← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)
thinking (113 chars)
The user is asking what happened — likely about the V1 failure and my fix. Let me answer briefly and then re-run.
The E-033 run failed only on check **V1** — a too-tight tolerance in my script, not a math problem.
**What happened:** V1 certifies Z₀ = |ζ′/ζ(2)| via a Dirichlet partial sum + certified tail bound. The bracket came out honest and correct:
- certified: Z₀ ∈ [0.5699210, 0.5703661] (width 4.5×10⁻⁴)
- true value (mpmath): 0.5699610 — **inside the bracket** ✓
But I had written the pass condition as `zhi < 0.5700`, and the certified upper edge is 0.57037. The K=25000 truncation gives a 4.45×10⁻⁴ tail, which can't fit that window. The math was fine; my assertion was wrong.
**The fix:** relaxed the V1 window to [0.5695, 0.5705] with an explicit width check (< 10⁻³) — that's all R(c) needs, since R is charged with the *upper* edge zhi = 0.57037 anyway (so the bound stays honest).
All other checks (V2–V7: q-table, R(c) vs E-032 measured, kernel charge, fold fit, margins, full fold) already passed. Re-running now.
tool: Bash
input
{
"command": "cd D:/Python/Quantum && ./.venv/Scripts/python.exe research/numerics/scripts/E-033-repaired-stepping-validation.py --force",
"description": "Re-run E-033 after V1 tolerance fix",
"timeout": 300000
}
raw content_json (database row)
[{"type":"thinking","thinking":"The user is asking what happened — likely about the V1 failure and my fix. Let me answer briefly and then re-run.","signature":""},{"type":"text","text":"The E-033 run failed only on check **V1** — a too-tight tolerance in my script, not a math problem.\n\n**What happened:** V1 certifies Z₀ = |ζ′/ζ(2)| via a Dirichlet partial sum + certified tail bound. The bracket came out honest and correct:\n\n- certified: Z₀ ∈ [0.5699210, 0.5703661] (width 4.5×10⁻⁴)\n- true value (mpmath): 0.5699610 — **inside the bracket** ✓\n\nBut I had written the pass condition as `zhi < 0.5700`, and the certified upper edge is 0.57037. The K=25000 truncation gives a 4.45×10⁻⁴ tail, which can't fit that window. The math was fine; my assertion was wrong.\n\n**The fix:** relaxed the V1 window to [0.5695, 0.5705] with an explicit width check (< 10⁻³) — that's all R(c) needs, since R is charged with the *upper* edge zhi = 0.57037 anyway (so the bound stays honest).\n\nAll other checks (V2–V7: q-table, R(c) vs E-032 measured, kernel charge, fold fit, margins, full fold) already passed. Re-running now."},{"type":"tool_use","id":"Bash_39","name":"Bash","input":{"command":"cd D:/Python/Quantum && ./.venv/Scripts/python.exe research/numerics/scripts/E-033-repaired-stepping-validation.py --force","description":"Re-run E-033 after V1 tolerance fix","timeout":300000},"extra_content":null}]