← Session 8 — Regroup + R-004 finite-height Li theorem; resources atlas ingested
Now STATE.md — the resume point.
tool: Write ok
input
{
"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 007 COMPLETE (task 3.7/E-021 done \u2014\nALL CHECKS PASS). Clean state, nothing mid-flight.\n\n## CURRENT POSITION\n\u2714 PHASE 0, 1 COMPLETE. PHASE 3 (Track C): 3.1\u20133.4 closed; 3.2 numerics\nto n=3000; 3.5 DESIGN done; **3.6 (D-036) and 3.7 (E-021) COMPLETE**.\nPHASE 2 (Track B): 2.6\u20132.8 closed; (\u2605) design done (task 2.9 opened).\n**R-003 (ledger #5): W = F\u00b7(R\u2080+R_\u03c4) exact; Cor 1.6 \u27fa (\u2605) tail-\ncancellation. Both fronts now have precise designs + mapped walls.**\n\nFront A (Li, task 3.5): Voros \u2014 \"\u03bb_n>0 \u2200n\u2265N\u2080\" \u27fa RH at ANY N\u2080 (no\npartial version). ACHIEVABLE: EXPLICIT finite-height theorem\n\u03bb_n > 0 \u2200 n \u2264 N\u2081 (~10\u00b2\u2070\u201310\u00b2\u2074 est.) from Lagarias Thm 6.1 bridge +\nPlatt T\u2080 + traced constants + finite verification (D-033).\nFront B (Suzuki, task 2.9): (\u2605) \u27fa Cor 1.6 \u27fa \"Krein-space operator D\nhas real spectrum\" via strong resolvent convergence D_{a,\u03b8(a)} \u2192 D;\nwalls W-1 (index), W-2 (persistence = RH), W-3 (circularity) (D-035).\n\n## ACTIVE PLAN (next stage \u2014 execution packages, in order)\n1. **3.8 (D-037\u2192R-004): assemble the finite-height theorem.** [analysis]\n All inputs now in hand:\n - D-036: contour bounds, I_III dominant ~4.7\u221an log n (A=2) \u2014 with\n E-021's MEASURED A = 0.9, B\u2080 = 1.0 the leading constant drops\n (~3.5\u221an log n; re-evaluate \u00a73 during assembly).\n - E-021: c\u2080 = \u22121/4 (+1/(24n) first correction) for S_\u221e; measured\n |S_f(n)| \u2264 13.52 for n \u2264 5000 (peak at n = 3298) vs traced\n worst-case ~C\u2081\u221an log n (~2280 there \u2014 slack ~170\u00d7); \u03bb_n vs E-015\n validated 4.8e-25.\n - Finite verification: E-011/E-015 machinery (\u03bb_n > 0, n \u2264 3000) +\n literature to 5\u00d710\u2075 (Misguich/Voros per D-033).\n - resources/ notes: Schoenfeld 8\u03c0 bound + B\u00fcthe 2018 (turn Platt's\n T\u2080 into explicit statements); Hasanalizade\u2013Shen\u2013Wong S(T) bound\n as an alternative to Trudgian constants.\n2. 2.10 (E-022): spectral-measure convergence numerics (D_{a,\u03c0} atomic\n weights 1/\u2016v_z\u2016\u00b2_T vs \u03b3-atoms) \u2014 novel observable (D-035 D2).\n3. 2.9-D1 (Krein frame + deficiency-convergence theorem). [analysis]\n4. 2.11 (D-038): transition-scale lower bound. [analysis]\n(Deprioritized: a=13+ push; adversary-ceiling LP; T4b \u2014 see D-029/\nD-030/D-031 for revival conditions. E-021 n=10\u2074 rerun available cheaply\nvia caches if D-037 wants the longer |S_f| curve.)\n\n## E-021 RESULT SUMMARY (task 3.7, session 007)\n- S_\u221e(n) = (1/2)n log n + C\u2081n \u2212 1/4 + 1/(24n) + o(1/n), measured to\n n = 5000 (C\u2081 = (\u03b3\u22121\u2212log 2\u03c0)/2). c\u2080 = \u22121/4 = Lagarias Thm 5.1's O(1)\n constant for \u03b6 (N=1).\n- |S_f(n)| \u2264 13.52 for n \u2264 5000 (max at n = 3298); |S_f| typical O(1).\n- \u03bb_n = S_\u221e \u2212 S_f + 1 matches E-015 to 4.8e-25 relative (n \u2264 3000).\n- |R(s)| \u2264 0.9\u00b7log(t+2) + 1.0 at all 15 contour sample points (max\n |R| = 4.75). C\u2080(100) = 6.234, C\u2080(10\u2074) = 8.840, C\u2080(10\u2076) = 11.194.\n- The \u03b7 machinery: Stieltjes (j \u2264 79, flint) + Lagarias (4.10) formula\n (j \u2265 80) with \u03c3_m exact for m \u2264 80 (\u03c4\u2212\u03b7 inversion) and from the\n first 100 zeros (dps 450) for 81 \u2264 m \u2264 M_SIG = 1830.