[{"type":"text","text":"# ii′-3b COMPLETE — committed (c0f2e78)\n\n**The moments capstone is proved:** `sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC : ZeroCountProp)` — sigmaP k = −gFun^{(k−1)}(0)/(k−1)! for **all k ≥ 1** (D-070 route: pure algebra + series calculus from 5e's `partialFraction_identity`, no contours; perimeter **ZeroCountProp only**).\n\n## What was built this session\n- **§5** (~190 lines): `iteratedDeriv_zpow_neg_one` → `iteratedDeriv_seriesTerm` → the M-test `seriesTerm_deriv_summableLocallyUniformlyOn` (dominator j!·2^{j+1}·(1/δ)^{j−1}·mult/‖ρ‖²) → `iteratedDeriv_seriesFun_zero` (the LiDigamma `iteratedDerivWithin_tsum` pattern verbatim)\n- **§6** (~100 lines): `gFun_eventuallyEq_zero` + the capstone — k=1 via §4's reindex, k≥2 via (G) + §5 + the sign algebra (−1)^k·(−1)^{k+1} = −1. First-pass green.\n\n## Verification\n- Full build **GREEN (8770 jobs)**; LiTightR + LiMoments now root-imported\n- Audit (`audit-session038-axioms.txt`): **23 declarations, [propext, Classical.choice, Quot.sound] only, 0 sorryAx**\n- Archive closed: journal-038, STATE.md, NGUYEN.md, research.db, commit c0f2e78\n\n## Notable gotchas banked\n- Factorial `!` is scoped notation — needs `open scoped Nat` (the parse error masquerades as a spacing issue)\n- `Summable.mul_left` dominators must be constant-first — `D ρ * C` whnf-loops the refine to 800k heartbeats (found by bisection)\n- `rw [seriesFun]` fails on the unapplied constant — use a `show` beta-expansion\n\n## Next (Session 039)\n**ii′-3c**: the (4.10-a) assembly → the crux identity Sf(n) = Res₁(n). All inputs in hand (3a pieces A+B, 3b capstone); one new ingredient: the FE derivative relation gFun^{(k−1)}(0) = (−1)^k·gFun^{(k−1)}(1) from `xiL_one_sub`. Then ii′-6 → ii′-7 closure."}]