[{"type":"text","text":"Session 016 complete. Status for you:\n\n## ii′-1b(i) + (ii) — DONE and committed (axiom-clean)\n\n**LiResidue.lean** (commit 1c35d31):\n- `zetaA = (w−1)·ζ(w)` with the pole filled in — proved **analytic at w=1** (removable singularity via Mathlib's machinery).\n- `hLi` — the analytic-at-1 form of `(w−1)(−ζ′/ζ)`, value 1.\n- `lcoeff k` — the Laurent coefficients of −ζ′/ζ at 1, defined operationally.\n- **`ResW1_eq_sum`**: the w=1 residue of the Lagarias-kernel integrand = **Σ_{j=1}^n C(n,j)·lcoeff(j−1)**, proved via Leibniz (`iteratedDeriv_mul`) — exactly the identity we verified numerically in session 014.\n\n**LiPrincipal.lean** (commit 973fe66):\n- **`rectInt_deriv_eq_zero`**: the rectangle integral of a derivative vanishes (per-side FTC, mixed-field chain rule).\n- **`rectInt'_ppart`**: the principal part **integrates to ResW1 n** on any rectangle with 1 in its interior (A₁ term by the vendored rectangle residue theorem; the i ≥ 2 tail vanishes by the primitive argument).\n\nBoth modules: **3 standard axioms only**, full build green.\n\n## Overall tier ii′ progress\n- ii′-0 ✔ (design + 2 discoveries) · ii′-1a ✔ (liCoeff defect repaired) · **ii′-1b: (i)✔ (ii)✔**, (iii) remaining\n- Remaining map: ii′-1b(iii) → ii′-2 → ii′-3 (long pole) → ii′-4 → ii′-5 → ii′-6 → ii′-7\n\n## Next (session 017): ii′-1b(iii)\nThe final residue piece: R = J − ppart shown holomorphic off {zeros ∪ {−2}} (Taylor-remainder order computation at w=1), simple poles at zeros with residue `mult·(1−(ρ/(ρ−1))ⁿ)`, assembly `sides(T) = ResW1 + Σ zeros + triv` via the vendored `residueTheorem_finset`.\n\nEverything is committed and crash-safe (21c7497). Paper A remains frozen/submittable. Say \"go\" to continue."}]