\n\n## COMPLETED (Sessions 001\u2013007)\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 (journal-007, script comments,\n memory note project_mpmath_dps_bug.md).\n\n## NEXT ACTION\nTask 3.8 (D-037 \u2192 R-004): assemble the finite-height Li theorem \u2014\nN\u2081 explicit from (a) Lagarias Thm 6.1 bridge, (b) Platt T\u2080 \u2248 3\u00d710\u00b9\u00b2,\n(c) D-036 traced constants with E-021's measured A = 0.9/B\u2080 = 1.0,\n(d) E-021's c\u2080 = \u22121/4 and the measured |S_f| curve; finite\nverification table; adversarial review; tag\n[PROVED-CONDITIONAL(computational RH-to-height-T\u2080)].\n\n## OPEN CONJECTURES / THREADS\n- (\u2605) (R-003): central conjectural target (now task 2.9).\n- Q-S1 (D-019 \u00a73): L\u00b2\u2192uniform lifting (Phase 4). Q-S2: \u210b(T_a) de\n Branges (2.4). \u03b8(a) theory: must explain both metrics (D-028 F3) +\n 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).\n\n## BLOCKERS\n(none)\n\n## HANDOFF NOTES\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n list. Row counts: recount from CSV after registration. Session\n registration via direct 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.\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/): the key external\n input for 3.8 (Thms 5.1/6.1 + \u00a76 contour argument).\n- research/resources/: 29-note RH-equivalence atlas (user-provided,\n session 007 \u2014 read in full; literature pointers for D-037/paper).\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- 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"
}
result 2026-08-19 06:57:32Z → 2026-08-19 06:57:32Z
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"filePath": "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 007 COMPLETE (task 3.7/E-021 done \u2014\nALL CHECKS PASS). Clean state, nothing mid-flight.\n\n## CURRENT POSITION\n\u2714 PHASE 0, 1 COMPLETE. PHASE 3 (Track C): 3.1\u20133.4 closed; 3.2 numerics\nto n=3000; 3.5 DESIGN done; **3.6 (D-036) and 3.7 (E-021) COMPLETE**.\nPHASE 2 (Track B): 2.6\u20132.8 closed; (\u2605) design done (task 2.9 opened).\n**R-003 (ledger #5): W = F\u00b7(R\u2080+R_\u03c4) exact; Cor 1.6 \u27fa (\u2605) tail-\ncancellation. Both fronts now have precise designs + mapped walls.**\n\nFront A (Li, task 3.5): Voros \u2014 \"\u03bb_n>0 \u2200n\u2265N\u2080\" \u27fa RH at ANY N\u2080 (no\npartial version). ACHIEVABLE: EXPLICIT finite-height theorem\n\u03bb_n > 0 \u2200 n \u2264 N\u2081 (~10\u00b2\u2070\u201310\u00b2\u2074 est.) from Lagarias Thm 6.1 bridge +\nPlatt T\u2080 + traced constants + finite verification (D-033).\nFront B (Suzuki, task 2.9): (\u2605) \u27fa Cor 1.6 \u27fa \"Krein-space operator D\nhas real spectrum\" via strong resolvent convergence D_{a,\u03b8(a)} \u2192 D;\nwalls W-1 (index), W-2 (persistence = RH), W-3 (circularity) (D-035).\n\n## ACTIVE PLAN (next stage \u2014 execution packages, in order)\n1. **3.8 (D-037\u2192R-004): assemble the finite-height theorem.** [analysis]\n All inputs now in hand:\n - D-036: contour bounds, I_III dominant ~4.7\u221an log n (A=2) \u2014 with\n E-021's MEASURED A = 0.9, B\u2080 = 1.0 the leading constant drops\n (~3.5\u221an log n; re-evaluate \u00a73 during assembly).\n - E-021: c\u2080 = \u22121/4 (+1/(24n) first correction) for S_\u221e; measured\n |S_f(n)| \u2264 13.52 for n \u2264 5000 (peak at n = 3298) vs traced\n worst-case ~C\u2081\u221an log n (~2280 there \u2014 slack ~170\u00d7); \u03bb_n vs E-015\n validated 4.8e-25.\n - Finite verification: E-011/E-015 machinery (\u03bb_n > 0, n \u2264 3000) +\n literature to 5\u00d710\u2075 (Misguich/Voros per D-033).