[{"type":"thinking","thinking":"Line 157:61 — `exact riemannZeta_ne_zero_of_one_le_re (by rw [hre2];` — col 61 is near the end of line 157: `(by rw [hre2];` — the issue: the `by rw [hre2];` followed by a NEWLINE then `linarith [...]` — inside an exact's parenthesized by-block with a semicolon and continuation — should be OK syntactically... \"unexpected identifier; expected ')', ',' or ':'\" — the parser choked. Maybe the issue: `riemannZeta_ne_zero_of_one_le_re (by ...)` — the by-block with `rw [hre2];\\n linarith [...])` — hmm the `(by rw [hre2];` — after the semicolon the tactic block continues on the next line — but the INDENTATION: the linarith is at column 11 (deeper than the `by`) — fine normally. \"unexpected identifier\" at 61: the 61st char of line 157 — let me count: `        exact riemannZeta_ne_zero_of_one_le_re (by rw [hre2];` — 8 + 6 + 1 + 36 + ... ≈ col 55-60 is `[hre2]` or the `;`. Hmm — maybe `hre2` isn't in scope?? No — \"unexpected identifier\" is a PARSE error, not scope.\n\nOH — I see it: `by rw [hre2];` — the semicolon after a rw inside a `by` TERM — the `by tac1; tac2` syntax requires the whole sequence: `by rw [hre2]; linarith [...]` on ONE logical line — the newline after `;` should be fine (tactic blocks allow newlines)... BUT the context: `(by rw [hre2];\\n          linarith [...])` — the linarith is indented to col 11 — the `by` started at col ~55 — the continuation must be indented MORE than the `by` keyword's column? The `by` is at col 55; the linarith at col 11 — LESS indented — the parser thinks the by-block ENDED and `linarith` is a new identifier! That's it — inside an exact argument, a by-block on the next line must be indented past the `by`. Fix: put the whole by-block on one line or use a have:\n\n```lean\n        exact riemannZeta_ne_zero_of_one_le_re (by rw [hre2]; linarith [Real.one_le_sqrt.mpr\n          (by exact_mod_cast hn : (1 : ℝ) ≤ n)]) hζ\n```\nHmm — still a newline inside. Simplest: extract to a have:\n```lean\n        have h1re : (1 : ℝ) ≤ s.re := by\n          rw [hre2]\n          linarith [Real.one_le_sqrt.mpr (by exact_mod_cast hn : (1 : ℝ) ≤ n)]\n        exact riemannZeta_ne_zero_of_one_le_re h1re hζ\n```\n\nWait — actually riemannZeta_ne_zero_of_one_le_re's signature: (h : 1 ≤ s.re)? From LiDisc:73: `exact riemannZeta_ne_zero_of_one_le_re h h2` — two args: h (the re-inequality) and h2 (ζ ≠ 0?)... no wait — riemannZeta_ne_zero_of_one_le_re : 1 ≤ s.re → riemannZeta s ≠ 0 — so `exact riemannZeta_ne_zero_of_one_le_re h1re hζ` — hζ : riemannZeta s = 0 — the goal is False (after intro hζ)... riemannZeta_ne_zero_of_one_le_re h1re : riemannZeta s ≠ 0 — applied to hζ : = 0 gives False ✓.\n\nAlso the `(by exact_mod_cast hn : (1 : ℝ) ≤ n)` ascription — exact_mod_cast hn : (1:ℝ) ≤ (n:ℝ) — Real.one_le_sqrt.mpr's arg is (1:ℝ) ≤ n where n : ℕ coerced — (n : ℝ) ✓.\n\nNow let me make all the fixes:\n1. §0: zeroBothWindow_finite → zerosIn_finite (-T - 1) T; zeroGlobalWindowNeg_finite → zerosIn_finite (-T - 1) 0.\n2. h1notb: the two `ne_of_gt` — replace with direct linarith-proved ≠: bottom: `absurd him (by linarith [hT1] : ((1 : ℂ).im) ≠ -T)`?? — him : (1:ℂ).im = −T after rectZ_im: with (1:ℂ).im — hmm Complex.one_im rewrote it to (0:ℝ): him : (0:ℝ) = −T: absurd him (by linarith [hT1] : (0:ℝ) ≠ -T)? Hmm wait — in h1notb I did rw [rectZ_im, Complex.one_im] at him — him : (0:ℝ) = −T?? wait — him : (1:ℂ).im = z.im → rectZ_im: z.im → −T: him : (1:ℂ).im = −T → Complex.one_im: (1:ℂ).im → 0: him : (0:ℝ) = −T? Hmm — but (1:ℂ).im is a ℂ-re — the equation is between ℝs ✓. So `exact absurd him (by linarith [hT1] : (0:ℝ) ≠ -T)`. Hmm — but does the target of the `exact` match? The case's goal is False: absurd him proof-of-¬ : False ✓ absurd : a → ¬a → b ✓.\n   Similarly top: him2 : (0:ℝ) = T → absurd him2 (by linarith [hT1] : (0:ℝ) ≠ T).\n   Left (h1notb): hre : (1:ℝ) = −5/2: norm_num at hre ✓ (already there).\n   Right: hre2 : (1:ℝ) = 2√n: ne_of_lt h2n : 1 ≠ 2√n ✓ — `exact absurd hre2 (ne_of_lt h2n)`.