← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)
thinking (1160 chars)
Progress — down to the norm_term comparison lemma. Errors:
1. `ArithmeticFunction.vonMangoldt_one` unknown — find the right name for Λ(1) = 0.
2. `Complex.norm_eq_abs` unknown — the norm-of-real-cast route.
3. Line 223: `rw [e]` — "No goals to be solved" then the goal shows e never got applied because of the hΛ rewrite ordering issue: after `rw [hΛ]` the goal is `ArithmeticFunction.vonMangoldt n / ↑n ^ 3 ≤ 1 / 2 * (ArithmeticFunction.vonMangoldt n / ↑n ^ 2)` — hmm, the hΛ rw happened (goal shows Λ without the norm ✓) but then "No goals to be solved" at 223 — meaning the goal was CLOSED after rw [hΛ]?! No wait — the errors cascade: line 223's `rw [e]` says no goals — because the PREVIOUS error (Complex.norm_eq_abs unknown) broke the hΛ proof, leaving the tactic state inconsistent. The root errors are the two unknown constants. Fix those first.
For Λ(1) = 0: grep the right name.
For ‖(x : ℂ)‖ = x (x ≥ 0 real): `Complex.norm_of_nonneg`? or `Complex.norm_ofReal`/`Complex.abs_of_nonneg`: in this Mathlib: `Complex.norm_of_nonneg (hx : 0 ≤ x) : ‖(x : ℂ)‖ = x`? — check. Or use `Complex.norm_ofReal : ‖(x : ℂ)‖ = |x|` then abs_of_nonneg. Let me grep.
Checking the right names for Λ(1) = 0 and norm-of-real-cast.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/zeta-23-lean && grep -rn \"vonMangoldt_one\\b\" .lake/packages/mathlib/Mathlib/NumberTheory/ 2>/dev/null | head -3; grep -rn \"theorem norm_of_nonneg\\|lemma norm_of_nonneg\" .lake/packages/mathlib/Mathlib/Analysis/Complex/*.lean .lake/packages/mathlib/Mathlib/Data/Complex/*.lean 2>/dev/null | head -3",
"description": "Find vonMangoldt_one and norm_of_nonneg"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Progress — down to the norm_term comparison lemma. Errors:\n\n1. `ArithmeticFunction.vonMangoldt_one` unknown — find the right name for Λ(1) = 0.\n2. `Complex.norm_eq_abs` unknown — the norm-of-real-cast route.\n3. Line 223: `rw [e]` — \"No goals to be solved\" then the goal shows e never got applied because of the hΛ rewrite ordering issue: after `rw [hΛ]` the goal is `ArithmeticFunction.vonMangoldt n / ↑n ^ 3 ≤ 1 / 2 * (ArithmeticFunction.vonMangoldt n / ↑n ^ 2)` — hmm, the hΛ rw happened (goal shows Λ without the norm ✓) but then \"No goals to be solved\" at 223 — meaning the goal was CLOSED after rw [hΛ]?! No wait — the errors cascade: line 223's `rw [e]` says no goals — because the PREVIOUS error (Complex.norm_eq_abs unknown) broke the hΛ proof, leaving the tactic state inconsistent. The root errors are the two unknown constants. Fix those first.\n\nFor Λ(1) = 0: grep the right name.\nFor ‖(x : ℂ)‖ = x (x ≥ 0 real): `Complex.norm_of_nonneg`? or `Complex.norm_ofReal`/`Complex.abs_of_nonneg`: in this Mathlib: `Complex.norm_of_nonneg (hx : 0 ≤ x) : ‖(x : ℂ)‖ = x`? — check. Or use `Complex.norm_ofReal : ‖(x : ℂ)‖ = |x|` then abs_of_nonneg. Let me grep.","signature":""},{"type":"text","text":"Checking the right names for Λ(1) = 0 and norm-of-real-cast."},{"type":"tool_use","id":"Bash_214","name":"Bash","input":{"command":"cd D:/Python/Quantum/zeta-23-lean && grep -rn \"vonMangoldt_one\\b\" .lake/packages/mathlib/Mathlib/NumberTheory/ 2>/dev/null | head -3; grep -rn \"theorem norm_of_nonneg\\|lemma norm_of_nonneg\" .lake/packages/mathlib/Mathlib/Analysis/Complex/*.lean .lake/packages/mathlib/Mathlib/Data/Complex/*.lean 2>/dev/null | head -3","description":"Find vonMangoldt_one and norm_of_nonneg"},"extra_content":null}]