\n - resources/ notes: Schoenfeld 8\u03c0 bound + B\u00fcthe 2018 (turn Platt's\n T\u2080 into explicit statements); Hasanalizade\u2013Shen\u2013Wong S(T) bound\n as an alternative to Trudgian constants.\n2. 2.10 (E-022): spectral-measure convergence numerics (D_{a,\u03c0} atomic\n weights 1/\u2016v_z\u2016\u00b2_T vs \u03b3-atoms) \u2014 novel observable (D-035 D2).\n3. 2.9-D1 (Krein frame + deficiency-convergence theorem). [analysis]\n4. 2.11 (D-038): transition-scale lower bound. [analysis]\n(Deprioritized: a=13+ push; adversary-ceiling LP; T4b \u2014 see D-029/\nD-030/D-031 for revival conditions. E-021 n=10\u2074 rerun available cheaply\nvia caches if D-037 wants the longer |S_f| curve.)\n\n## E-021 RESULT SUMMARY (task 3.7, session 007)\n- S_\u221e(n) = (1/2)n log n + C\u2081n \u2212 1/4 + 1/(24n) + o(1/n), measured to\n n = 5000 (C\u2081 = (\u03b3\u22121\u2212log 2\u03c0)/2). c\u2080 = \u22121/4 = Lagarias Thm 5.1's O(1)\n constant for \u03b6 (N=1).\n- |S_f(n)| \u2264 13.52 for n \u2264 5000 (max at n = 3298); |S_f| typical O(1).\n- \u03bb_n = S_\u221e \u2212 S_f + 1 matches E-015 to 4.8e-25 relative (n \u2264 3000).\n- |R(s)| \u2264 0.9\u00b7log(t+2) + 1.0 at all 15 contour sample points (max\n |R| = 4.75). C\u2080(100) = 6.234, C\u2080(10\u2074) = 8.840, C\u2080(10\u2076) = 11.194.\n- The \u03b7 machinery: Stieltjes (j \u2264 79, flint) + Lagarias (4.10) formula\n (j \u2265 80) with \u03c3_m exact for m \u2264 80 (\u03c4\u2212\u03b7 inversion) and from the\n first 100 zeros (dps 450) for 81 \u2264 m \u2264 M_SIG = 1830.\n\n## COMPLETED (Sessions 001\u2013007)\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 (journal-007, script comments,\n memory note project_mpmath_dps_bug.md).\n\n## NEXT ACTION\nTask 3.8 (D-037 \u2192 R-004): assemble the finite-height Li theorem \u2014\nN\u2081 explicit from (a) Lagarias Thm 6.1 bridge, (b) Platt T\u2080 \u2248 3\u00d710\u00b9\u00b2,\n(c) D-036 traced constants with E-021's measured A = 0.9/B\u2080 = 1.0,\n(d) E-021's c\u2080 = \u22121/4 and the measured |S_f| curve; finite\nverification table; adversarial review; tag\n[PROVED-CONDITIONAL(computational RH-to-height-T\u2080)].\n\n## OPEN CONJECTURES / THREADS\n- (\u2605) (R-003): central conjectural target (now task 2.9).\n- Q-S1 (D-019 \u00a73): L\u00b2\u2192uniform lifting (Phase 4). Q-S2: \u210b(T_a) de\n Branges (2.4). \u03b8(a) theory: must explain both metrics (D-028 F3) +\n 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).\n\n## BLOCKERS\n(none)\n\n## HANDOFF NOTES\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n list. Row counts: recount from CSV after registration. Session\n registration via direct 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.\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/): the key external\n input for 3.8 (Thms 5.1/6.1 + \u00a76 contour argument).\n- research/resources/: 29-note RH-equivalence atlas (user-provided,\n session 007 \u2014 read in full; literature pointers for D-037/paper).\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- 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",
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" # STATE.md \u2014 NGUYEN-RH-1 RESUME POINT",
" # \u2b50 READ THIS FIRST at the start of every session.",
"-Last updated: 2026-08-18 | Session 006 cont.9 (MID-TASK STOP at 3.7/E-021 \u2014 resume instructions below)",
"+Last updated: 2026-08-19 | Session 007 COMPLETE (task 3.7/E-021 done \u2014",
"+ALL CHECKS PASS). Clean state, nothing mid-flight.",
" ",
" ## CURRENT POSITION",
