← Session 28 — ii′-5e: partial-fraction identity (zero series + F entire)
thinking (231 chars)
All clean. Session 030 closed properly:
- Commits: 5d24756 (5e-v-a), e6a654b (5e-v-b chunk 1), cf1e28c (closure).
- Everything committed, STATE.md has NEXT ACTION, journal-030 has the full design.
Summarize for the user concisely.
**Session 030 COMPLETE — ii′-5e-v started, two chunks landed** (commits `5d24756`, `e6a654b`, `cf1e28c`).
**LiCircleBound.lean** (~340 lines, clean elaboration):
**5e-v-a** — the count + Dirichlet inputs:
- `A0count` + `Ncount_window_le` — Zeta23's RvM local count (mult-weighted, two-sided, all t, **unconditional** — this is the series-bound count input, no perimeter needed).
- `Ncount_add_of_le` / `Ncount_chain_le` / `Ncount_le_of_interval(_gen)` — the dyadic interval count `A₀·(b−a+1)·log(3 max|a||b|+5)`.
- `norm_logDeriv_zeta_le_dirichlet` — ‖ζ′/ζ s‖ ≤ dirichletC2 for re ≥ 2 (the right near-axis arc input).
- `isNontrivialZero_conj` (lower-half arcs).
**5e-v-b chunk 1** — the split machinery:
- `tsum_split_finset` — a summable tsum = finset sum + if-zeroed tail (the structural tool for the shell decomposition).
- `lowZeros`/`lowZeroConst` — the small-zero symbolic finite constant.
**Design fully worked out and recorded in journal-030** for the remaining chunks: the dyadic tail bound (`ENNReal.tsum_fiberwise` is free in ℝ≥0∞ + Zeta23's `key` window machinery), the main `seriesFun` circle bound (one tsum split + four shell bounds, γ-gap only in the critical band), the logDeriv/elem assembly, the Schwarz squeeze (Mathlib's `dist_le_div_mul_mapsTo_ball`), and the `∃ B` capstone. Explicit numerics for the k ≥ 4000 threshold verified (Ĉ₀(16006) ≤ 9.36 via `2.718281828¹⁰ ≥ 22026`).
Banked 11 new gotchas (notably: `le_or_lt` absent→`le_or_gt`; `tsum_eq_sum` form; endpoint-pinning for HOU-heavy lemmas; a parser fragility with nested `calc…:= by` in deep case blocks).
**Next session: 5e-v-b chunk 2** (tail bound + main series circle bound).
raw content_json (database row)
[{"type":"thinking","thinking":"All clean. Session 030 closed properly:\n- Commits: 5d24756 (5e-v-a), e6a654b (5e-v-b chunk 1), cf1e28c (closure).\n- Everything committed, STATE.md has NEXT ACTION, journal-030 has the full design.\n\nSummarize for the user concisely.","signature":""},{"type":"text","text":"**Session 030 COMPLETE — ii′-5e-v started, two chunks landed** (commits `5d24756`, `e6a654b`, `cf1e28c`).\n\n**LiCircleBound.lean** (~340 lines, clean elaboration):\n\n**5e-v-a** — the count + Dirichlet inputs:\n- `A0count` + `Ncount_window_le` — Zeta23's RvM local count (mult-weighted, two-sided, all t, **unconditional** — this is the series-bound count input, no perimeter needed).\n- `Ncount_add_of_le` / `Ncount_chain_le` / `Ncount_le_of_interval(_gen)` — the dyadic interval count `A₀·(b−a+1)·log(3 max|a||b|+5)`.\n- `norm_logDeriv_zeta_le_dirichlet` — ‖ζ′/ζ s‖ ≤ dirichletC2 for re ≥ 2 (the right near-axis arc input).\n- `isNontrivialZero_conj` (lower-half arcs).\n\n**5e-v-b chunk 1** — the split machinery:\n- `tsum_split_finset` — a summable tsum = finset sum + if-zeroed tail (the structural tool for the shell decomposition).\n- `lowZeros`/`lowZeroConst` — the small-zero symbolic finite constant.\n\n**Design fully worked out and recorded in journal-030** for the remaining chunks: the dyadic tail bound (`ENNReal.tsum_fiberwise` is free in ℝ≥0∞ + Zeta23's `key` window machinery), the main `seriesFun` circle bound (one tsum split + four shell bounds, γ-gap only in the critical band), the logDeriv/elem assembly, the Schwarz squeeze (Mathlib's `dist_le_div_mul_mapsTo_ball`), and the `∃ B` capstone. Explicit numerics for the k ≥ 4000 threshold verified (Ĉ₀(16006) ≤ 9.36 via `2.718281828¹⁰ ≥ 22026`).\n\nBanked 11 new gotchas (notably: `le_or_lt` absent→`le_or_gt`; `tsum_eq_sum` form; endpoint-pinning for HOU-heavy lemmas; a parser fragility with nested `calc…:= by` in deep case blocks).\n\n**Next session: 5e-v-b chunk 2** (tail bound + main series circle bound)."}]