← Session 21 — Tier ii′ planning + launch: close SfBoundProp in Lean (D-064)
thinking (1127 chars)
The pervasive issue: my hd's lambda `fun x => G (x + y * I)` is being elaborated with x : ℂ (because G : ℂ → ℂ forces the argument to be ℂ), but the parametrization needs x : ℝ (with coercion). The lambda `fun x => G (x + y * I)` — G's argument must be ℂ, so x : ℂ! Of course — I need to write `fun x : ℝ => G (↑x + ↑y * I)` — the lambda domain annotation x : ℝ makes the coercion explicit. That's the root of ALL these mismatches: the parametrized function must be `fun x : ℝ => G (x + y * I)` where x : ℝ and (x + y*I) coerces — but writing G (x + y*I) with x : ℝ requires the coercion — Lean inserts it: G (↑x + ↑y * I) ✓. So in hd, h2, the FTC f/f' args — ALL lambdas must be annotated (x : ℝ).
Fixes:
1. hd's statement: `HasDerivAt (fun x : ℝ => G (x + y * I)) (deriv G (x + y * I)) x` — with x : ℝ annotated ✓.
2. h2: `HasDerivAt (fun x : ℝ => x + y * I) 1 x` — already annotated? The error at 69 says expected `(fun (x : ℂ) => ...)` — so the h2 in the file still has the unannotated form. My earlier replacement didn't match. Let me look at the actual file content for these lines and fix them all by direct line edits.
The root issue is now clear: every parametrized lambda needs explicit `(x : ℝ)` annotations. Let me look at the current state and fix them all directly.
tool: Read ok
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiPrincipal.lean",
"offset": 42,
"limit": 80
}
result 2026-08-21 21:43:48Z → 2026-08-25 05:28:45Z
{
"type": "text",
"file": {
"filePath": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiContour.lean",
"content": "\nnoncomputable section\n\nnamespace NguyenRH1\n\n/-! ## 1. The unit ordinate window and the perimeter count hypothesis -/\n\n/-- The nontrivial zeros with ordinate in the unit window [a, a+1]. -/\ndef zeroWindow (a : \u211d) : Set \u2102 :=\n {\u03c1 | IsNontrivialZero \u03c1 \u2227 a \u2264 \u03c1.im \u2227 \u03c1.im \u2264 a + 1}\n\n/-- Finiteness of the unit ordinate window (via Zeta23 `zerosIn_finite`). -/\ntheorem zeroWindow_finite (a : \u211d) : (zeroWindow a).Finite := by\n apply Set.Finite.subset (zerosIn_finite (a - 1) (a + 1))\n intro \u03c1 h\u03c1\n refine \u27e8h\u03c1.1, ?_, h\u03c1.2.2\u27e9\n linarith [h\u03c1.2.1]\n\n/-- A nontrivial zero has multiplicity \u2265 1 (zeroMult is the analytic\norder). Bridges the mult-weighted perimeter count to the plain window\ncardinality (card \u2264 \u03a3 mult). -/\ntheorem one_le_zeroMult {\u03c1 : \u2102} (h\u03c1 : IsNontrivialZero \u03c1) : 1 \u2264 zeroMult \u03c1 := by\n have h\u03c11 : \u03c1 \u2260 1 := by\n rintro rfl\n have h := h\u03c1.2.2\n rw [Complex.one_re] at h\n exact (lt_irrefl (1 : \u211d)) h\n have htop := zeta_order_ne_top_of_ne h\u03c11\n have hne : analyticOrderAt riemannZeta \u03c1 \u2260 0 :=\n (analyticAt_riemannZeta h\u03c11).analyticOrderAt_ne_zero.mpr h\u03c1.1\n exact ENat.toNat_pos hne htop\n\n/-- [PERIMETER \u2014 Trudgian 2014 N(T)/S(T), D-062 \u00a74] The unit-window\nzero-count bound: the multiplicity-weighted count of nontrivial zeros\nwith ordinates in [t, t+1] is at most \u0108\u2080(t+1) (t \u2265 2). Declared\ncounting input for the L3 pigeonhole and the tight R-bound; \u0108\u2080 =\n`C0hat` is D-056 \u00a72's honest majorant (LiSkeleton).\n[Erratum 2026-08-23 (session 035): strengthened from the unweighted\nset-card form `(Nat.card (zeroWindow t) : \u211d) \u2264 \u0108\u2080(t+1)` to the\nmult-weighted form \u2014 Trudgian's N(T) counts zeros with multiplicity,\nand the mult-weighted form is what the 5f/ii\u2032-6 near sums\n(zeroMult-weighted, from `seriesFun`) consume; the set-card encoding\nunder-captured the declared source (a second ii\u2032-1a-class encoding\ndefect, found at the point of consumption). The set-card bound follows\nfrom this form via `one_le_zeroMult` (card \u2264 \u03a3 mult); the two\nconsumers (exists_zero_avoiding_T, exists_gapCircle_radius) adapted.] -/\ndef ZeroCountProp : Prop :=\n \u2200 t : \u211d, 2 \u2264 t \u2192\n (((zeroWindow_finite t).toFinset.sum fun \u03c1 => zeroMult \u03c1) : \u211d) \u2264 C0hat (t + 1)\n",
"numLines": 50,
"startLine": 40,
"totalLines": 647
}
}
raw content_json (database row)
[{"type":"thinking","thinking":"The pervasive issue: my hd's lambda `fun x => G (x + y * I)` is being elaborated with x : ℂ (because G : ℂ → ℂ forces the argument to be ℂ), but the parametrization needs x : ℝ (with coercion). The lambda `fun x => G (x + y * I)` — G's argument must be ℂ, so x : ℂ! Of course — I need to write `fun x : ℝ => G (↑x + ↑y * I)` — the lambda domain annotation x : ℝ makes the coercion explicit. That's the root of ALL these mismatches: the parametrized function must be `fun x : ℝ => G (x + y * I)` where x : ℝ and (x + y*I) coerces — but writing G (x + y*I) with x : ℝ requires the coercion — Lean inserts it: G (↑x + ↑y * I) ✓. So in hd, h2, the FTC f/f' args — ALL lambdas must be annotated (x : ℝ).\n\nFixes:\n1. hd's statement: `HasDerivAt (fun x : ℝ => G (x + y * I)) (deriv G (x + y * I)) x` — with x : ℝ annotated ✓.\n2. h2: `HasDerivAt (fun x : ℝ => x + y * I) 1 x` — already annotated? The error at 69 says expected `(fun (x : ℂ) => ...)` — so the h2 in the file still has the unannotated form. My earlier replacement didn't match. Let me look at the actual file content for these lines and fix them all by direct line edits.","signature":""},{"type":"text","text":"The root issue is now clear: every parametrized lambda needs explicit `(x : ℝ)` annotations. Let me look at the current state and fix them all directly."},{"type":"tool_use","id":"Read_240","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiPrincipal.lean","offset":42,"limit":80},"extra_content":null}]