[{"type":"thinking","thinking":"Committed. Now — this session has already been long (website fixes + full ii′-4 + ii′-5a design). Per §8.5 break prompt, I should pause and ask the user whether to continue into ii′-5b (the B̃₂/IBP build, ~1 session estimated) or take a break/log off.\n\nLet me give a concise status + the question.","signature":""},{"type":"text","text":"**ii′-5a (design) committed.** The full inventory is verified and the route is settled — notably, the two feared builds evaporated:\n\n- **No complex Stirling for Γ needed.** The left half of the strip is reached by FE-reflection where the zero sums cancel *exactly* (R(s) = −R(1−s) + digamma bracket), and Zeta23's `digamma_stirling` (‖ψ(w) − log w + 1/(2w)‖ ≤ 3/w.im²) subsumes D-056's Lemma D entirely.\n- **No Hadamard product needed.** The disc handles the zero sum via Blaschke removal; Zeta23's StrongPNTPrefix has the full Davenport toolkit (`BorelCaratheodoryDeriv`, `LogOfAnalyticFunction`, `ZeroFactorization`).\n\nThe one genuine new build: ‖ζ(s)‖ ≤ C(1+|t|)² on σ ≥ −1/2 via **one extra Euler–Maclaurin level** (B̃₂) on top of Zeta23's existing ζ₀ representation — forced by the geometric fact that every disc covering the |γ−t|<1 zeros dips left of σ = 0.\n\nRemaining ii′-5 sub-stages: 5b (B̃₂ + ζ bound, ~1 sess) → 5c (Davenport disc, ~1–1.5) → 5d (FE-reflection, ~0.5) → 5e (constants fold, ~0.25).\n\nThis session has already been a long one (website fixes + all of ii′-4 + this design). Per the pacing rule — continue into **ii′-5b** now, or break here?"}]