MISSION: Weil positivity propagation across window size

Opened 2026-09-23 on branch teal-sea/weil-propagation, which merges teal-sea/rh-strategy-council-sep17 (the Davenport-Heilbronn negativity result at (c, N) = (31, 60)) onto origin/main.

The question

RH is equivalent to nonnegativity of the Weil quadratic form on every compact window. Positivity is established on small windows: classically for support log 2 (Yoshida; Connes-Consani), and by a computer-checked argument for support 1.6 (arXiv:2608.24827). The positive margin decays doubly exponentially in the window length L, so no window-by-window certificate can reach RH.

This hunt asks for a propagation mechanism: a statement of the form

positivity on window L + the Euler product => positivity on window L + delta

or any structural relation between the ground states at L and L + delta that could carry positivity forward uniformly.

The kill-control

Davenport-Heilbronn (DH) shares the functional equation and gamma factor class of an L-function but has no Euler product, and its truncated Weil form turns negative at c = 31 (hunts/rogue_frontier/weil_trunc/RESULTS.md s8, THEOREM_FEASIBILITY.md). Any candidate mechanism that does not use the Euler product must also hold for DH, and is therefore refuted. Every candidate is tested against DH between c = 30 and c = 31 before it is developed further.

Workers and ownership

• numerics/: measurement of ground-state transport between windows, for zeta and DH. Branch teal-sea/weil-propagation.
• theory/: literature and candidate lemmas. Branch teal-sea/weil-propagation-theory.

Each worker writes only in its own subdirectory. Other hunts are read-only inputs.

Rules

• No claim about RH. A candidate lemma is a candidate until proved, and the certainty ladder in AGENTS.md governs every statement.
• Nothing heavy on the laptop. Local runs stay under 10 minutes and a few GB. Anything larger goes to GitHub Actions with an estimate in RUNS.md first.
• No lake build locally.
• No publication, deployment, or edits outside hunts/weil_propagation/.
• The reserved word banned under hunts/ stays banned (tests/test_hunt_probe_discipline.py).

Kill conditions

• A candidate mechanism holds for DH across c = 30 -> 31: refuted.
• A candidate reduces to a restatement of RH with no new estimate: record it as a reformulation, not progress.
• A claimed transport relation fails an independent precision or basis-size check: measurement artifact.