← Session 32 — ii′-3b start: capstone axiom audit + moments
thinking (86 chars)
Journal-036 exists, matching STATE.md. Everything is consistent. Now answer concisely.
Archive is consistent (session-036 journal matches STATE.md). Here's where things stand:
## Next on the list: **Session 037 — ii′-3b (contour moments)**
The immediate task is proving the **contour moment evaluations** in Lean:
$$\sigma_k = -\frac{g^{(k-1)}(0)}{(k-1)!}$$
per design **D-066 route β4** — the R2(iii) Lagarias (4.10) moments, using the ii′-1b residue machinery plus the tight R-bound that was just completed in session 036 (`logDeriv_riemannZeta_sub_nearZeros_le_tight`, the 10.5·log(|t|+2) + 48 bound — this is what unblocks the moment estimates).
**Remaining tier ii′ pipeline after that:**
1. **ii′-3b** — contour moments ← *next*
2. **ii′-3c** — assemble Lagarias (4.10): τ_j = c_j + (−1)ʲσ_{j+1} − (−1)ʲ, yielding the crux identity Sf(n) = Res₁(n)
3. **ii′-6** — L0 assembly: sides identity + bridge |λ_n(T)| ≤ 2·FAlt(T) (hRH) + |Sf n| ≤ Bn FAlt n on [10⁵, N₁]; includes D-069 Finding 2's H(T) near-sum repair
4. **ii′-7** — closure: `sfBoundProp : SfBoundProp` proved, final `lambda_pos_finite_height_closed` with only the 3 perimeter hypotheses, full axiom audit, paper Appendix B + tag upgrade, archive closure
**Context:** Phase 5B is the active phase — closing `SfBoundProp` in Lean before Paper A submission (user directive, option (a)). ii′-5f just finished (session 036, 8 commits, ~4300-line LiTightR.lean, full build green at 8762 jobs, audits clean: 3 standard axioms only). No blockers.
**Prep reading for ii′-3b** (from STATE.md): journal-036 + journal-035 banked Lean gotchas, and the D-066 design doc. One housekeeping note: LiTightR.lean is not yet root-imported — it should be imported from the root at ii′-3b or ii′-6.
Ready to start ii′-3b whenever you are.
raw content_json (database row)
[{"type":"thinking","thinking":"Journal-036 exists, matching STATE.md. Everything is consistent. Now answer concisely.","signature":""},{"type":"text","text":"Archive is consistent (session-036 journal matches STATE.md). Here's where things stand:\n\n## Next on the list: **Session 037 — ii′-3b (contour moments)**\n\nThe immediate task is proving the **contour moment evaluations** in Lean:\n$$\\sigma_k = -\\frac{g^{(k-1)}(0)}{(k-1)!}$$\nper design **D-066 route β4** — the R2(iii) Lagarias (4.10) moments, using the ii′-1b residue machinery plus the tight R-bound that was just completed in session 036 (`logDeriv_riemannZeta_sub_nearZeros_le_tight`, the 10.5·log(|t|+2) + 48 bound — this is what unblocks the moment estimates).\n\n**Remaining tier ii′ pipeline after that:**\n1. **ii′-3b** — contour moments ← *next*\n2. **ii′-3c** — assemble Lagarias (4.10): τ_j = c_j + (−1)ʲσ_{j+1} − (−1)ʲ, yielding the crux identity Sf(n) = Res₁(n)\n3. **ii′-6** — L0 assembly: sides identity + bridge |λ_n(T)| ≤ 2·FAlt(T) (hRH) + |Sf n| ≤ Bn FAlt n on [10⁵, N₁]; includes D-069 Finding 2's H(T) near-sum repair\n4. **ii′-7** — closure: `sfBoundProp : SfBoundProp` proved, final `lambda_pos_finite_height_closed` with only the 3 perimeter hypotheses, full axiom audit, paper Appendix B + tag upgrade, archive closure\n\n**Context:** Phase 5B is the active phase — closing `SfBoundProp` in Lean before Paper A submission (user directive, option (a)). ii′-5f just finished (session 036, 8 commits, ~4300-line LiTightR.lean, full build green at 8762 jobs, audits clean: 3 standard axioms only). No blockers.\n\n**Prep reading for ii′-3b** (from STATE.md): journal-036 + journal-035 banked Lean gotchas, and the D-066 design doc. One housekeeping note: LiTightR.lean is not yet root-imported — it should be imported from the root at ii′-3b or ii′-6.\n\nReady to start ii′-3b whenever you are."}]