← Session 24 — ii′-2…4: swaps, (4.10) design, contour + website roadmap fixes
thinking (142 chars)
The user asked a simple status question about tier ii′. I have all the info from STATE.md and NGUYEN.md. Let me give a concise status summary.
## Tier ii′ status — ii′-3a done, next is ii′-4
**Goal:** close `SfBoundProp` in Lean before submitting Paper A. Paper A stays frozen/submittable throughout (freeze protocol in force).
### Completed (sessions 014–020)
| Stage | Content | Status |
|---|---|---|
| ii′-0 | Design (D-064); found the liCoeff encoding defect + the crux identity Sf(n) = Res₁(n) ⟹ tail-free assembly | ✅ |
| ii′-1a | liCoeff pairing fix + `liSummable` proved | ✅ |
| ii′-1b | Residue machinery: `ResW1_eq_sum`, `rectInt'_ppart`, **`rectInt'_Jlag`** (rectangle residue theorem for the Lagarias kernel) | ✅ |
| ii′-2 | Elementary swaps: `liCoeff_eq_sum_sigma`, `sInfty_eq_sum` | ✅ |
| ii′-3 (design) | Route β4 adopted (contour moments + coefficient split); R-bound shared with ii′-5 ⟹ resequenced pipeline (D-066) | ✅ |
| ii′-3a | Pieces A+B: `iteratedDeriv_hLiExt` (ζ-piece) + **`iteratedDeriv_logDeriv_Gammaℝ`** (archimedean coefficients = (−1)^{j+1}·j!·a_{j+1}; digamma partial-fraction series built from scratch) | ✅ |
All builds green (8749 jobs), 3 standard axioms only on every audited declaration.
### Remaining (resequenced order, D-066 §5)
1. **ii′-4** — L3 zero-avoiding T (pigeonhole on perimeter N(T)/S(T)) + L1 kernel bounds (|k_n| ≤ 2, e⁴+1, e^{√n/2}+1; trivial-zero residue via zeroMult(−2) = 1) — **next up, ~1 session, elementary**
2. ii′-5 — R-bound (D-056: A = 10.5, B₀ = 48) via Borel–Carathéodory + Jensen + Blaschke — 2–3 sessions, the heavy lift
3. ii′-3b — contour moments σ_k = −g^{(k−1)}(0)/(k−1)!
4. ii′-3c — assembly → crux (4.10)
5. ii′-6 — L0 assembly: |Sf n| ≤ Bn FAlt n on [10⁵, N₁]
6. ii′-7 — closure: `sfBoundProp : SfBoundProp`, final axiom audit, paper Appendix B + tag upgrade
Roughly 5–9 sessions remain. No blockers. Ready to start ii′-4 whenever you are.
raw content_json (database row)
[{"type":"thinking","thinking":"The user asked a simple status question about tier ii′. I have all the info from STATE.md and NGUYEN.md. Let me give a concise status summary.","signature":""},{"type":"text","text":"## Tier ii′ status — ii′-3a done, next is ii′-4\n\n**Goal:** close `SfBoundProp` in Lean before submitting Paper A. Paper A stays frozen/submittable throughout (freeze protocol in force).\n\n### Completed (sessions 014–020)\n| Stage | Content | Status |\n|---|---|---|\n| ii′-0 | Design (D-064); found the liCoeff encoding defect + the crux identity Sf(n) = Res₁(n) ⟹ tail-free assembly | ✅ |\n| ii′-1a | liCoeff pairing fix + `liSummable` proved | ✅ |\n| ii′-1b | Residue machinery: `ResW1_eq_sum`, `rectInt'_ppart`, **`rectInt'_Jlag`** (rectangle residue theorem for the Lagarias kernel) | ✅ |\n| ii′-2 | Elementary swaps: `liCoeff_eq_sum_sigma`, `sInfty_eq_sum` | ✅ |\n| ii′-3 (design) | Route β4 adopted (contour moments + coefficient split); R-bound shared with ii′-5 ⟹ resequenced pipeline (D-066) | ✅ |\n| ii′-3a | Pieces A+B: `iteratedDeriv_hLiExt` (ζ-piece) + **`iteratedDeriv_logDeriv_Gammaℝ`** (archimedean coefficients = (−1)^{j+1}·j!·a_{j+1}; digamma partial-fraction series built from scratch) | ✅ |\n\nAll builds green (8749 jobs), 3 standard axioms only on every audited declaration.\n\n### Remaining (resequenced order, D-066 §5)\n1. **ii′-4** — L3 zero-avoiding T (pigeonhole on perimeter N(T)/S(T)) + L1 kernel bounds (|k_n| ≤ 2, e⁴+1, e^{√n/2}+1; trivial-zero residue via zeroMult(−2) = 1) — **next up, ~1 session, elementary**\n2. ii′-5 — R-bound (D-056: A = 10.5, B₀ = 48) via Borel–Carathéodory + Jensen + Blaschke — 2–3 sessions, the heavy lift\n3. ii′-3b — contour moments σ_k = −g^{(k−1)}(0)/(k−1)!\n4. ii′-3c — assembly → crux (4.10)\n5. ii′-6 — L0 assembly: |Sf n| ≤ Bn FAlt n on [10⁵, N₁]\n6. ii′-7 — closure: `sfBoundProp : SfBoundProp`, final axiom audit, paper Appendix B + tag upgrade\n\nRoughly 5–9 sessions remain. No blockers. Ready to start ii′-4 whenever you are."}]