← Session 28 — ii′-5e: partial-fraction identity (zero series + F entire)
thinking (331 chars)
The user asks if I'm still working or ready for the next session. Session 030 was closed cleanly (all commits done, STATE.md updated). I'm ready to start the next session (5e-v-b chunk 2). Per the session-start protocol, STATE.md is already read (I wrote it). I can begin immediately. Let me confirm readiness and offer to proceed.
Session 030 is fully closed — all work committed, STATE.md updated, nothing in flight. I'm ready to start the next session immediately on your word.
**Session 031's first item** (per STATE.md): **ii′-5e-v chunk 2** —
1. `zero_tail_inv_sq_le`: the dyadic tail bound `Σ_{|γ|>X} m/(1+γ²) ≤ 16·A₀·log X / X` (via `ENNReal.tsum_fiberwise` + window counts),
2. `seriesFun_norm_le_gapCircle`: the main series circle bound (one tsum split at `{‖ρ‖ ≤ 2R}` + four shell bounds: low / inner-dyadic / critical-band γ-gap / upper-dyadic).
Then chunk 3 (logDeriv/elem assembly ⟹ ‖Fexpr‖ ≤ C(log R)³ on circles) and chunk 4 (Schwarz squeeze ⟹ ∃ B capstone).
Say the word and I'll start.
raw content_json (database row)
[{"type":"thinking","thinking":"The user asks if I'm still working or ready for the next session. Session 030 was closed cleanly (all commits done, STATE.md updated). I'm ready to start the next session (5e-v-b chunk 2). Per the session-start protocol, STATE.md is already read (I wrote it). I can begin immediately. Let me confirm readiness and offer to proceed.","signature":""},{"type":"text","text":"Session 030 is fully closed — all work committed, STATE.md updated, nothing in flight. I'm ready to start the next session immediately on your word.\n\n**Session 031's first item** (per STATE.md): **ii′-5e-v chunk 2** —\n1. `zero_tail_inv_sq_le`: the dyadic tail bound `Σ_{|γ|>X} m/(1+γ²) ≤ 16·A₀·log X / X` (via `ENNReal.tsum_fiberwise` + window counts),\n2. `seriesFun_norm_le_gapCircle`: the main series circle bound (one tsum split at `{‖ρ‖ ≤ 2R}` + four shell bounds: low / inner-dyadic / critical-band γ-gap / upper-dyadic).\n\nThen chunk 3 (logDeriv/elem assembly ⟹ ‖Fexpr‖ ≤ C(log R)³ on circles) and chunk 4 (Schwarz squeeze ⟹ ∃ B capstone).\n\nSay the word and I'll start."}]