
    {
      "oldStart": 101,
      "oldLines": 43,
      "newStart": 97,
      "newLines": 43,
      "lines": [
        " - venv: ./.venv/Scripts/python.exe. git: git -c user.name=\"NGUYEN-RH-1\"",
        "   -c user.email=\"research@local\" commit (config NOT modified).",
        " - LONG RUNS: DETACHED + sandbox DISABLED + log file; poll. For lake:",
        "-  SINGLE command per detached spawn (chained && died silently once);",
        "-  short PrintAxioms runs in foreground.",
        "+  SINGLE command per detached spawn; short PrintAxioms in foreground.",
        " - LEAN: elan 4.2.3 at ~/.elan/bin (export PATH per shell); toolchain",
        "   v4.33.0-rc2; zeta-23-lean fully built (9010 jobs) + cache ~7 GB;",
        "-  NguyenRH1 at research/lean/NguyenRH1 with path requires (vendored",
        "-  repo untouched). Lean 4 gotchas: end-ordering (namespace before",
        "-  anonymous section); no Unicode \u208a/\u208b in identifiers; Complex.sin not",
        "-  csin.",
        "-- flint for ALL \u03b6/Stieltjes >16 digits; mp.zetazero safe (Riemann\u2013",
        "-  Siegel path); mpmath complex-\u03b6 OK to ~1e-10 (E-018 C2); mpmath",
        "-  zeta (integer+Hurwitz) UNTRUSTWORTHY beyond ~57 digits at any dps.",
        "-- PRECISION RULES (session 007, hard-won \u2014 see memory note):",
        "-  (1) mp.mp.dps = X BEFORE every mp.mpf(string) parse, including right",
        "-  after flint calls (entry dps is 15); (2) long decimal constants as",
        "-  STRINGS (bare float literal = 53-bit silently); (3) float64 zero",
        "-  ordinates insufficient for \u03c3_m = \u03a3\u03c1^{\u2212m} (C(n,j) amplification);",
        "-  (4) in Li binomial sums, truncating any ~14^{\u2212j}-sized series at M",
        "-  leaves boundary error ~C(n,M)\u00b714^{\u2212M} peaking at M = n/15 ~ (15/14)\u207f.",
        "+  NguyenRH1 at research/lean/NguyenRH1 with path requires. Iterate",
        "+  single-file with `lake env lean NguyenRH1/LiSkeleton.lean` from the",
        "+  package dir (elan errors \"no default toolchain\" outside it).",
        "+- LEAN 4 gotchas (session 011, hard-won \u2014 full list in journal-011):",
        "+  HasDerivAt.add_const adds to VALUE (use .comp for precomposition);",
        "+  Pi.mul_apply/Pi.add_apply/Pi.sub_apply simp after .mul/.add/.sub;",
        "+  convert leaves instance side-goals \u2192 `first | rfl | ring`;",
        "+  field_simp often closes goals (trailing ring errors);",
        "+  Finset.sum_image takes Set.InjOn, map = g, summand = f;",
        "+  deriv^[2] \u2260 deriv (deriv \u00b7) syntactically (show bridges);",
        "+  subtype coercions (m : \u211d) vs (m.1 : \u211d) can explode isDefEq \u2014 pin",
        "+  families explicitly; -a*b vs -(a*b) breaks Real.exp_neg rewrites;",
        "+  check norm_num digit-bounds by hand (two tight ones failed);",
        "+  set_option maxHeartbeats goes BEFORE the doc comment;",
        "+  iimaj_bracket_bound needs maxHeartbeats 800000.",
        "+- flint for ALL \u03b6/Stieltjes >16 digits; mp.zetazero safe; mpmath",
        "+  complex-\u03b6 OK to ~1e-10; mpmath zeta (integer+Hurwitz)",
        "+  UNTRUSTWORTHY beyond ~57 digits at any dps.",
        "+- PRECISION RULES (session 007): (1) mp.mp.dps = X BEFORE every",
        "+  mp.mpf(string) parse; (2) long decimal constants as STRINGS;",
        "+  (3) float64 zero ordinates insufficient for \u03c3_m; (4) Li binomial",
        "+  truncation boundary error ~C(n,M)\u00b714^{\u2212M} peaks at M = n/15.",