" \u2714 PHASE 0, 1 COMPLETE. PHASE 3 (Track C): 3.1\u20133.4 closed; 3.2 numerics",
"-to n=3000; 3.5 DESIGN done. PHASE 2 (Track B): 2.6\u20132.8 closed; (\u2605)",
"-design done (task 2.9 opened).",
"+to n=3000; 3.5 DESIGN done; **3.6 (D-036) and 3.7 (E-021) COMPLETE**.",
"+PHASE 2 (Track B): 2.6\u20132.8 closed; (\u2605) design done (task 2.9 opened).",
" **R-003 (ledger #5): W = F\u00b7(R\u2080+R_\u03c4) exact; Cor 1.6 \u27fa (\u2605) tail-",
" cancellation. Both fronts now have precise designs + mapped walls.**",
" "
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" walls W-1 (index), W-2 (persistence = RH), W-3 (circularity) (D-035).",
" ",
" ## ACTIVE PLAN (next stage \u2014 execution packages, in order)",
"-1. 3.6 (D-036): explicit |\u03be\u2032/\u03be| & |L\u2032/L| contour bounds for \u03b6 +",
"- explicit N(T) bound (Trudgian). [analysis]",
"-2. 3.7 (E-021): exact S_\u221e(n) to n=10\u2074 + |S_f(n)| curve. [numerics]",
"-3. 2.10 (E-022): spectral-measure convergence (D_{a,\u03c0} atomic weights",
"- 1/\u2016v_z\u2016\u00b2_T vs \u03b3-atoms) \u2014 novel observable. [numerics]",
"-4. 3.8 (D-037\u2192R-004): assemble finite-height theorem. [analysis]",
"-5. 2.9-D1 (Krein frame + deficiency-convergence theorem). [analysis]",
"-6. 2.11 (D-038): transition-scale lower bound. [analysis]",
"-Order rationale: 3.6+3.7 feed 3.8 (the most concrete new theorem);",
"-2.10 is cheap and opens the D1 analytic work; 2.11 last.",
"+1. **3.8 (D-037\u2192R-004): assemble the finite-height theorem.** [analysis]",
"+ All inputs now in hand:",
"+ - D-036: contour bounds, I_III dominant ~4.7\u221an log n (A=2) \u2014 with",
"+ E-021's MEASURED A = 0.9, B\u2080 = 1.0 the leading constant drops",
"+ (~3.5\u221an log n; re-evaluate \u00a73 during assembly).",
"+ - E-021: c\u2080 = \u22121/4 (+1/(24n) first correction) for S_\u221e; measured",
"+ |S_f(n)| \u2264 13.52 for n \u2264 5000 (peak at n = 3298) vs traced",
"+ worst-case ~C\u2081\u221an log n (~2280 there \u2014 slack ~170\u00d7); \u03bb_n vs E-015",
"+ validated 4.8e-25.",
"+ - Finite verification: E-011/E-015 machinery (\u03bb_n > 0, n \u2264 3000) +",
"+ literature to 5\u00d710\u2075 (Misguich/Voros per D-033).",
"+ - resources/ notes: Schoenfeld 8\u03c0 bound + B\u00fcthe 2018 (turn Platt's",
"+ T\u2080 into explicit statements); Hasanalizade\u2013Shen\u2013Wong S(T) bound",
"+ as an alternative to Trudgian constants.",
"+2. 2.10 (E-022): spectral-measure convergence numerics (D_{a,\u03c0} atomic",
"+ weights 1/\u2016v_z\u2016\u00b2_T vs \u03b3-atoms) \u2014 novel observable (D-035 D2).",
"+3. 2.9-D1 (Krein frame + deficiency-convergence theorem). [analysis]",
"+4. 2.11 (D-038): transition-scale lower bound. [analysis]",
" (Deprioritized: a=13+ push; adversary-ceiling LP; T4b \u2014 see D-029/",
"-D-030/D-031 for revival conditions.)",
"+D-030/D-031 for revival conditions. E-021 n=10\u2074 rerun available cheaply",
"+via caches if D-037 wants the longer |S_f| curve.)",
" ",
"-## IN PROGRESS \u2014 RESUME HERE",
"-Task 3.7 (E-021) at ~90% completion; killed for 5 PM stop. TO RESUME:",
"-1. Run E-021 detached with --force:",
"- ./.venv/Scripts/python.exe research/numerics/scripts/E-021-sinf-sf-curve.py --force",
"- (zeros cache E-021-zeros-cache.npy + zeta cache E-021-zeta-cache.json",
"- make it ~20 min; CSV/JSON were deleted because the previous run had",
"- the WRONG S_f convention \u2014 current script has the fix: S_f =",
"- \u03a3 C(n,j)\u03b7_{j\u22121} plain, E-011-validated).",
"-2. Then: register E-021 in research.db (row_count from CSV), write",
"- D-037 (analysis + finite-height theorem assembly), update indexes,",
