← Session 21 — Tier ii′ planning + launch: close SfBoundProp in Lean (D-064)
Done. Summary of this session's work:
## Documentation (per your request)
- **NGUYEN.md §5: new "PHASE 5B — TIER ii′" checklist** — 9 items (ii′-0 through ii′-7) with freeze protocol, perimeter, and discovery summaries; also session logs for 014/015 (committed 7a395b2).
- D-064 design doc, journal entries, STATE.md resume point, research.db — all current.
## Session 015 — ii′-1a COMPLETE: the liCoeff defect is repaired
- **Replaced** the defective unordered-tsum `liCoeff` with the classical **paired symmetric form** `liSummand = ½·mult·(f ρ + f ρ̄)` — manifestly real, and the mathematically correct Keiper–Li summand.
- **Proved `liSummable`** (~340 new lines in LiSkeleton.lean §1): the geometric-sum tail bound `|Re f(ρ)| ≤ 2n²/‖ρ‖²`, the `(9/4)·‖ρ‖²` comparison, the `(9/2)n²·mult/(1+‖γ‖²)` dominator built on Zeta23's *proved* `zero_sum_inv_sq`, plus the finite-ball argument for small zeros.
- **Full rebuild green** (8741 jobs) with **zero downstream changes** — and now `LiVerifiedUpTo`/`SfBoundProp` are *true* statements instead of vacuous ones.
- **Axiom audit clean**: 3 standard axioms only, on all new declarations and both main theorems.
Committed as be1ffb2. **Next (session 016): ii′-1b — the residue machinery** (finite-order residue, rectangle theorem extension beyond simple poles, the w=1 Leibniz residue, zero residues). Ready when you are.
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[{"type":"text","text":"Done. Summary of this session's work:\n\n## Documentation (per your request)\n- **NGUYEN.md §5: new \"PHASE 5B — TIER ii′\" checklist** — 9 items (ii′-0 through ii′-7) with freeze protocol, perimeter, and discovery summaries; also session logs for 014/015 (committed 7a395b2).\n- D-064 design doc, journal entries, STATE.md resume point, research.db — all current.\n\n## Session 015 — ii′-1a COMPLETE: the liCoeff defect is repaired\n- **Replaced** the defective unordered-tsum `liCoeff` with the classical **paired symmetric form** `liSummand = ½·mult·(f ρ + f ρ̄)` — manifestly real, and the mathematically correct Keiper–Li summand.\n- **Proved `liSummable`** (~340 new lines in LiSkeleton.lean §1): the geometric-sum tail bound `|Re f(ρ)| ≤ 2n²/‖ρ‖²`, the `(9/4)·‖ρ‖²` comparison, the `(9/2)n²·mult/(1+‖γ‖²)` dominator built on Zeta23's *proved* `zero_sum_inv_sq`, plus the finite-ball argument for small zeros.\n- **Full rebuild green** (8741 jobs) with **zero downstream changes** — and now `LiVerifiedUpTo`/`SfBoundProp` are *true* statements instead of vacuous ones.\n- **Axiom audit clean**: 3 standard axioms only, on all new declarations and both main theorems.\n\nCommitted as be1ffb2. **Next (session 016): ii′-1b — the residue machinery** (finite-order residue, rectangle theorem extension beyond simple poles, the w=1 Leibniz residue, zero residues). Ready when you are."}]