← Session 7 — All-forks plan approved; E-016 Herglotz work
thinking (37 chars)
Summarize last session (004) briefly.
Nothing is broken — the project is in a clean, committed state. Here's where things stand after **Session 004** (yesterday, 2026-08-17):
## What happened last session
Session 004 was a big one — all 4 forks from the fork rule were completed:
1. **Recovery** — found and fixed an orphaned E-011 run (killed mid-edit by a crashed session). Root cause: a wrong hardcoded λ₁ constant (digit 22+) plus an `mp.dps` typo causing silent 53-bit contamination.
2. **Fork 2 (Task 3.2)** — Li coefficients λₙ > 0 certified for all **n ≤ 2000** from the arithmetic side (zero-free, dps 1000, λ₁ to 102 digits). → **R-001**, ledger entry #3.
3. **Fork 3 (Task 3.3)** — Answered **NO**: density theorems can't constrain the de Bruijn–Newman constant Λ (one-sided information + two other obstructions). → D-021, graveyard **G-003**, toy model E-012.
4. **Fork 4 (T4)** — **CLOSED**: the ξ′-certificate's strength comes from a *perfect-square node* in the diagonal law D₁ ≈ s(1−2s)² (prime-scale cancellation at p ~ √(T/2π)). Reproduced the paper's Remark 7.1 constants to 5e-6. Gain is **not portable** to ξ. → D-022, **R-002**.
5. **Q-S3 attack** (your chosen direction) — mapped Suzuki's Cor 1.6 density wall up to a=10: the lattice is still maximal (no density collapse yet — a *scale* limitation, not a wall). Found a promising candidate rule **θ = π** (selected by read-off at every a with perfect phase agreement). → E-014, D-023.
## Current position
- Phase 0 ✔, Phase 1 ✔ (Track A → monitoring mode)
- Phase 3: 3.1 mapped, 3.2 done to n=2000, 3.3 closed, 3.4 complete
- **Clean stop — no blockers, nothing in progress.** Per the fork rule, the queue is waiting on your pick.
## Queued next actions (your choice)
| # | Direction | Cost |
|---|-----------|------|
| **A1** | Q-S3a: analytic — does v±(a,·) → A_∞⁻¹e^{±·} in a norm controlling W? | cheap |
| **A2** | Q-S3b: prime-sum backend redesign → reach a ~ 12–14, track θ=π zero flow | medium numerics |
| **A3** | Q-S3c: Herglotz W′/W fine structure at θ=π, a = 4..10 | cheap |
| **B** | T4b scoping: node mechanism on higher derivatives ξ⁽ᵏ⁾ | scoping |
| **C** | ξ′-world bandwidth-one ceiling (LawN256 analogue) | cheap |
| **D** | Task 3.2 continuation: push Li past n=2000 (detached runs) or asymptotics | medium |
Which direction do you want to take?
raw content_json (database row)
[{"type":"thinking","thinking":"Summarize last session (004) briefly.","signature":""},{"type":"text","text":"Nothing is broken — the project is in a clean, committed state. Here's where things stand after **Session 004** (yesterday, 2026-08-17):\n\n## What happened last session\n\nSession 004 was a big one — all 4 forks from the fork rule were completed:\n\n1. **Recovery** — found and fixed an orphaned E-011 run (killed mid-edit by a crashed session). Root cause: a wrong hardcoded λ₁ constant (digit 22+) plus an `mp.dps` typo causing silent 53-bit contamination.\n2. **Fork 2 (Task 3.2)** — Li coefficients λₙ > 0 certified for all **n ≤ 2000** from the arithmetic side (zero-free, dps 1000, λ₁ to 102 digits). → **R-001**, ledger entry #3.\n3. **Fork 3 (Task 3.3)** — Answered **NO**: density theorems can't constrain the de Bruijn–Newman constant Λ (one-sided information + two other obstructions). → D-021, graveyard **G-003**, toy model E-012.\n4. **Fork 4 (T4)** — **CLOSED**: the ξ′-certificate's strength comes from a *perfect-square node* in the diagonal law D₁ ≈ s(1−2s)² (prime-scale cancellation at p ~ √(T/2π)). Reproduced the paper's Remark 7.1 constants to 5e-6. Gain is **not portable** to ξ. → D-022, **R-002**.\n5. **Q-S3 attack** (your chosen direction) — mapped Suzuki's Cor 1.6 density wall up to a=10: the lattice is still maximal (no density collapse yet — a *scale* limitation, not a wall). Found a promising candidate rule **θ = π** (selected by read-off at every a with perfect phase agreement). → E-014, D-023.\n\n## Current position\n\n- Phase 0 ✔, Phase 1 ✔ (Track A → monitoring mode)\n- Phase 3: 3.1 mapped, 3.2 done to n=2000, 3.3 closed, 3.4 complete\n- **Clean stop — no blockers, nothing in progress.** Per the fork rule, the queue is waiting on your pick.\n\n## Queued next actions (your choice)\n\n| # | Direction | Cost |\n|---|-----------|------|\n| **A1** | Q-S3a: analytic — does v±(a,·) → A_∞⁻¹e^{±·} in a norm controlling W? | cheap |\n| **A2** | Q-S3b: prime-sum backend redesign → reach a ~ 12–14, track θ=π zero flow | medium numerics |\n| **A3** | Q-S3c: Herglotz W′/W fine structure at θ=π, a = 4..10 | cheap |\n| **B** | T4b scoping: node mechanism on higher derivatives ξ⁽ᵏ⁾ | scoping |\n| **C** | ξ′-world bandwidth-one ceiling (LawN256 analogue) | cheap |\n| **D** | Task 3.2 continuation: push Li past n=2000 (detached runs) or asymptotics | medium |\n\nWhich direction do you want to take?"}]