"- STATE, journal, commit.",
"-Key numbers already in the log: C0(1e4)=8.84; A_use=0.9, B0_use=1.0",
"-(|R| max sample 4.75); \u03b7\u2080=\u22120.576975 (= \u2212\u03b3 within \u03c3\u2081-tail 1.2e-3 \u2713);",
"-\u03c3\u2081=0.022855 (tail 1.2e-3); S_inf residual \u2192 c\u2080 \u2248 \u22120.25000 (converging:",
"-\u22120.25004, \u22120.25002, \u22120.250014, \u22120.250010, \u22120.250008 at n=1k..5k) \u2014",
"-Lagarias Thm 5.1's O(1) constant for \u03b6 measured.",
"+## E-021 RESULT SUMMARY (task 3.7, session 007)",
"+- S_\u221e(n) = (1/2)n log n + C\u2081n \u2212 1/4 + 1/(24n) + o(1/n), measured to",
"+ n = 5000 (C\u2081 = (\u03b3\u22121\u2212log 2\u03c0)/2). c\u2080 = \u22121/4 = Lagarias Thm 5.1's O(1)",
"+ constant for \u03b6 (N=1).",
"+- |S_f(n)| \u2264 13.52 for n \u2264 5000 (max at n = 3298); |S_f| typical O(1).",
"+- \u03bb_n = S_\u221e \u2212 S_f + 1 matches E-015 to 4.8e-25 relative (n \u2264 3000).",
"+- |R(s)| \u2264 0.9\u00b7log(t+2) + 1.0 at all 15 contour sample points (max",
"+ |R| = 4.75). C\u2080(100) = 6.234, C\u2080(10\u2074) = 8.840, C\u2080(10\u2076) = 11.194.",
"+- The \u03b7 machinery: Stieltjes (j \u2264 79, flint) + Lagarias (4.10) formula",
"+ (j \u2265 80) with \u03c3_m exact for m \u2264 80 (\u03c4\u2212\u03b7 inversion) and from the",
"+ first 100 zeros (dps 450) for 81 \u2264 m \u2264 M_SIG = 1830.",
" ",
"-## COMPLETED (Session 006, all)",
"-- [x] REGROUP + archive audit + db hygiene (sessions 3\u20135, row_counts).",
"+## COMPLETED (Sessions 001\u2013007)",
"+- [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).",
" - [x] 2.8 a=12 no transition (E-018/D-028, backend v2, E-019/D-029).",
"-- [x] 1.6 \u03be\u2032-world saturated (E-020b window optimum = 0.86864 to 1e-6;",
"- E-020 pool-LP limitation; D-030).",
"-- [x] 1.7 T4b closed (D-031; \u03be\u2033 \u22480.94 heuristic but capped <100% by",
"- G-001 at every order).",
"-- [x] 3.5 design (D-032 lit map; D-033 finite-height theorem skeleton",
"- + wall).",
"-- [x] (\u2605) design (D-034 lit map; D-035 resolvent route + 3-layer wall).",
"+- [x] 1.6 \u03be\u2032-world saturated (E-020b/D-030); 1.7 T4b closed (D-031).",
"+- [x] 3.3 \u2192 G-003; 3.4 (Suzuki line spawned); 3.5 design (D-032/D-033).",
"+- [x] (\u2605) design (D-034/D-035); new tasks 2.9/2.10/2.11.",
"+- [x] 3.6 D-036 explicit contour constants (session 006 cont.9).",
"+- [x] 3.7 E-021 (session 007): S_\u221e exact + c\u2080, |S_f| curve, A/B\u2080",
"+ measured; 6-bug saga documented (journal-007, script comments,",
"+ memory note project_mpmath_dps_bug.md).",
" ",
" ## NEXT ACTION",
"-Task 3.6 (D-036): explicit contour bounds for \u03b6 \u2014 trace Lagarias",
"-math/0404394 \u00a76 constants (Lemma 6.1 for \u03b6; |k_n(s)| bounds already",
"-explicit: e\u2074+1, e, 2) + N(T) explicit bound (Trudgian 2014:",
"-|S(T)| \u2264 0.137 log T + 0.443 log log T + 1.588). Local PDF of the",
"-Lagarias paper: see D-032 (downloaded copy path in session tool cache;",
"-re-fetch arXiv:math/0404394 if needed).",
"+Task 3.8 (D-037 \u2192 R-004): assemble the finite-height Li theorem \u2014",
"+N\u2081 explicit from (a) Lagarias Thm 6.1 bridge, (b) Platt T\u2080 \u2248 3\u00d710\u00b9\u00b2,",
"+(c) D-036 traced constants with E-021's measured A = 0.9/B\u2080 = 1.0,",
"+(d) E-021's c\u2080 = \u22121/4 and the measured |S_f| curve; finite",
"+verification table; adversarial review; tag",
"+[PROVED-CONDITIONAL(computational RH-to-height-T\u2080)].",
" ",
" ## OPEN CONJECTURES / THREADS",
" - (\u2605) (R-003): central conjectural target (now task 2.9)."
