Brief: numerics worker (out-of-band envelopes)

Read first: hunts/oob_envelope/MISSION.md, then AGENTS.md (certainty ladder, compute discipline, reserved words), then arXiv:2608.24827v2 (Zhu) §1–5 and §7. Seed probes: hunts/oob_envelope/probes/. Your worktree: <worktree> (branch teal-sea/oob-cert). Write only in hunts/oob_envelope/numerics/. Python: <repo>/.venv/bin/python (numpy, scipy, mpmath, python-flint 0.9 are installed; the worktree has no venv of its own).

Phases, in order

1. H with enclosures. For L ∈ {0.8, 1.0, 1.19}, build the per-prime out-of-band correction (Fejér-smoothed Carathéodory–Toeplitz, as in probes/separable.py) with rational or ball coefficients, and bound S = sup_t (P_L − H)(t) rigorously. Per prime the claim is Φ_p = M_p − φ_p + h_p ≥ 0 as a trigonometric polynomial in θ; prove it by exhibiting Φ_p as a nonnegative combination of Fejér kernels (exact arithmetic) or by an arb enclosure of its minimum. Then S ≤ Σ_p M_p. Report both the separable constant and, as a stretch, a joint LP/SDP constant on the first few primes' torus.
2. K3, then L = 0.8 replication with H: assemble Zhu's reduced form (eq. (4)) with Ψ_L + H, the threshold now T# > 2π e^{S}, and compute λ_min of the leading block. Expect a much smaller matrix than Zhu's N = 200. Check K1: your lower bound must not exceed 2.27e-17. Float first (measured), then with mpmath / arb enclosures and Zhu's two-block bound (13) with explicit ε_D, ε_B (hardened). Remember H adds out-of-band terms to the symbol, so the frequency-cut matrix entries must include them: they are not zero inside [0, T#].
3. L = 1.19 (support 2.38). Estimate cost from phase 2 (N, precision near the Landau–Widom floor ~1e-47 per Zhu §7/§12), write the estimate in numerics/RUNS.md, put QUESTION: approve Modal run at the top of PROGRESS.md, and stop. Do not launch it yourself before the supervisor answers.
4. K2 on Epstein (1,1,6) or Davenport–Heilbronn at a window where the form is known negative (see MISSION.md). The reduction must not return a positive bound there.

Output

hunts/oob_envelope/numerics/RESULTS.md, opening with a 5-line graded summary (each line with its ladder grade and the commit/JSON it rests on), raw numbers in JSON beside it, reproduction commands at the end. PROGRESS.md updated at each phase. Small commits; do not push.

Limits

Local runs under 10 minutes and 2 GB (Ghost has 8 GB and hosts the chat gateway; an out-of-memory hangs it). Anything heavier: Modal, after the supervisor approves. Never GitHub Actions. When blocked, write QUESTION: ... at the top of PROGRESS.md and end your turn.