        " - prime_backend_v2: blockwise \u039b to e\u00b2\u2074, cache E-019-backend-cache.npz;",
        "   monkeypatch E16.prime_sum_vec + E16._BUILD.clear().",
        " - Winding diagnostic: \u22654000 pts/edge near real zeros.",
        "-- E-016/E-016b FROZEN (historical record); correct machinery: E-016c",
        "-  (stable eval + recon), E-017/E-018 (R\u2080/R_\u03c4/M).",
        "+- E-016/E-016b FROZEN; correct machinery: E-016c, E-017/E-018.",
        " - \u03b3-locking claim protocol: D-029 \u00a73.",
        "-- Lagarias paper math/0404394 (research/paper/): \u00a75\u20136 read in full for",
        "-  D-037 (Thm 5.1/6.1, bridge (1.16), interpolation \u00a77).",
        "-- research/resources/: 43-note RH-equivalence atlas = R7 (registered",
        "-  session 008; index.md with per-note project-use map).",
        "-- E-021 caches: E-021-zeta-cache.json (\u03b6 strings 1650 digits, \u03b6*(1)",
        "-  patched), E-021-zeros100-hi-cache.json (100 zeros, 400 digits),",
        "+- Lagarias paper math/0404394 (research/paper/): \u00a75\u20136 read in full.",
        "+- research/resources/: 43-note RH-equivalence atlas = R7.",
        "+- E-021 caches: E-021-zeta-cache.json, E-021-zeros100-hi-cache.json,",
        "   E-021-zeros-cache.npy (4624 zeros float64 \u2014 P1 use ONLY).",
        " - E-023: E-023-assembly.csv + .json (M\u2080, N\u2080, N\u2081, margins).",
        "-- E-027: detector stress test; script E-027-detector.py; zeros cache",
        "-  E-027-zeros-cache.npy (2500 zeros); rerun 16 s with cache (--force).",
        "-  Machinery reusable for D-H/Epstein builds (swap the zero list).",
        "-- n=10\u2074 E-021 rerun: needs zeta strings at 0.31\u00b710\u2074+100 digits \u2014",
        "-  bump n_max-dependent cache filename or delete zeta cache.",
        "+- E-027: detector stress test; zeros cache E-027-zeros-cache.npy;",
        "+  rerun 16 s with cache (--force).",
        " - PAPER: build with pdflatex+bibtex in research/paper/ (MiKTeX);",
        "   draft.pdf is gitignored. Audit rule (D-060 \u00a75): any edit to",
        "   draft.tex re-opens the audit for the edited lines."
      ]
    }
  ],
  "originalFile": "# STATE.md \u2014 NGUYEN-RH-1 RESUME POINT\n# \u2b50 READ THIS FIRST at the start of every session.\nLast updated: 2026-08-19 | Session 010 COMPLETE (Phase 5: 5.3 paper\ndraft complete + 5.4 honesty audit complete (D-060) + 5.1/5.2 Lean at\nskeleton stage (D-061): toolchain installed, zeta-23-lean full build\ngreen, live axiom audit passed, NguyenRH1 package compiling).\n\n## CURRENT POSITION\n\u2714 PHASE 0, 1, 4 COMPLETE. PHASE 3 (Track C): 3.1\u20133.8 CLOSED (R-004,\nfull tag). PHASE 2 (Track B): mapped to exhaustion at current\ntechnology (2.6\u20132.13). PHASE 5: 5.3 \u2714, 5.4 \u2714, 5.1/5.2 skeleton \u2714\n(proof tiers remain).\n\n**Theorem status (post-repair, post-audit \u2014 unchanged by audit):**\n- T-1 (R-004): [PROVED-CONDITIONAL(computational RH-to-T\u2080;\n  computational finite verification)]. D-056: A = 10.5, B\u2080 = 48\n  (honest C\u2080 with log log term); digamma |r| \u2264 1.2/|w|\u00b2 proved.\n  E-028: 26\u00d7 slack, N\u2080 = 80 000, overlap 6.25\u00d7, margin(N\u2081) =\n  2.458e26. D-057: convexity PROVED (E-029). Remaining tagged inputs:\n  Platt\u2013Trudgian (interval arithmetic), Misguich\u2013Voros (literature),\n  M\u2080 grid+Lipschitz (E-023; E-023b acb upgrade optional).