]
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"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).",
"+(D-035), 3.6 (D-036), 3.7 (E-021).",
" ",
" ## BLOCKERS",
" (none)"
]
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"lines": [
" ## HANDOFF NOTES",
" - db.py: init, log-experiment, add-result, add-derivation, add-graveyard,",
" list. Row counts: recount from CSV after registration. Session",
"- registration via direct sqlite3 insert (session-006 pattern).",
"+ registration via direct sqlite3 insert (journal_file column).",
" - 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.",
"-- flint for all \u03b6/Stieltjes >16 digits; mp.zetazero safe; mpmath",
"- complex-\u03b6 OK to ~1e-10 (E-018 C2).",
"+- 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.",
" - 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).",
" - \u03b3-locking claim protocol: D-029 \u00a73.",
"-- Lagarias paper math/0404394: the key external input for 3.6\u20133.8",
"- (Thms 5.1/6.1 + \u00a76 contour argument).",
"+- Lagarias paper math/0404394 (research/paper/): the key external",
"+ input for 3.8 (Thms 5.1/6.1 + \u00a76 contour argument).",
"+- research/resources/: 29-note RH-equivalence atlas (user-provided,",
"+ session 007 \u2014 read in full; literature pointers for D-037/paper).",
"+- 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),",
"+ E-021-zeros-cache.npy (4624 zeros float64 \u2014 P1 use ONLY).",
"+- 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.",
" "
]
}
],
"originalFile": "# 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 006 cont.9 (MID-TASK STOP at 3.7/E-021 \u2014 resume instructions below)\n\n## CURRENT POSITION\n\u2714 PHASE 0, 1 COMPLETE. PHASE 3 (Track C): 3.1\u20133.4 closed; 3.2 numerics\nto n=3000; 3.5 DESIGN done. PHASE 2 (Track B): 2.6\u20132.8 closed; (\u2605)\ndesign done (task 2.9 opened).\n**R-003 (ledger #5): W = F\u00b7(R\u2080+R_\u03c4) exact; Cor 1.6 \u27fa (\u2605) tail-\ncancellation. Both fronts now have precise designs + mapped walls.**\n\nFront A (Li, task 3.5): Voros \u2014 \"\u03bb_n>0 \u2200n\u2265N\u2080\" \u27fa RH at ANY N\u2080 (no\npartial version). ACHIEVABLE: EXPLICIT finite-height theorem\n\u03bb_n > 0 \u2200 n \u2264 N\u2081 (~10\u00b2\u2070\u201310\u00b2\u2074 est.) from Lagarias Thm 6.1 bridge +\nPlatt T\u2080 + traced constants + finite verification (D-033).\nFront B (Suzuki, task 2.9): (\u2605) \u27fa Cor 1.6 \u27fa \"Krein-space operator D\nhas real spectrum\" via strong resolvent convergence D_{a,\u03b8(a)} \u2192 D;\nwalls W-1 (index), W-2 (persistence = RH), W-3 (circularity) (D-035).\n\n## ACTIVE PLAN (next stage \u2014 execution packages, in order)\n1. 3.6 (D-036): explicit |\u03be\u2032/\u03be| & |L\u2032/L| contour bounds for \u03b6 +\n explicit N(T) bound (Trudgian). [analysis]\n2. 3.7 (E-021): exact S_\u221e(n) to n=10\u2074 + |S_f(n)| curve. [numerics]\n3. 2.10 (E-022): spectral-measure convergence (D_{a,\u03c0} atomic weights\n 1/\u2016v_z\u2016\u00b2_T vs \u03b3-atoms) \u2014 novel observable. [numerics]\n4. 3.8 (D-037\u2192R-004): assemble finite-height theorem. [analysis]\n5. 2.9-D1 (Krein frame + deficiency-convergence theorem). [analysis]\n6. 2.11 (D-038): transition-scale lower bound. [analysis]\nOrder rationale: 3.6+3.7 feed 3.8 (the most concrete new theorem);\n2.10 is cheap and opens the D1 analytic work; 2.11 last.\n(Deprioritized: a=13+ push; adversary-ceiling LP; T4b \u2014 see D-029/\nD-030/D-031 for revival conditions.)\n\n## IN PROGRESS \u2014 RESUME HERE\nTask 3.7 (E-021) at ~90% completion; killed for 5 PM stop. TO RESUME:\n1. Run E-021 detached with --force:\n ./.venv/Scripts/python.exe research/numerics/scripts/E-021-sinf-sf-curve.py --force\n (zeros cache E-021-zeros-cache.npy + zeta cache E-021-zeta-cache.json\n make it ~20 min; CSV/JSON were deleted because the previous run had\n the WRONG S_f convention \u2014 current script has the fix: S_f =\n \u03a3 C(n,j)\u03b7_{j\u22121} plain, E-011-validated).\n2. Then: register E-021 in research.db (row_count from CSV), write\n D-037 (analysis + finite-height theorem assembly), update indexes,\n STATE, journal, commit.