/teal-sea
teal-sea / zeta-labstate of record · compiled 28 Sep 2026 · revision e4945c4 · source

Library · hunts/oob_envelope/referee/L119_PLAN.md

L = 1.19 bounded referee plan

362 words · 40 lines · source

Authorized by Thomas's 2026-09-27 task, received 2026-09-28. This supersedes only the earlier prohibition on new L=1.19 work. No push or PR. All writes stay under referee/. Modal profile teal-sea, at most four core-hours total.

Read BRIEF, PROGRESS, REVIEW and RUNS first. Author input: prose/results only, 9419552, 500a803 and b876f0a. Exact witness copied from b876f0a envelope JSON. No author implementation read or imported. Shared arithmetic library remains python-flint, while quadrature, series and analytic budgets are independent.

First unit: last ten half-unit panels, [495,500], CC degree 192, 1024 bits, 500 even Legendre modes. Anticipated 60 to 600 seconds, unmeasured. Hard limit 900 seconds, 1 CPU, 1792 MiB. Write each panel's progress and final exact-dyadic matrix to oob-envelope-referee/l119/REVISION/UNIT. No retries. Measure this unit and record a total estimate in RUNS before the other 99 units. Refuse the full dispatch if measured extrapolation plus reducer and startup allowance exceeds four core-hours. Monitor every app to stopped.

The independent positivity witness uses a fixed exact shift 5.718e-48, chosen before assembly. Its midpoint Cholesky factor is converted to exact dyadics and checked by Arb matrix multiplication. Row sums bound both the symmetric residual and all entry errors. Full bound subtracts independently computed tail and coupling norms. Desired outward-safe endpoint 5.7179e-48. Failure of the fixed shift or arithmetic widths is inconclusive, not a negative theorem. No optimization toward the last successful digit planned.

The deciding constant in-band mutation is H -> H-1e-47 together with beta -> beta-1e-47, changing the reduced form by exactly -1e-47 I. Before reduction, the initial large -100 proposal was replaced by this lesion at the actual spectral scale. Inverse iteration proposes a vector; its exact dyadic version must give an Arb Rayleigh upper bound <5.776e-48 for the original block and <-4.224e-48 for the mutant. The same factor step must reject the mutant. This targets positivity rejection and the violated Fourier support premise; it does not purport to be a legitimate alternative zeta envelope.

The published L=1.1 upper bound is 2.78e-38 (Zhu Table 3, read from v2). Nested even windows give the necessary one-sided K1 ceiling at L=1.19. No odd-sector conclusion, novelty claim or uniform RH conclusion is sought.