Six-agent original-theta continuation audit
Rendered report · review record · assignment brief
Wall check: Same open gap — ZERO-GEOMETRY, NS100/101, PR72/73.
No original-theta all-height sign method is admitted. The original nonlinear
evolution remains unexcluded. Six agents assessed independent proof checks,
a local nonlinear certificate, smooth reciprocal completions, arXiv reference
methods, matched controls, and adversarial admission.
The concrete supporting findings are:
- PR73’s pair identity and fixed-prefix obstruction survive independent
review. Its net tail cancellation must include the cross terms.
- A specified local drift-cancelling integration-by-parts certificate fails
on the original theta tail. Its diagonal residual is eventually negative;
no general local/nonlinear closure is claimed.
- A specified smooth reciprocal completion avoids the reflected-prefix cusp
and has explicit complete transform/derivative error bounds for all real
heights and integer M>=1. Pointwise growing M retains fixed-M derivatives.
Its differential kernel has a negative artificial real tail, and no lower
Laguerre margin is proved. The real-tail sign alone does not decide L1.
- Gasper’s Bessel square identity gives an all-height positive reference
margin, with an elementary explicit lower bound recorded here. No complete
original-theta-to-Bessel comparison is supplied; this reference is not the
preceding completion, so their estimates cannot be combined silently.
- The NS101 reciprocal-mixture family directly fails L1 at pi/beta when
beta>=max(2,pi*sqrt(m2/m0)), using complete theta moments. Its off-axis zeros
are not the sign argument. This does not separately certify the historical
beta=2 member or preserve the original Jacobi IVP.
- A separate smooth positive strictly log-concave double-exponential control
shows that all odd boundary cancellations plus those shape properties do
not suffice. It lacks the original arithmetic and IVP.
Internal reviews
- Independent PR73 audit and shape control
- Local nonlinear residual certificate
- Smooth reciprocal completion and complete error
- Four-source arXiv applicability review
- Direct matched first-Laguerre control
- Adversarial admission and correction check
The global quotient-regularity paragraph in Review 2 is explicitly conditional
on p’(t)<0 at every real t; strict log-concavity alone is not substituted for
that pointwise statement. Its diagonal rejection does not need this premise.
No numerical/symbolic scan, interval certificate, NS row, node, thaw or
manuscript version. The new bound is for approximation error, not for the
signed target. Both original-evidence recovery groups remain OPEN. Historical
proofs and external curvature certificates were not replayed. Publication
validation and the completed proposal-gate block are recorded in the PR body.
Next admission requires a concrete original-arithmetic method for the complete
signed lower bound or reference comparison, including every height and all
mixed terms. No adjacent parameter scan or automatic extension is scheduled.
RH, G2 and the cofinal signed-arithmetic lower bound remain open.