← Session 8 — Regroup + R-004 finite-height Li theorem; resources atlas ingested
thinking (1017 chars)
Worse! V1 = 2.00e3 now. Hmm. The K_SPLIT=80 change made it worse somewhere. The σ_m exact for m ≤ 80: σ_m = (−1)^{m−1}(τ_{m−1} − η_{m−1}) + 1 — at m=80, the subtraction τ_79 − η_79 loses ~92 digits (σ_80 ~ 14^{−80} = 1e-91.7 — from O(1) values) — at dps full_digits+50 = 1700 → fine (1e-1608). Hmm, but WAIT — η from Stieltjes strings at full_digits+100 = 1750 digits — fine.
But maybe the σ_m for m ≥ 81 from zeros — the sums at dps 1700: r**(−m) for m up to 1830: ρ^{−1830} = 14.13^{−1830} = 10^{−2105}: at dps 1700 — mpf exponent OK.
The σ exact m ≤ 80 — did the exact values come out right? σ_25 printed 2.66319e-29 (from zeros? or exact?) — the print says "sigma_25 (zeros)" but with K_SPLIT=80, σ_25 is EXACT now (m ≤ 80) — the print label is stale but the value 2.66319e-29 matched the earlier zeros-based value ✓ consistent.
So where does 2e3 worst dev come from? Need the dev profile again — first bad n. Let me profile with the CSV (12-digit floor 1e-12): find first n with dev > 1e-11 and the dev curve.
Worse — 2.00e3. Profile the dev curve to find where it starts now.
tool: Bash
input
{
"command": "cd /d/Python/Quantum && ./.venv/Scripts/python.exe - <<'EOF'\nimport mpmath as mp\nmp.mp.dps = 100\ne015 = {}\nfor line in open(\"research/numerics/data/E-015-li-coefficients-n3000.csv\"):\n p = line.strip().split(\",\")\n if p[0].isdigit(): e015[int(p[0])] = mp.mpf(p[1])\nrows = {}\nfor line in open(\"research/numerics/data/E-021-sinf-sf-curve.csv\"):\n p = line.strip().split(\",\")\n if p[0].isdigit(): rows[int(p[0])] = p\nworst = (0, 0)\nfor n in sorted(e015):\n lam = mp.mpf(rows[n][3])\n dev = float(abs(lam - e015[n]) / abs(e015[n]))\n if dev > worst[0]: worst = (dev, n)\n if dev > 1e-11:\n print(f\"first bad n={n}: dev={dev:.3e}\")\n break\nprint(\"worst:\", worst)\nfor n in (500, 1000, 1500, 2000, 2200, 2400, 2600, 2800, 3000):\n lam = mp.mpf(rows[n][3])\n dev = float(abs(lam - e015[n]) / abs(e015[n]))\n print(f\"n={n:>5}: dev={dev:.3e} S_f={rows[n][2]}\")\nEOF",
"description": "Profile dev curve after K_SPLIT=80",
"timeout": 300000
}
raw content_json (database row)
[{"type":"thinking","thinking":"Worse! V1 = 2.00e3 now. Hmm. The K_SPLIT=80 change made it worse somewhere. The σ_m exact for m ≤ 80: σ_m = (−1)^{m−1}(τ_{m−1} − η_{m−1}) + 1 — at m=80, the subtraction τ_79 − η_79 loses ~92 digits (σ_80 ~ 14^{−80} = 1e-91.7 — from O(1) values) — at dps full_digits+50 = 1700 → fine (1e-1608). Hmm, but WAIT — η from Stieltjes strings at full_digits+100 = 1750 digits — fine.\n\nBut maybe the σ_m for m ≥ 81 from zeros — the sums at dps 1700: r**(−m) for m up to 1830: ρ^{−1830} = 14.13^{−1830} = 10^{−2105}: at dps 1700 — mpf exponent OK.\n\nThe σ exact m ≤ 80 — did the exact values come out right? σ_25 printed 2.66319e-29 (from zeros? or exact?) — the print says \"sigma_25 (zeros)\" but with K_SPLIT=80, σ_25 is EXACT now (m ≤ 80) — the print label is stale but the value 2.66319e-29 matched the earlier zeros-based value ✓ consistent.\n\nSo where does 2e3 worst dev come from? Need the dev profile again — first bad n. Let me profile with the CSV (12-digit floor 1e-12): find first n with dev > 1e-11 and the dev curve.","signature":""},{"type":"text","text":"Worse — 2.00e3. Profile the dev curve to find where it starts now."},{"type":"tool_use","id":"Bash_117","name":"Bash","input":{"command":"cd /d/Python/Quantum && ./.venv/Scripts/python.exe - <<'EOF'\nimport mpmath as mp\nmp.mp.dps = 100\ne015 = {}\nfor line in open(\"research/numerics/data/E-015-li-coefficients-n3000.csv\"):\n p = line.strip().split(\",\")\n if p[0].isdigit(): e015[int(p[0])] = mp.mpf(p[1])\nrows = {}\nfor line in open(\"research/numerics/data/E-021-sinf-sf-curve.csv\"):\n p = line.strip().split(\",\")\n if p[0].isdigit(): rows[int(p[0])] = p\nworst = (0, 0)\nfor n in sorted(e015):\n lam = mp.mpf(rows[n][3])\n dev = float(abs(lam - e015[n]) / abs(e015[n]))\n if dev > worst[0]: worst = (dev, n)\n if dev > 1e-11:\n print(f\"first bad n={n}: dev={dev:.3e}\")\n break\nprint(\"worst:\", worst)\nfor n in (500, 1000, 1500, 2000, 2200, 2400, 2600, 2800, 3000):\n lam = mp.mpf(rows[n][3])\n dev = float(abs(lam - e015[n]) / abs(e015[n]))\n print(f\"n={n:>5}: dev={dev:.3e} S_f={rows[n][2]}\")\nEOF","description":"Profile dev curve after K_SPLIT=80","timeout":300000},"extra_content":null}]