← Session 3 — Project kickoff: RH blueprint, staged workflow + archive design
thinking (227 chars)
User asks: is 10,000 zeros where we need to be? Explain: 10⁴ is the Phase 0.6 sandbox requirement from the blueprint; the mission prompt mentions up to 10⁵ for experiments; for different purposes different scales. Brief answer.
10,000 is just the **Phase 0 starting requirement** from the blueprint (task 0.6: "compute first 10⁴ zeros; build finite G̃"). It's the minimum sandbox size to sanity-check the paper's machinery.
Different stages will want different scales:
| Scale | Purpose |
|---|---|
| 10⁴ (running now) | Phase 0.6 sandbox — verify tr G̃, ‖G̃‖²_HS, inertia predictions |
| up to 10⁵ | Mission prompt's execution loop — deeper numerical experiments (Li coefficients to n ~ 10⁵ in Phase 3.2, spacing statistics, window/SDP tests) |
| 10⁵+ (maybe much larger) | Stress tests in Phase 4.4 against known zero data; also large tables exist publicly (e.g. Odlyzko's tables, LMFDB) we can fetch per the web-research directive instead of computing ourselves |
One important nuance: our conclusions will never *depend* on numerics — the zeros table is for testing conjectures, catching errors, and building intuition. All claimed results still need the `[PROVED]` tag via rigorous proof (and eventually Lean). Numerics tell us what's worth trying to prove and immediately falsify bad ideas.
So: 10,000 gets us through Phase 0; we'll scale up later only as the research demands it. And per the pacing rule — no rush, we'll take whatever time each stage needs to be done right.
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[{"type":"thinking","thinking":"User asks: is 10,000 zeros where we need to be? Explain: 10⁴ is the Phase 0.6 sandbox requirement from the blueprint; the mission prompt mentions up to 10⁵ for experiments; for different purposes different scales. Brief answer.","signature":""},{"type":"text","text":"10,000 is just the **Phase 0 starting requirement** from the blueprint (task 0.6: \"compute first 10⁴ zeros; build finite G̃\"). It's the minimum sandbox size to sanity-check the paper's machinery.\n\nDifferent stages will want different scales:\n\n| Scale | Purpose |\n|---|---|\n| 10⁴ (running now) | Phase 0.6 sandbox — verify tr G̃, ‖G̃‖²_HS, inertia predictions |\n| up to 10⁵ | Mission prompt's execution loop — deeper numerical experiments (Li coefficients to n ~ 10⁵ in Phase 3.2, spacing statistics, window/SDP tests) |\n| 10⁵+ (maybe much larger) | Stress tests in Phase 4.4 against known zero data; also large tables exist publicly (e.g. Odlyzko's tables, LMFDB) we can fetch per the web-research directive instead of computing ourselves |\n\nOne important nuance: our conclusions will never *depend* on numerics — the zeros table is for testing conjectures, catching errors, and building intuition. All claimed results still need the `[PROVED]` tag via rigorous proof (and eventually Lean). Numerics tell us what's worth trying to prove and immediately falsify bad ideas.\n\nSo: 10,000 gets us through Phase 0; we'll scale up later only as the research demands it. And per the pacing rule — no rush, we'll take whatever time each stage needs to be done right."}]