← Session 28 — ii′-5e: partial-fraction identity (zero series + F entire)
thinking (628 chars)
GOLD. The Zeta23 proof uses `Tail.LocalCount.ofWindowCount` producing `hLC.window n` — a per-INTEGER-window mult-weighted count: `(∑ ρ ∈ filter, mult) ≤ A₀ * Real.log(|n|+3)`-ish. And there's a `key` function (⌊⌋-style window key) and `totalWeight` := ∑' over ℤ of log(|n|+3)/(1+n²) with `summable_weight` and `weight_le`, `one_add_sq_ge` etc. — the whole unit-window dyadic machinery is PACKAGED in Zeta23's `Tail` namespace!
Let me look at what `Tail.LocalCount` offers — specifically `hLC.window` and whether there's a ready-made TAIL bound (sum over windows above a threshold). Let me check Zeta23/Tail.lean's declarations.
The whole unit-window machinery is packaged in Zeta23's `Tail` module. Let me see what's available there.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/zeta-23-lean && grep -n \"theorem\\|lemma\\|def\\|structure\" Zeta23/Tail.lean | head -30",
"description": "Zeta23 Tail.lean declarations"
}
raw content_json (database row)
[{"type":"thinking","thinking":"GOLD. The Zeta23 proof uses `Tail.LocalCount.ofWindowCount` producing `hLC.window n` — a per-INTEGER-window mult-weighted count: `(∑ ρ ∈ filter, mult) ≤ A₀ * Real.log(|n|+3)`-ish. And there's a `key` function (⌊⌋-style window key) and `totalWeight` := ∑' over ℤ of log(|n|+3)/(1+n²) with `summable_weight` and `weight_le`, `one_add_sq_ge` etc. — the whole unit-window dyadic machinery is PACKAGED in Zeta23's `Tail` namespace!\n\nLet me look at what `Tail.LocalCount` offers — specifically `hLC.window` and whether there's a ready-made TAIL bound (sum over windows above a threshold). Let me check Zeta23/Tail.lean's declarations.","signature":""},{"type":"text","text":"The whole unit-window machinery is packaged in Zeta23's `Tail` module. Let me see what's available there."},{"type":"tool_use","id":"Bash_335","name":"Bash","input":{"command":"cd D:/Python/Quantum/zeta-23-lean && grep -n \"theorem\\|lemma\\|def\\|structure\" Zeta23/Tail.lean | head -30","description":"Zeta23 Tail.lean declarations"},"extra_content":null}]