← Session 3 — Project kickoff: RH blueprint, staged workflow + archive design
thinking (347 chars)
User asks what E-002 does exactly. Explain clearly and concisely: it computes the ordinates of the first 10,000 nontrivial zeros of ζ(s) using mpmath's zetazero, at 25-digit precision, writes CSV+JSON, with sanity checks. Explain why we need it (task 0.6a; feeds E-003 finite G̃ experiment). Also reassure: the question doesn't affect the process.
Not at all — the background job is unaffected. Here's exactly what E-002 is doing:
**What it computes:** the imaginary parts (ordinates) γₙ of the first 10,000 nontrivial zeros of ζ(s), i.e. the values 14.134725…, 21.022040…, 25.010858…, … such that ζ(½ + iγₙ) = 0. It uses `mpmath.zetazero(n)`, which computes the n-th zero via the Riemann–Siegel formula, at **25-digit precision**.
**Output files** (in `research/numerics/data/`):
- `E-002-zeros-first-10000.csv` — two columns: `n, gamma_n` (10,000 rows)
- `E-002-zeros-first-10000.json` — metadata: precision, parameters, timestamp, and the results of built-in sanity checks:
1. the sequence is strictly increasing (as it must be),
2. γ₁ matches the known value 14.13472514173469379… to 20 digits,
3. the count agrees with the Riemann–von Mangoldt formula N(T),
4. gap statistics (min/max/mean spacing between consecutive zeros).
**Why we need it:** this is Phase 0 task 0.6a — the raw data foundation of our numerical sandbox. The next experiment, **E-003**, loads these zeros to build the paper's finite matrix G̃ (the Weil-form compression) and empirically confirm its three key predictions — trace ≈ N, Hilbert–Schmidt norm² ≈ R(ψ)·N, and positive semi-definiteness — before we rely on that machinery in Phase 1. Later phases (Li coefficients, de Bruijn–Newman flows, zero-spacing statistics) will also reuse this table, which is why it's computed once at high precision and cached permanently.
**Why it's slow:** `zetazero` gets more expensive as n grows; we measured ~8.7 zeros/second, so 10,000 zeros ≈ 19 minutes. It got killed once by a 2-minute default timeout at n=1000; I added resume support, so it's now continuing from where it stopped — no work lost.
raw content_json (database row)
[{"type":"thinking","thinking":"User asks what E-002 does exactly. Explain clearly and concisely: it computes the ordinates of the first 10,000 nontrivial zeros of ζ(s) using mpmath's zetazero, at 25-digit precision, writes CSV+JSON, with sanity checks. Explain why we need it (task 0.6a; feeds E-003 finite G̃ experiment). Also reassure: the question doesn't affect the process.","signature":""},{"type":"text","text":"Not at all — the background job is unaffected. Here's exactly what E-002 is doing:\n\n**What it computes:** the imaginary parts (ordinates) γₙ of the first 10,000 nontrivial zeros of ζ(s), i.e. the values 14.134725…, 21.022040…, 25.010858…, … such that ζ(½ + iγₙ) = 0. It uses `mpmath.zetazero(n)`, which computes the n-th zero via the Riemann–Siegel formula, at **25-digit precision**.\n\n**Output files** (in `research/numerics/data/`):\n- `E-002-zeros-first-10000.csv` — two columns: `n, gamma_n` (10,000 rows)\n- `E-002-zeros-first-10000.json` — metadata: precision, parameters, timestamp, and the results of built-in sanity checks:\n 1. the sequence is strictly increasing (as it must be),\n 2. γ₁ matches the known value 14.13472514173469379… to 20 digits,\n 3. the count agrees with the Riemann–von Mangoldt formula N(T),\n 4. gap statistics (min/max/mean spacing between consecutive zeros).\n\n**Why we need it:** this is Phase 0 task 0.6a — the raw data foundation of our numerical sandbox. The next experiment, **E-003**, loads these zeros to build the paper's finite matrix G̃ (the Weil-form compression) and empirically confirm its three key predictions — trace ≈ N, Hilbert–Schmidt norm² ≈ R(ψ)·N, and positive semi-definiteness — before we rely on that machinery in Phase 1. Later phases (Li coefficients, de Bruijn–Newman flows, zero-spacing statistics) will also reuse this table, which is why it's computed once at high precision and cached permanently.\n\n**Why it's slow:** `zetazero` gets more expensive as n grows; we measured ~8.7 zeros/second, so 10,000 zeros ≈ 19 minutes. It got killed once by a 2-minute default timeout at n=1000; I added resume support, so it's now continuing from where it stopped — no work lost."}]