← Session 8 — Regroup + R-004 finite-height Li theorem; resources atlas ingested
thinking (128 chars)
Clean (only the user's paper/ duplicate remains untracked — their file, leaving it). Session 007 is fully wrapped up. Summarize.
Session 007 is complete and committed. Summary:
## Task 3.7 (E-021) — COMPLETE, ALL CHECKS PASS
**Results** (`E-021-sinf-sf-curve.{csv,json}`, 5000 rows, db-registered):
- **S_∞(n) = (n/2)log n + C₁n − 1/4 + 1/(24n) + o(1/n)** — Lagarias's O(1) constant for ζ measured exactly (c₀ = −1/4)
- **|S_f(n)| ≤ 13.52 for n ≤ 5000** (peak at n=3298) vs the D-036 traced worst-case bound ~2280 — the bound is loose by ~170×, exactly the benchmark D-037 needs
- λ_n = S_∞ − S_f + 1 matches E-015 to **4.8e-25** (n ≤ 3000)
- Contour constants measured: **A = 0.9, B₀ = 1.0** (tightened from D-036's 2.0/2.0)
**The 6-bug saga** (all root-caused, documented in journal-007 + script + memory):
1. mpmath zeta silently caps at ~57–58 digits (Hurwitz *and* integer) → all ζ/Stieltjes now flint
2. GAMMA_E as bare float literal → 53-bit (constants must be strings)
3. `mp.mpf(string)` parsed before `mp.mp.dps` set — three separate instances
4. σ_m truncation boundary error ~C(n,M)·14^{−M}, peaking at M=n/15 as (15/14)ⁿ → adaptive M_SIG=1830
5. float64 zero ordinates insufficient for σ_m (first 100 zeros at dps 450 fix it)
6. Stieltjes-recursion reference also loses digits at k~80 (noted for future k>3000 work)
**Resources folder** — all **43 notes** read (the RH-equivalence atlas: Li, Weil, Nyman–Beurling, Robin/Lagarias, Speiser, Salem, Volchkov, Franel–Landau, Riesz, de Bruijn–Newman, Hilbert–Pólya, Montgomery, Keating–Snaith, Selberg, Lindelöf, special values, explicit formulas + the 60-equation compendium). Direct D-037 inputs identified: Schoenfeld's 8π bound, Büthe 2018, Hasanalizade–Shen–Wong S(T) bound.
**Next action** (in STATE.md): task **3.8 (D-037 → R-004)** — assemble the explicit finite-height Li theorem (λ_n > 0 ∀ n ≤ N₁), tagged [PROVED-CONDITIONAL(computational RH-to-height-T₀)].
One note: `research/paper/Detailed_Derivations_...Compeddium....txt` is still untracked — it's a duplicate of the copy now in `research/resources/`. Delete it or keep it?
raw content_json (database row)
[{"type":"thinking","thinking":"Clean (only the user's paper/ duplicate remains untracked — their file, leaving it). Session 007 is fully wrapped up. Summarize.","signature":""},{"type":"text","text":"Session 007 is complete and committed. Summary:\n\n## Task 3.7 (E-021) — COMPLETE, ALL CHECKS PASS\n\n**Results** (`E-021-sinf-sf-curve.{csv,json}`, 5000 rows, db-registered):\n- **S_∞(n) = (n/2)log n + C₁n − 1/4 + 1/(24n) + o(1/n)** — Lagarias's O(1) constant for ζ measured exactly (c₀ = −1/4)\n- **|S_f(n)| ≤ 13.52 for n ≤ 5000** (peak at n=3298) vs the D-036 traced worst-case bound ~2280 — the bound is loose by ~170×, exactly the benchmark D-037 needs\n- λ_n = S_∞ − S_f + 1 matches E-015 to **4.8e-25** (n ≤ 3000)\n- Contour constants measured: **A = 0.9, B₀ = 1.0** (tightened from D-036's 2.0/2.0)\n\n**The 6-bug saga** (all root-caused, documented in journal-007 + script + memory):\n1. mpmath zeta silently caps at ~57–58 digits (Hurwitz *and* integer) → all ζ/Stieltjes now flint\n2. GAMMA_E as bare float literal → 53-bit (constants must be strings)\n3. `mp.mpf(string)` parsed before `mp.mp.dps` set — three separate instances\n4. σ_m truncation boundary error ~C(n,M)·14^{−M}, peaking at M=n/15 as (15/14)ⁿ → adaptive M_SIG=1830\n5. float64 zero ordinates insufficient for σ_m (first 100 zeros at dps 450 fix it)\n6. Stieltjes-recursion reference also loses digits at k~80 (noted for future k>3000 work)\n\n**Resources folder** — all **43 notes** read (the RH-equivalence atlas: Li, Weil, Nyman–Beurling, Robin/Lagarias, Speiser, Salem, Volchkov, Franel–Landau, Riesz, de Bruijn–Newman, Hilbert–Pólya, Montgomery, Keating–Snaith, Selberg, Lindelöf, special values, explicit formulas + the 60-equation compendium). Direct D-037 inputs identified: Schoenfeld's 8π bound, Büthe 2018, Hasanalizade–Shen–Wong S(T) bound.\n\n**Next action** (in STATE.md): task **3.8 (D-037 → R-004)** — assemble the explicit finite-height Li theorem (λ_n > 0 ∀ n ≤ N₁), tagged [PROVED-CONDITIONAL(computational RH-to-height-T₀)].\n\nOne note: `research/paper/Detailed_Derivations_...Compeddium....txt` is still untracked — it's a duplicate of the copy now in `research/resources/`. Delete it or keep it?"}]