← Session 24 — ii′-2…4: swaps, (4.10) design, contour + website roadmap fixes
thinking (268 chars)
Session 023 fully closed. Everything is committed and the archive is consistent:
- journal-023.md written
- NGUYEN.md updated (checklist + session log)
- STATE.md updated with NEXT ACTION for session 024
- research.db registered
- All commits in
Summary for the user.
Session 023 closed cleanly. Everything is committed and the archive is in a resumable state.
## Where things stand
**Today's arc (sessions 021–023):**
- **ii′-4 COMPLETE** — L3 zero-avoiding T + L1 kernel bounds + `zeroMult(−2) = 1` (LiContour.lean)
- **ii′-5a** — R-bound design D-067 (Stirling-free, Hadamard-free route)
- **ii′-5b COMPLETE** — the level-2 Euler–Maclaurin ζ representation + the disc bound ‖ζ‖ ≤ (3/4)|t|² (LiRBound.lean)
- **Route revision (D-067 §6)** — the key finding: no disc-only constant can reach the baked A = 10.5, B₀ = 48 (the BC derivative factor loses ≥16×), so the disc bound becomes the *growth input* for the partial-fraction identity, and the tight constants come from D-056's analysis of the identity (new sub-stages 5e/5f)
- **ii′-5c part 1** — LiDisc.lean through the Jensen count, including the full multiplicity-invariance chain you flagged (`analyticOrderNatAt_riemannZeta_affine/const_mul/scaledZeta`) and `scaledZeta_jensen_count` via Zeta23's `ZerosBound` + `zeta_lower_bound_two` (‖ζ(2+it)‖ ≥ 1/3)
**Next session (024) — ii′-5c back half:** R-gap selection (scaled midpoint pigeonhole) → g := ζ/∏(s−ρₖ)^mₖ analytic + nonvanishing → outer-circle/center bounds → `LogOfAnalyticFunction` + `BorelCaratheodoryDeriv` → the loose R-bound ‖logDeriv ζ s − Σ_near m/(s−ρ)‖ ≤ C·(log|t|)².
All clean: builds green, axiom audits at 3 standard axioms only, STATE.md has the resume point.
raw content_json (database row)
[{"type":"thinking","thinking":"Session 023 fully closed. Everything is committed and the archive is consistent:\n- journal-023.md written\n- NGUYEN.md updated (checklist + session log)\n- STATE.md updated with NEXT ACTION for session 024\n- research.db registered\n- All commits in\n\nSummary for the user.","signature":""},{"type":"text","text":"Session 023 closed cleanly. Everything is committed and the archive is in a resumable state.\n\n## Where things stand\n\n**Today's arc (sessions 021–023):**\n- **ii′-4 COMPLETE** — L3 zero-avoiding T + L1 kernel bounds + `zeroMult(−2) = 1` (LiContour.lean)\n- **ii′-5a** — R-bound design D-067 (Stirling-free, Hadamard-free route)\n- **ii′-5b COMPLETE** — the level-2 Euler–Maclaurin ζ representation + the disc bound ‖ζ‖ ≤ (3/4)|t|² (LiRBound.lean)\n- **Route revision (D-067 §6)** — the key finding: no disc-only constant can reach the baked A = 10.5, B₀ = 48 (the BC derivative factor loses ≥16×), so the disc bound becomes the *growth input* for the partial-fraction identity, and the tight constants come from D-056's analysis of the identity (new sub-stages 5e/5f)\n- **ii′-5c part 1** — LiDisc.lean through the Jensen count, including the full multiplicity-invariance chain you flagged (`analyticOrderNatAt_riemannZeta_affine/const_mul/scaledZeta`) and `scaledZeta_jensen_count` via Zeta23's `ZerosBound` + `zeta_lower_bound_two` (‖ζ(2+it)‖ ≥ 1/3)\n\n**Next session (024) — ii′-5c back half:** R-gap selection (scaled midpoint pigeonhole) → g := ζ/∏(s−ρₖ)^mₖ analytic + nonvanishing → outer-circle/center bounds → `LogOfAnalyticFunction` + `BorelCaratheodoryDeriv` → the loose R-bound ‖logDeriv ζ s − Σ_near m/(s−ρ)‖ ≤ C·(log|t|)².\n\nAll clean: builds green, axiom audits at 3 standard axioms only, STATE.md has the resume point."}]