\n3. hborder h0-branch and −2n-branch: same ≠ fixes (already written with ne_of_gt — replace with ne_of_lt or linarith-≠): my current h0-branch code: `exact absurd him (ne_of_gt (by linarith [hT1] : (0 : ℝ) > -T))` — same problem (ne_of_gt (−T < 0) : 0 ≠ −T ✓ — WAIT: ne_of_gt (h : b < a) : a ≠ b: h : −T < 0 gives 0 ≠ −T ✓ — and (0:ℝ) > -T IS −T < 0 ✓ — hmm so that SHOULD work. The error at 117 said \"expected T < 0\" — so the elaboration of `(0 : ℝ) > -T` gave `0 < T`... Let me look at the ACTUAL error line: \"117:34: error: Application type mismatch: The argument ?m.604 has type 0 < T but is expected to have type T < 0 in the application ne_of_gt ?m.604\" — hmm \"expected T < 0\" — so ne_of_gt's expected argument after unification is T < 0. ne_of_gt (h : b < a) : a ≠ b — unify conclusion a ≠ b with goal ¬(0 = −T) = (0 ≠ −T): a := 0, b := −T: expected arg : b < a = −T < 0 — which displays as `−T < 0`, i.e. `T < 0`?? — hmm `−T < 0` and `T < 0` display differently... unless Lean NEG-normalizes `−T < 0` to `T > 0`... no — maybe this Mathlib's ne_of_gt is `ne_of_gt : a > b → b ≠ a`?? — flipped conclusion! If ne_of_gt : a > b → b ≠ a: then unifying conclusion with 0 ≠ −T: b := 0, a := −T: expected arg : a > b = −T > 0 = 0 < T... no — error says \"expected T < 0\"...\n\nUgh — simplest: replace ALL these with `ne_of_lt` where the equation is 0 = X with X > 0: ne_of_lt (h : a < b) : a ≠ b ✓: for 0 ≠ T: ne_of_lt (0 < T) ✓; for 0 ≠ −T: ne_of_lt (−T < 0) — written as `ne_of_lt (by linarith [hT1] : (-T) < 0)`. And for 1 ≠ 2√n: ne_of_lt h2n ✓.\n\nLet me just standardize: use `ne_of_lt (by linarith [hT1] : (0:ℝ) < T)` for 0 ≠ T cases, `ne_of_lt (by linarith [hT1] : (-(T:ℝ)) < 0)` for 0 ≠ −T cases, `ne_of_lt h2n` for the 1 ≠ 2√n case. Check ne_of_lt signature: `ne_of_lt : a < b → a ≠ b` ✓ standard.\n\n4. neg_neg in the conj hzero.\n5. Line 157's exact-with-by-block → the have form.","signature":""},{"type":"text","text":"Applying all fixes: §0 windows, the ne_of_lt directions, neg_neg, and the line-157 by-block."},{"type":"tool_use","id":"Bash_286","name":"Bash","input":{"command":"cd D:/Python/Quantum && python - << 'EOF'\np = 'research/lean/NguyenRH1/NguyenRH1/LiAssembly.lean'\nsrc = open(p, encoding='utf-8').read()\nsubs = [\n# §0: strict-lower windows\n(\"\"\"  apply Set.Finite.subset (zerosIn_finite (-T) T)\n  intro ρ hρ\n  refine ⟨hρ.1, ?_, ?_⟩\n  · linarith [abs_le.mp hρ.2 |>.1]\n  · exact abs_le.mp hρ.2 |>.2\"\"\",\n \"\"\"  apply Set.Finite.subset (zerosIn_finite (-T - 1) T)\n  intro ρ hρ\n  refine ⟨hρ.1, ?_, ?_⟩\n  · linarith [abs_le.mp hρ.2 |>.1]\n  · exact abs_le.mp hρ.2 |>.2\"\"\"),\n(\"\"\"  apply Set.Finite.subset (zerosIn_finite (-T) 0)\n  intro ρ hρ\n  refine ⟨hρ.1, hρ.2.1, by linarith [hρ.2.2]⟩\"\"\",\n \"\"\"  apply Set.Finite.subset (zerosIn_finite (-T - 1) 0)\n  intro ρ hρ\n  refine ⟨hρ.1, by linarith [hρ.2.1], by linarith [hρ.2.2]⟩\"\"\"),\n# h1notb fixes\n(\"\"\"      exact absurd him (ne_of_gt (by linarith [hT1] : (0 : ℝ) > -T))\n    · have h := Set.mem_singleton_iff.mp hb.1\n      rw [rectZ_re, Complex.one_re] at h\n      norm_num at h\n    · have h := Set.mem_singleton_iff.mp hb.2\n      rw [rectW_im, Complex.one_im] at h\n      exact absurd h (ne_of_gt (by linarith [hT1] : (0 : ℝ) < T))\n    · have h := Set.mem_singleton_iff.mp hb.1\n      rw [rectW_re, Complex.one_re] at h\n      exact absurd h (ne_of_gt h2n)\"\"\",\n \"\"\"      exact absurd him (ne_of_lt (by linarith [hT1] : (-(T : ℝ)) < 0))\n    · have h := Set.mem_singleton_iff.mp hb.1\n      rw [rectZ_re, Complex.one_re] at h\n      norm_num at h\n    · have h := Set.mem_singleton_iff.mp hb.2\n      rw [rectW_im, Complex.one_im] at h\n      exact absurd h (ne_of_lt (by linarith [hT1] : (0 : ℝ) < T))\n    · have h := Set.mem_singleton_iff.mp hb.1\n      rw [rectW_re, Complex.one_re] at h\n      exact absurd h (ne_of_lt h2n)\"\"\"),\n]\ncount = 0\nfor old, new in subs:\n    if old in src:\n        src = src.replace(old, new)\n        count += 1\n    else:\n        print('MISS:', old[:60].replace('\\n',' | '))\nopen(p, 'w', encoding='utf-8').write(src)\nprint(f'{count}/{len(subs)} applied')\nEOF","description":"Fix §0 windows + h1notb directions"},"extra_content":null}]