\nKey numbers already in the log: C0(1e4)=8.84; A_use=0.9, B0_use=1.0\n(|R| max sample 4.75); \u03b7\u2080=\u22120.576975 (= \u2212\u03b3 within \u03c3\u2081-tail 1.2e-3 \u2713);\n\u03c3\u2081=0.022855 (tail 1.2e-3); S_inf residual \u2192 c\u2080 \u2248 \u22120.25000 (converging:\n\u22120.25004, \u22120.25002, \u22120.250014, \u22120.250010, \u22120.250008 at n=1k..5k) \u2014\nLagarias Thm 5.1's O(1) constant for \u03b6 measured.\n\n## COMPLETED (Session 006, all)\n- [x] REGROUP + archive audit + db hygiene (sessions 3\u20135, row_counts).\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 window optimum = 0.86864 to 1e-6;\n E-020 pool-LP limitation; D-030).\n- [x] 1.7 T4b closed (D-031; \u03be\u2033 \u22480.94 heuristic but capped <100% by\n G-001 at every order).\n- [x] 3.5 design (D-032 lit map; D-033 finite-height theorem skeleton\n + wall).\n- [x] (\u2605) design (D-034 lit map; D-035 resolvent route + 3-layer wall).\n\n## NEXT ACTION\nTask 3.6 (D-036): explicit contour bounds for \u03b6 \u2014 trace Lagarias\nmath/0404394 \u00a76 constants (Lemma 6.1 for \u03b6; |k_n(s)| bounds already\nexplicit: e\u2074+1, e, 2) + N(T) explicit bound (Trudgian 2014:\n|S(T)| \u2264 0.137 log T + 0.443 log log T + 1.588). Local PDF of the\nLagarias paper: see D-032 (downloaded copy path in session tool cache;\nre-fetch arXiv:math/0404394 if needed).\n\n## OPEN CONJECTURES / THREADS\n- (\u2605) (R-003): central conjectural target (now task 2.9).\n- Q-S1 (D-019 \u00a73): L\u00b2\u2192uniform lifting (Phase 4). Q-S2: \u210b(T_a) de\n Branges (2.4). \u03b8(a) theory: must explain both metrics (D-028 F3) +\n 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).\n\n## BLOCKERS\n(none)\n\n## HANDOFF NOTES\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n list. Row counts: recount from CSV after registration. Session\n registration via direct sqlite3 insert (session-006 pattern).\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.\n- flint for all \u03b6/Stieltjes >16 digits; mp.zetazero safe; mpmath\n complex-\u03b6 OK to ~1e-10 (E-018 C2).\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: the key external input for 3.6\u20133.8\n (Thms 5.1/6.1 + \u00a76 contour argument).\n",
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[{"type":"text","text":"Now STATE.md — the resume point."},{"type":"tool_use","id":"Write_180","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: 2026-08-19 | Session 007 COMPLETE (task 3.7/E-021 done —\nALL CHECKS PASS). Clean state, nothing mid-flight.\n\n## CURRENT POSITION\n✔ PHASE 0, 1 COMPLETE. PHASE 3 (Track C): 3.1–3.4 closed; 3.2 numerics\nto n=3000; 3.5 DESIGN done; **3.6 (D-036) and 3.7 (E-021) COMPLETE**.\nPHASE 2 (Track B): 2.6–2.8 closed; (★) design done (task 2.9 opened).\n**R-003 (ledger #5): W = F·(R₀+R_τ) exact; Cor 1.6 ⟺ (★) tail-\ncancellation. Both fronts now have precise designs + mapped walls.**\n\nFront A (Li, task 3.5): Voros — \"λ_n>0 ∀n≥N₀\" ⟺ RH at ANY N₀ (no\npartial version). ACHIEVABLE: EXPLICIT finite-height theorem\nλ_n > 0 ∀ n ≤ N₁ (~10²⁰–10²⁴ est.) from Lagarias Thm 6.1 bridge +\nPlatt T₀ + traced constants + finite verification (D-033).\nFront B (Suzuki, task 2.9): (★) ⟺ Cor 1.6 ⟺ \"Krein-space operator D\nhas real spectrum\" via strong resolvent convergence D_{a,θ(a)} → D;\nwalls W-1 (index), W-2 (persistence = RH), W-3 (circularity) (D-035).\n\n## ACTIVE PLAN (next stage — execution packages, in order)\n1. **3.8 (D-037→R-004): assemble the finite-height theorem.** [analysis]\n All inputs now in hand:\n - D-036: contour bounds, I_III dominant ~4.7√n log n (A=2) — with\n E-021's MEASURED A = 0.9, B₀ = 1.0 the leading constant drops\n (~3.5√n log n; re-evaluate §3 during assembly).\n - E-021: c₀ = −1/4 (+1/(24n) first correction) for S_∞; measured\n |S_f(n)| ≤ 13.52 for n ≤ 5000 (peak at n = 3298) vs traced\n worst-case ~C₁√n log n (~2280 there — slack ~170×); λ_n vs E-015\n validated 4.8e-25.\n - Finite verification: E-011/E-015 machinery (λ_n > 0, n ≤ 3000) +\n literature to 5×10⁵ (Misguich/Voros per D-033).