Read first: hunts/weil_propagation/MISSION.md, AGENTS.md (hard rules, certainty ladder, compute discipline), then hunts/rogue_frontier/weil_trunc/RESULTS.md sections 2, 4, 8 and THEOREM_FEASIBILITY.md. The Galerkin assembly lives in hunts/rogue_frontier/weil_trunc/galerkin.py (float/mpmath) and enclosures.py (Arb). Import them; do not rewrite them.
Python: .venv/bin/python with PYTHONPATH=<this worktree root>. python-flint is installed there.
Question
How does the ground state of the truncated Weil form at window L = log c relate to the ground state at L' = log c' with c' slightly larger? We want a transport relation that could carry positivity forward, and we want to see it break for Davenport-Heilbronn exactly where DH turns negative.
Tasks, in order
- Reproduce, cheaply, lambda_min and ground vector v(c) for zeta and DH at a few (c, N) cells already in the record (e.g. c = 13, 29, 30, 31 at modest N). Match the recorded values before going further.
- Build a common function-space picture across c: map ground states at different c into one space (for example the entire transforms F_v(z) on the real line, or the functions on [0, L] extended by zero). Measure overlap, energy of v(c) under the form at c', and the Rayleigh quotient of the transported vector, on a fine c-grid (non-integer c allowed).
- Decompose the change of the form from c to c' into: archimedean change, new prime-power terms entering (n in (c, c']), and the rescaling of the basis. Report which term drives the ground-state energy up or down, for zeta and for DH, especially across DH's c = 30 -> 31 crossing.
- State any candidate monotonicity or transport inequality you observe, with its range and grade. Test it on DH. If it holds for DH it is refuted.
Output
Write only in hunts/weil_propagation/numerics/: scripts, JSON with every number, and RESULTS.md with measured or hardened grades stated per claim. Commit to this branch in small commits. Do not push.
Limits
Local runs under 10 minutes each and a few GB of memory. Record estimates in hunts/weil_propagation/numerics/RUNS.md before any run over a minute. If a larger run is needed, stop and write the proposed CI job in RESULTS.md instead of running it. No lake build.
Finish by running tests/test_hunt_probe_discipline.py and writing a five-line summary at the top of RESULTS.md: what was found, grade, what refutes it, next step.