\n- T-2 (R-003 + D-041): factorization + (\u2605) \u27fa (1.12) [PROVED modulo\n  Phase-5 formalities, itemized D-059]; (1.12) \u27f9 spec(D) \u2282 \u211d [PROVED\n  via Suzuki + D1]; \u21d0 [SKELETON L3/L4]. **The paper now states this\n  split explicitly (5.4 audit correction).**\n- T-3 (valley theorem, D-049 + D-058): upper bounds\n  [PROVED-CONDITIONAL(RH)] with K(\u03b3,\u03b3) \u2264 1/m_\u03b3; floors/profile B1\u2032/B3\u2032\n  [PROVED-CONDITIONAL(RH)] (isolated zeros clean rate; general form\n  with Gram constant + annulus count E(\u03b3,a)); detector three levels\n  (E-027/D-055): bare immediate / pencil magnitude / carrier \u03c0/(2a)\n  exact (crossings measured within 0.02%\u20132.3%).\n\n**Paper:** research/paper/draft.tex \u2014 complete draft, 12 pp, MiKTeX\ncompiles clean; every claim audited (D-060). Numerics appendix +\nobstruction analysis included. No figures yet (CSVs available).\n\n**Lean:** research/lean/NguyenRH1/ \u2014 9 skeleton theorems compile\n(sorryAx-marked); inherited zeta-23-lean fully built + live-audited\n(D-061). elan at ~/.elan/bin (PATH export needed per shell).\n\n## ACTIVE PLAN (next stage)\n1. Prove the elementary Lean tier: sInfty_lower_bound,\n   marginTilde_convex (11-block table), chain_rule_sqrt_shift\n   (D-061 \u00a75 tier (i)).\n2. Optional: E-023b (acb box cover for M\u2080 \u2014 removes the last\n   grid-verified constant in R-004).\n3. Optional: E-021 n = 10\u2074 rerun (cheap via caches; needs zeta-cache\n   filename bump).\n4. Optional: paper figures/tables from numerics/data CSVs.\nDeprioritized: a=13+ push; adversary-ceiling LP; T4b; \u03bb-channel\n(G-004); \u03b8-channel (dead, E-024). Live research opening: symbol-space\nroute on (\u2605) (D-046 revival condition (ii)).\n\n## NEXT ACTION\nSession 011: user picks \u2014 (a) Lean proof tier (i) (sInfty_lower_bound\nfirst: Bernoulli + harmonic bounds, positivity-friendly); (b) E-023b\nacb M\u2080 upgrade; (c) paper figures; (d) new research on the (\u2605)\nsymbol-space opening.\n\n## COMPLETED (Sessions 001\u2013009)\n- [x] Phase 0, Phase 1 (Track A \u2192 monitoring mode, D-013).\n- [x] 2.6 V3 root-cause + repair (E-016b/c, D-025).\n- [x] 2.7 R-003 exact factorization (D-026, E-017/D-027, ledger #5).\n- [x] 2.8 a=12 no transition (E-018/D-028, backend v2, E-019/D-029).\n- [x] 1.6 \u03be\u2032-world saturated (E-020b/D-030); 1.7 T4b closed (D-031).\n- [x] 3.3 \u2192 G-003; 3.4 (Suzuki line spawned); 3.5 design (D-032/D-033).\n- [x] (\u2605) design (D-034/D-035); new tasks 2.9/2.10/2.11.\n- [x] 3.6 D-036 explicit contour constants (session 006 cont.9).\n- [x] 3.7 E-021 (session 007): S_\u221e exact + c\u2080, |S_f| curve, A/B\u2080\n      measured; 6-bug saga documented.\n- [x] Session 008: regroup; R7 resources atlas registered; 3.8\n      COMPLETE (D-037, E-023, R-004 ledger #6); 2.10 COMPLETE\n      (E-022/E-022b + D-040, valley observable); 2.9-D1 COMPLETE\n      (D-041); 2.11 COMPLETE (D-038); 2.12 COMPLETE (E-024 + D-042,\n      \u03b8-independence); 2.13 COMPLETE (E-025 + D-043, discretization\n      floor; quadratic locking correction).\n- [x] Session 009: PHASE 4 COMPLETE (D-052/D-053/D-054, E-027 + D-055,\n      repairs 4.5a\u2013d: D-056\u2013D-059; R-004 tag restored).\n\n## OPEN CONJECTURES / THREADS\n- (\u2605) (R-003): central conjectural target (task 2.9).\n- Q-S1 (D-019 \u00a73): L\u00b2\u2192uniform lifting. Q-S2: \u210b(T_a) de Branges (2.4).\n  \u03b8(a) theory: must explain both metrics (D-028 F3) + z\u2081\u00b7a\u22484.5 law.\n- Q6 (D-001); Q14 Gutzwiller (Phase 2); T2 Christoffel/CMS (D-006).\nCLOSED: T1, T3, T4, T4b (D-031), T5 (\u2192G-001), 3.4a/b/c, 3.3 (\u2192G-003),\n2.8 (D-029), 1.6 (D-030), 1.7 (D-031), 3.5-design (D-033), (\u2605)-design\n(D-035), 3.6 (D-036), 3.7 (E-021), 3.8 (D-037/R-004), 5.3, 5.4.