Every certificate in the current race reads pair-correlation data on [-1,1] and nothing else. The configuration ceiling for that information class is 0.6818286874638, and the whole public race is fighting over the interval from 0.6725007 to 0.6734165, a span of 9.2e-4.
One fact is already known outside the band and needs no hypothesis. Baluyot, Goldston, Suriajaya and Turnage-Butterbaugh (arXiv:2306.04799, Theorem 1) prove the weighted form factor is nonnegative for every alpha, unconditionally, because conjugate-closure of the zero multiset writes it as an integral of a square and the Cauchy weight's poles at ±2i cover every pair of strip zeros. This laboratory re-derived that before finding it; hunts/frontier_math/RESULTS-frontier-math.md §4 records it so nobody derives it a third time.
Chirre, Goncalves and de Laat reach 0.6792 for zeta with two zero-side inputs: that positivity, and a diagonal-isolation drop. Their positivity input is exactly the BGSTB fact, so it costs no hypothesis. Their second input does not transfer, and the reason is one sentence: their argument counts inertia against a kernel that must be the Gram matrix of a window family, autocorrelations are nonnegative, and a kernel with ghat <= 0 outside [-1,1] is not one. Their §4 does not apply as written.
That single obstruction is this hunt. It is not a ceiling proof and not a bridge over somebody's theorem. It is a missing argument, and the thing it would buy is about 6.7e-3 on the unconditional record, roughly seven times the entire public race's progress to date.
The data class this hunt may read is bandwidth-one data plus the BGSTB out-of-band nonnegativity, and nothing else. Every input must be traceable to an unconditional source. F1 beyond the band via Farmer-Gonek-Lee Theorem 1.1, and every CGdL constant that uses it, ride on RH and are inadmissible as unconditional input here.
id: outband_intake
question: Is there a diagonal-isolation argument valid for a kernel with ghat <= 0 outside [-1,1], and what unconditional proportion does the resulting certificate deliver for the simple on-line zeros of zeta?
frontier: unconditional record 0.6725007036794116 (AF2026 Theorem D); public race leader 0.6734164909714992949; bandwidth-one configuration ceiling 0.6818286874638; CGdL RH-conditional 0.6792; LP class value with BGSTB positivity added 0.6863 at (X=80, J=320) and descending in X
proposed_attack: measured before analytic, analytic before Lean: (1) converge the LP in X with the out-of-band constraint on and extrapolate the class value the information actually supports, so the prize is a measured number rather than an inherited one; (2) sweep the out-of-band reach A_out to price the information, asking how much of the gain comes from the first slice past alpha = 1 and where it saturates; (3) attack the obstruction directly by finding an inertia or isolation count that does not require the kernel to be a Gram matrix, candidate directions being a signed decomposition splitting ghat into an autocorrelation part and a residual whose inertia is counted separately, and replacing the isolation drop with a moment inequality that reads only the positivity; (4) if (3) yields an argument, realize it as a finite inequality of the shape the existing certificate pipeline already proves, and only then formalize, in CI
dead_routes:
- Farmer-Gonek-Lee Theorem 1.1 as unconditional input; it is proved under RH
- re-deriving BGSTB Theorem 1; done twice already in this tree
- any route to 0.70 for zeta by widening the band; the sieve wall of frontier_math §2 is quantified and 0.70 needs support near 1.04, which is Hardy-Littlewood grade and does not exist unconditionally
- transplanting CGdL §4 as written; the Gram requirement is the obstruction, not a detail of presentation
required_oracles:
- the in-band LP reproducing the Montgomery-Taylor dual with the out-of-band constraint off, as a control on every run
- monotonicity of the class value under grid refinement, in the direction the discretisation forces; a floor that rises under refinement is a defect, as hunts/frontier_math §5 records at cost
- any candidate isolation argument tested against the Davenport-Heilbronn function through zeta.epstein.battery before it is believed
kill_conditions:
- the converged LP value with out-of-band positivity lands at or below 0.6725007, so the information buys nothing this certificate class can spend
- the obstruction is shown to be essential rather than presentational, by exhibiting a kernel with ghat <= 0 out of band whose inertia count provably fails
- any candidate argument passes the Davenport-Heilbronn control, which means it distinguishes nothing
agents_may:
- search, derive, code, attack
- formalize on GitHub Actions only
- state positions on whether a step is bookkeeping or analysis
agents_may_not:
- present an RH-conditional input as unconditional, in any sentence
- claim above measured grade before an artifact exists
- write language implying any of this bears on RH itself
- run lake build locally