← Session 24 — ii′-2…4: swaps, (4.10) design, contour + website roadmap fixes
thinking (310 chars)
Session 022 is complete. Summary for the user:
- ii′-5a: design D-067 (route b″) — Stirling-free, Hadamard-free
- ii′-5b: complete — LiRBound.lean with the level-2 representation + disc bound
- Everything committed, axiom-audited, archive updated.
Next: ii′-5c (the Davenport disc argument), ~1–1.5 sessions.
Session 022 closed out. Summary:
## ii′-5 progress: design + first build complete
**ii′-5a — design D-067 (route b″):** the R-bound in Lean is now fully designed, and the two feared builds are gone:
- **No complex Stirling for Γ** — the |ζ| control on the disc's left dip comes from one extra Euler–Maclaurin level (B̃₂), and the left strip (σ ∈ [−5/2, 1/2]) comes from FE-reflection where **the zero sums cancel exactly**: R(s) = −R(1−s) + digamma bracket.
- **No Hadamard product** — disc Blaschke removal via Zeta23's StrongPNTPrefix instead.
- Bonus: Zeta23's `digamma_stirling` subsumes D-056's Lemma D entirely.
**ii′-5b — complete, all green** (LiRBound.lean, ~640 lines):
- `b2Fun` — the periodic Bernoulli primitive (continuity for free via `comp_fract''`)
- `integral_b1_cpow_eq` — the level-2 IBP identity ∫₁^∞ B̃₁x^{−s−1} = (s+1)∫₁^∞ B̃₂x^{−s−2}
- `hasDerivAt_b2Integral` — analyticity of the parameter integral on re > −1
- `riemannZeta_eq_level2` — ζ(s) = 1/2 + 1/(s−1) − s(s+1)∫₁^∞ B̃₂x^{−s−2}dx, extended across re = 0 via the identity principle on the **convex** regions W± = {re > −1, ±im > 5} (sidestepping the punctured-halfplane connectedness grind)
- **`norm_riemannZeta_le_disc`: ‖ζ(s)‖ ≤ (3/4)|t|² on B(2+it, 5/2), |t| ≥ 10**
Full build green (8752 jobs), 27 declarations audited: 3 standard axioms only. Commits: `de6ab52` (design), `ab2df3f` (WIP1), `f607489` (5b), `9bcc0d1` (closure).
**Next (session 023): ii′-5c** — the Davenport disc argument proper: g = ζ/∏(s−ρₖ)^mₖ, `LogOfAnalyticFunction` + `BorelCaratheodoryDeriv`, giving the R-bound on σ ∈ [1/2, 7/2]. Estimated 1–1.5 sessions.
raw content_json (database row)
[{"type":"thinking","thinking":"Session 022 is complete. Summary for the user:\n\n- ii′-5a: design D-067 (route b″) — Stirling-free, Hadamard-free\n- ii′-5b: complete — LiRBound.lean with the level-2 representation + disc bound\n- Everything committed, axiom-audited, archive updated.\n\nNext: ii′-5c (the Davenport disc argument), ~1–1.5 sessions.","signature":""},{"type":"text","text":"Session 022 closed out. Summary:\n\n## ii′-5 progress: design + first build complete\n\n**ii′-5a — design D-067 (route b″):** the R-bound in Lean is now fully designed, and the two feared builds are gone:\n- **No complex Stirling for Γ** — the |ζ| control on the disc's left dip comes from one extra Euler–Maclaurin level (B̃₂), and the left strip (σ ∈ [−5/2, 1/2]) comes from FE-reflection where **the zero sums cancel exactly**: R(s) = −R(1−s) + digamma bracket.\n- **No Hadamard product** — disc Blaschke removal via Zeta23's StrongPNTPrefix instead.\n- Bonus: Zeta23's `digamma_stirling` subsumes D-056's Lemma D entirely.\n\n**ii′-5b — complete, all green** (LiRBound.lean, ~640 lines):\n- `b2Fun` — the periodic Bernoulli primitive (continuity for free via `comp_fract''`)\n- `integral_b1_cpow_eq` — the level-2 IBP identity ∫₁^∞ B̃₁x^{−s−1} = (s+1)∫₁^∞ B̃₂x^{−s−2}\n- `hasDerivAt_b2Integral` — analyticity of the parameter integral on re > −1\n- `riemannZeta_eq_level2` — ζ(s) = 1/2 + 1/(s−1) − s(s+1)∫₁^∞ B̃₂x^{−s−2}dx, extended across re = 0 via the identity principle on the **convex** regions W± = {re > −1, ±im > 5} (sidestepping the punctured-halfplane connectedness grind)\n- **`norm_riemannZeta_le_disc`: ‖ζ(s)‖ ≤ (3/4)|t|² on B(2+it, 5/2), |t| ≥ 10**\n\nFull build green (8752 jobs), 27 declarations audited: 3 standard axioms only. Commits: `de6ab52` (design), `ab2df3f` (WIP1), `f607489` (5b), `9bcc0d1` (closure).\n\n**Next (session 023): ii′-5c** — the Davenport disc argument proper: g = ζ/∏(s−ρₖ)^mₖ, `LogOfAnalyticFunction` + `BorelCaratheodoryDeriv`, giving the R-bound on σ ∈ [1/2, 7/2]. Estimated 1–1.5 sessions."}]