\n\n## BLOCKERS\n(none)\n\n## HANDOFF NOTES\n- db.py add-derivation/log-experiment use INSERT OR REPLACE keyed by\n  id \u2014 a mistyped re-register OVERWRITES the row (session 009:\n  restored a clobbered D-052 row; session 010: deliberately re-keyed\n  D-056 with corrected title).\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n  list. add-derivation signature: positional id, --title --task\n  --status --file (NO --date flag). Session registration via direct\n  sqlite3 insert (journal_file column).\n- venv: ./.venv/Scripts/python.exe. git: git -c user.name=\"NGUYEN-RH-1\"\n  -c user.email=\"research@local\" commit (config NOT modified).\n- LONG RUNS: DETACHED + sandbox DISABLED + log file; poll. For lake:\n  SINGLE command per detached spawn (chained && died silently once);\n  short PrintAxioms runs in foreground.\n- LEAN: elan 4.2.3 at ~/.elan/bin (export PATH per shell); toolchain\n  v4.33.0-rc2; zeta-23-lean fully built (9010 jobs) + cache ~7 GB;\n  NguyenRH1 at research/lean/NguyenRH1 with path requires (vendored\n  repo untouched). Lean 4 gotchas: end-ordering (namespace before\n  anonymous section); no Unicode \u208a/\u208b in identifiers; Complex.sin not\n  csin.\n- flint for ALL \u03b6/Stieltjes >16 digits; mp.zetazero safe (Riemann\u2013\n  Siegel path); mpmath complex-\u03b6 OK to ~1e-10 (E-018 C2); mpmath\n  zeta (integer+Hurwitz) UNTRUSTWORTHY beyond ~57 digits at any dps.\n- PRECISION RULES (session 007, hard-won \u2014 see memory note):\n  (1) mp.mp.dps = X BEFORE every mp.mpf(string) parse, including right\n  after flint calls (entry dps is 15); (2) long decimal constants as\n  STRINGS (bare float literal = 53-bit silently); (3) float64 zero\n  ordinates insufficient for \u03c3_m = \u03a3\u03c1^{\u2212m} (C(n,j) amplification);\n  (4) in Li binomial sums, truncating any ~14^{\u2212j}-sized series at M\n  leaves boundary error ~C(n,M)\u00b714^{\u2212M} peaking at M = n/15 ~ (15/14)\u207f.\n- prime_backend_v2: blockwise \u039b to e\u00b2\u2074, cache E-019-backend-cache.npz;\n  monkeypatch E16.prime_sum_vec + E16._BUILD.clear().\n- Winding diagnostic: \u22654000 pts/edge near real zeros.\n- E-016/E-016b FROZEN (historical record); correct machinery: E-016c\n  (stable eval + recon), E-017/E-018 (R\u2080/R_\u03c4/M).\n- \u03b3-locking claim protocol: D-029 \u00a73.\n- Lagarias paper math/0404394 (research/paper/): \u00a75\u20136 read in full for\n  D-037 (Thm 5.1/6.1, bridge (1.16), interpolation \u00a77).\n- research/resources/: 43-note RH-equivalence atlas = R7 (registered\n  session 008; index.md with per-note project-use map).\n- E-021 caches: E-021-zeta-cache.json (\u03b6 strings 1650 digits, \u03b6*(1)\n  patched), E-021-zeros100-hi-cache.json (100 zeros, 400 digits),\n  E-021-zeros-cache.npy (4624 zeros float64 \u2014 P1 use ONLY).\n- E-023: E-023-assembly.csv + .json (M\u2080, N\u2080, N\u2081, margins).\n- E-027: detector stress test; script E-027-detector.py; zeros cache\n  E-027-zeros-cache.npy (2500 zeros); rerun 16 s with cache (--force).\n  Machinery reusable for D-H/Epstein builds (swap the zero list).\n- n=10\u2074 E-021 rerun: needs zeta strings at 0.31\u00b710\u2074+100 digits \u2014\n  bump n_max-dependent cache filename or delete zeta cache.\n- PAPER: build with pdflatex+bibtex in research/paper/ (MiKTeX);\n  draft.pdf is gitignored. Audit rule (D-060 \u00a75): any edit to\n  draft.tex re-opens the audit for the edited lines.\n",
  "autoRead": false
}