Rendered report · Complete derivation · Review record · Twelve-reviewer brief
Wall check: Same open gap — ZERO-GEOMETRY, NS100/101, PR74/75.
The complete original theta kernel has a positive, smooth, exponentially decaying primitive f=2*cosh(u/2)-h. It gives integrable pair moments A_0,A_2, so the differential kernel can now be Fourier transformed term by term with the complete boundaries retained. Recovering X multiplies its primitive transform Y by (r^2+1/4)/4, and the Laguerre inequality acquires an explicit correction. That correction is indispensable.
The exact NS101 control retains primitive positivity, the exponential envelope and its unit leading tail, yet violates the corrected target in PR74’s stated analytic range. These shared structural properties therefore do not supply the original sign. The control loses the original arithmetic coefficients and Jacobi IVP, so the nonlinear arithmetic route stays open.
The primitive transform is meromorphic, with poles at +/-i/2; Csordas’s entire-transform admissible-kernel hypotheses cannot be imported for it. No scan, research row, node, thaw, certificate or manuscript version. No new original-arithmetic sign estimate. Both original-recovery groups remain OPEN; RH, G2 and the cofinal signed-arithmetic lower bound remain open.
Twelve focused agent reviews are complete and integrated. No mathematical correction to the primitive, pair constants or control margin was required. Clarifications make the old/new complete boundary cancellation explicit, distinguish ordinary integral convergence from meromorphic continuation, and allow derivative/remainder constants to depend on the control parameter. The review record now distinguishes this team review from the initial paper self-review. No historical proof or certificate replay is claimed.
The estimating-method checks found no admitted candidate: complete moments supply a local interval, the proposed Jacobi separation-clock transport has no nonsingular positivity-preserving generator, and the Euler derivative series has no justified signed transfer to the critical line. Its pointwise second-logarithmic-derivative target is not the older NS47 all-test comparison; that recorded closure must not be broadened. A source normalization caution is preserved in review 11; the pair constants here were derived independently.