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← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)

#2066 assistant 2026-08-26 01:53:43.136 UTC · 1682→433 tok open ⤢
thinking (702 chars)
ALL CHECKS PASS: - V0 envelope reproduces E-031 ✓ (n=10⁴: 1.026e4 vs 1.05e4; n=10⁵: 4.707e10 vs 5.87e10 — hmm, 4.707e10 vs E-031's 5.87e10 — within the [4e10, 8e10] check window ✓; the difference is E-031's coarse step-2 grid and K=300 Λ-sum + dropping the −1 in k_n; fine) - VA validation max 6.0e-10 ✓ (mpmath vs Dirichlet agree to 6e-10) - VC convergence ✓ - V3 repair ✓ Verdict numbers (c=1): - n=10³: |I_right| = 7.185, env = 50.82, ratio 0.141, |I|/√n = 0.227 - n=10⁴: |I_right| = 16.7, env = 1.026e4, ratio 0.00163, |I|/√n = 0.167 - n=10⁵: |I_right| = 26.23, env = 4.707e10, ratio 5.57e-10, |I|/√n = 0.083 Let me read the full CSV/JSON for Re/Im and the mid/full parts before writing D-073 §2.
**ALL CHECKS PASS.** Reading the full results (Re/Im, mid-part, full side) for the D-073 §2 write-up.
tool: Read
input
{
  "file_path": "D:\\Python\\Quantum\\research\\numerics\\data\\E-032-horizontal-true-integral.csv"
}
raw content_json (database row)
[{"type":"thinking","thinking":"ALL CHECKS PASS:\n- V0 envelope reproduces E-031 ✓ (n=10⁴: 1.026e4 vs 1.05e4; n=10⁵: 4.707e10 vs 5.87e10 — hmm, 4.707e10 vs E-031's 5.87e10 — within the [4e10, 8e10] check window ✓; the difference is E-031's coarse step-2 grid and K=300 Λ-sum + dropping the −1 in k_n; fine)\n- VA validation max 6.0e-10 ✓ (mpmath vs Dirichlet agree to 6e-10)\n- VC convergence ✓\n- V3 repair ✓\n\nVerdict numbers (c=1):\n- n=10³: |I_right| = 7.185, env = 50.82, ratio 0.141, |I|/√n = 0.227\n- n=10⁴: |I_right| = 16.7, env = 1.026e4, ratio 0.00163, |I|/√n = 0.167\n- n=10⁵: |I_right| = 26.23, env = 4.707e10, ratio 5.57e-10, |I|/√n = 0.083\n\nLet me read the full CSV/JSON for Re/Im and the mid/full parts before writing D-073 §2.","signature":""},{"type":"text","text":"**ALL CHECKS PASS.** Reading the full results (Re/Im, mid-part, full side) for the D-073 §2 write-up."},{"type":"tool_use","id":"Read_19","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\numerics\\data\\E-032-horizontal-true-integral.csv"},"extra_content":null}]