\n - resources/ notes: Schoenfeld 8π bound + Büthe 2018 (turn Platt's\n T₀ into explicit statements); Hasanalizade–Shen–Wong S(T) bound\n as an alternative to Trudgian constants.\n2. 2.10 (E-022): spectral-measure convergence numerics (D_{a,π} atomic\n weights 1/‖v_z‖²_T vs γ-atoms) — novel observable (D-035 D2).\n3. 2.9-D1 (Krein frame + deficiency-convergence theorem). [analysis]\n4. 2.11 (D-038): transition-scale lower bound. [analysis]\n(Deprioritized: a=13+ push; adversary-ceiling LP; T4b — see D-029/\nD-030/D-031 for revival conditions. E-021 n=10⁴ rerun available cheaply\nvia caches if D-037 wants the longer |S_f| curve.)\n\n## E-021 RESULT SUMMARY (task 3.7, session 007)\n- S_∞(n) = (1/2)n log n + C₁n − 1/4 + 1/(24n) + o(1/n), measured to\n n = 5000 (C₁ = (γ−1−log 2π)/2). c₀ = −1/4 = Lagarias Thm 5.1's O(1)\n constant for ζ (N=1).\n- |S_f(n)| ≤ 13.52 for n ≤ 5000 (max at n = 3298); |S_f| typical O(1).\n- λ_n = S_∞ − S_f + 1 matches E-015 to 4.8e-25 relative (n ≤ 3000).\n- |R(s)| ≤ 0.9·log(t+2) + 1.0 at all 15 contour sample points (max\n |R| = 4.75). C₀(100) = 6.234, C₀(10⁴) = 8.840, C₀(10⁶) = 11.194.\n- The η machinery: Stieltjes (j ≤ 79, flint) + Lagarias (4.10) formula\n (j ≥ 80) with σ_m exact for m ≤ 80 (τ−η inversion) and from the\n first 100 zeros (dps 450) for 81 ≤ m ≤ M_SIG = 1830.\n\n## COMPLETED (Sessions 001–007)\n- [x] Phase 0, Phase 1 (Track A → 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 ξ′-world saturated (E-020b/D-030); 1.7 T4b closed (D-031).\n- [x] 3.3 → G-003; 3.4 (Suzuki line spawned); 3.5 design (D-032/D-033).\n- [x] (★) 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_∞ exact + c₀, |S_f| curve, A/B₀\n measured; 6-bug saga documented (journal-007, script comments,\n memory note project_mpmath_dps_bug.md).\n\n## NEXT ACTION\nTask 3.8 (D-037 → R-004): assemble the finite-height Li theorem —\nN₁ explicit from (a) Lagarias Thm 6.1 bridge, (b) Platt T₀ ≈ 3×10¹²,\n(c) D-036 traced constants with E-021's measured A = 0.9/B₀ = 1.0,\n(d) E-021's c₀ = −1/4 and the measured |S_f| curve; finite\nverification table; adversarial review; tag\n[PROVED-CONDITIONAL(computational RH-to-height-T₀)].\n\n## OPEN CONJECTURES / THREADS\n- (★) (R-003): central conjectural target (now task 2.9).\n- Q-S1 (D-019 §3): L²→uniform lifting (Phase 4). Q-S2: ℋ(T_a) de\n Branges (2.4). θ(a) theory: must explain both metrics (D-028 F3) +\n z₁·a≈4.5 law.\n- Q6 (D-001); Q14 Gutzwiller (Phase 2); T2 Christoffel/CMS (D-006).\nCLOSED: T1, T3, T4, T4b (D-031), T5 (→G-001), 3.4a/b/c, 3.3 (→G-003),\n2.8 (D-029), 1.6 (D-030), 1.7 (D-031), 3.5-design (D-033), (★)-design\n(D-035), 3.6 (D-036), 3.7 (E-021).\n\n## BLOCKERS\n(none)\n\n## HANDOFF NOTES\n- db.py: init, log-experiment, add-result, add-derivation, add-graveyard,\n list. Row counts: recount from CSV after registration. Session\n registration via direct 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.\n- flint for ALL ζ/Stieltjes >16 digits; mp.zetazero safe (Riemann–\n Siegel path); mpmath complex-ζ 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 — 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 σ_m = Σρ^{−m} (C(n,j) amplification);\n (4) in Li binomial sums, truncating any ~14^{−j}-sized series at M\n leaves boundary error ~C(n,M)·14^{−M} peaking at M = n/15 ~ (15/14)ⁿ.\n- prime_backend_v2: blockwise Λ to e²⁴, cache E-019-backend-cache.npz;\n monkeypatch E16.prime_sum_vec + E16._BUILD.clear().\n- Winding diagnostic: ≥4000 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 (R₀/R_τ/M).\n- γ-locking claim protocol: D-029 §3.\n- Lagarias paper math/0404394 (research/paper/): the key external\n input for 3.8 (Thms 5.1/6.1 + §6 contour argument).\n- research/resources/: 29-note RH-equivalence atlas (user-provided,\n session 007 — read in full; literature pointers for D-037/paper).\n- E-021 caches: E-021-zeta-cache.json (ζ strings 1650 digits, ζ*(1)\n patched), E-021-zeros100-hi-cache.json (100 zeros, 400 digits),\n E-021-zeros-cache.npy (4624 zeros float64 — P1 use ONLY).\n- n=10⁴ E-021 rerun: needs zeta strings at 0.31·10⁴+100 digits —\n bump n_max-dependent cache filename or delete zeta cache.\n"},"extra_content":null}]