← Session 33 — ii′-3b/3c crux + F-D finding; Lagarias letter package
thinking (661 chars)
Committed. This is a good milestone. Per the pacing rule (§8.5), the session has been long — I should report the milestone. The session accomplished ii′-3b AND ii′-3c — a big day. The next sub-stage is ii′-6 (L0 assembly), which is a large new design task.
Let me give a concise summary. Should I ask about continuing to ii′-6? The fork rule and pacing rule say: work is running long — but there's no explicit time signal (the 5:00 PM break prompt is about local time; I don't know the current time). Let me check the time... Actually, since a natural milestone is reached (ii′-3 fully complete, all committed), I'll summarize and let the user decide on ii′-6.
# ii′-3 COMPLETE — the crux Sf(n) = Res₁(n) is Lean-proved (committed ec80e64)
Two sub-stages finished today, both with perimeter **ZeroCountProp only**:
**ii′-3b** (commit c0f2e78): `sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC)` — sigmaP k = −gFun^{(k−1)}(0)/(k−1)! for all k ≥ 1 (D-070 route: pure algebra + series calculus from the partial-fraction identity).
**ii′-3c** (commit ec80e64, new LiCrux.lean ~430 lines):
- `lagarias_4_10_a (hZC)` — Lagarias's (4.10): lcoeff (k−1) = (−1)^k·(a_k + σ_k) + (−1)^{k−1}, all k ≥ 1
- **`sf_eq_resW1 (hZC)`** — **THE CRUX**: (ResW1 n).re = Sf n for n ≥ 1 — the identity that makes the ii′-6 assembly tail-free
The chain: FE relation (via the unconditional `iteratedDeriv_comp_const_sub` — no induction needed) → shift expansion gFun(1+s) = 1/(1+s) + hLiExt s + ΓR′/ΓR(1+s) → coefficient extraction → multiplied-out linear_combination → per-term (4.10-a) + both ii′-2 swaps + the binomial sum.
**Verification**: full build GREEN (8771 jobs); 31 declarations audited today total — all [propext, Classical.choice, Quot.sound], 0 sorryAx.
**Remaining in Phase 5B**: ii′-6 (L0 assembly: sides identity + bridge |λ_n(T)| ≤ 2·FAlt(T) + |Sf n| ≤ Bn FAlt n — including D-069 Finding 2's H(T) near-sum repair) → ii′-7 (closure: `sfBoundProp` theorem, paper tag upgrade).
Good stopping point — everything is committed and resumable. Continue to ii′-6 now, or break here?
raw content_json (database row)
[{"type":"thinking","thinking":"Committed. This is a good milestone. Per the pacing rule (§8.5), the session has been long — I should report the milestone. The session accomplished ii′-3b AND ii′-3c — a big day. The next sub-stage is ii′-6 (L0 assembly), which is a large new design task.\n\nLet me give a concise summary. Should I ask about continuing to ii′-6? The fork rule and pacing rule say: work is running long — but there's no explicit time signal (the 5:00 PM break prompt is about local time; I don't know the current time). Let me check the time... Actually, since a natural milestone is reached (ii′-3 fully complete, all committed), I'll summarize and let the user decide on ii′-6.","signature":""},{"type":"text","text":"# ii′-3 COMPLETE — the crux Sf(n) = Res₁(n) is Lean-proved (committed ec80e64)\n\nTwo sub-stages finished today, both with perimeter **ZeroCountProp only**:\n\n**ii′-3b** (commit c0f2e78): `sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC)` — sigmaP k = −gFun^{(k−1)}(0)/(k−1)! for all k ≥ 1 (D-070 route: pure algebra + series calculus from the partial-fraction identity).\n\n**ii′-3c** (commit ec80e64, new LiCrux.lean ~430 lines):\n- `lagarias_4_10_a (hZC)` — Lagarias's (4.10): lcoeff (k−1) = (−1)^k·(a_k + σ_k) + (−1)^{k−1}, all k ≥ 1\n- **`sf_eq_resW1 (hZC)`** — **THE CRUX**: (ResW1 n).re = Sf n for n ≥ 1 — the identity that makes the ii′-6 assembly tail-free\n\nThe chain: FE relation (via the unconditional `iteratedDeriv_comp_const_sub` — no induction needed) → shift expansion gFun(1+s) = 1/(1+s) + hLiExt s + ΓR′/ΓR(1+s) → coefficient extraction → multiplied-out linear_combination → per-term (4.10-a) + both ii′-2 swaps + the binomial sum.\n\n**Verification**: full build GREEN (8771 jobs); 31 declarations audited today total — all [propext, Classical.choice, Quot.sound], 0 sorryAx.\n\n**Remaining in Phase 5B**: ii′-6 (L0 assembly: sides identity + bridge |λ_n(T)| ≤ 2·FAlt(T) + |Sf n| ≤ Bn FAlt n — including D-069 Finding 2's H(T) near-sum repair) → ii′-7 (closure: `sfBoundProp` theorem, paper tag upgrade).\n\nGood stopping point — everything is committed and resumable. Continue to ii′-6 now, or break here?"}]