Inconclusive: no original candidate reached the preregistered root threshold. This is a diagnostic, not an interval certificate, a zero-free-region result, or an original first-Laguerre lower bound. No research row, node, thaw or manuscript version. Both original-evidence recovery groups remain OPEN.
Reviewed main bc3ff0c962c485ac8104ce8cd832c119c260c871 (PR79).
The full registered conclusions and continuation demands were reviewed;
historical proofs/certificates were not all replayed. The frozen proposal
was in draft PR80
before the original evaluation: commit 728cc6c; checked evaluator and
controls commit 0604699.
Wall check: Distinct test. Closest PR78/79, NS100/101. The test seeks an original uncancelled M-zero, which would reject general quotient PD, beyond PR78’s rejected positive sech-power mixture. It supplies no new arithmetic lower estimate. The original signed theta target remains the same open gap.
The single rectangle was 1/8<=Re z<=2, 1/8<=Im z<=5/8.
81 initial points, four selected cells and same-cell 128/256-bit refinements
used 171 evaluations in 48.46 seconds (a runtime observation, not a bound).
Both precision runs stopped each refinement at its allowed cell boundary.
There was no automatic domain extension or second scan.
| Selected cell (zero based) | 256-bit normalized endpoint residual | Stop |
|---|---|---|
| (0,7) | 0.03914163844 | step leaves cell after 16 halvings |
| (1,7) | 0.54809426972 | step leaves cell after 16 halvings |
| (0,6) | 0.49442807092 | step leaves cell after 16 halvings |
| (0,5) | 0.64851255786 | step leaves cell after 16 halvings |
Residual means abs(B*M) divided by the largest corner value in the same
cell, at the same precision. The root-candidate threshold was 2^-40,
about 9.095e-13. None passed. The four-corner sampled winding rounded to
zero in all64 cells, which proves nothing about continuous boundary winding.
The minimum in this table is not a lower bound over a cell or region.
The complete original theta coefficients were retained through explicit lattice remainder and real-integration tail formulas. Their floating values are not outward-rounded certificates. Finite quadrature and roundoff are not rigorously bounded; increasing working precision alone does not bound integration error. Normalizing by a nonzero analytic factor preserves zeros but does not prevent sampled phase aliasing.
The planned finite falsification attempt is complete without a candidate
for certification. General PD of k=C/M remains undecided. A rigorous
uncancelled pole would exclude that sufficient construction, but a signed
Fourier transform of k need not make its convolution with X^2 negative.
Original L1[X]>=0, RH, G2 and cofinal arithmetic inputs remain open.
No original interval certificate was attempted; without a candidate there
was no reason to spend its conditional two-hour budget.
Stop this bounded test. Do not widen the box because refinements met its boundaries, treat the finite null as evidence for PD, or revisit the rejected sech mixture. A future test needs a separately specified arithmetic input or analytic estimate and its decision edge; none is supplied by this null.
The actual pipeline found the known denominator zero of z^4+1 in
[0.7,0.72]^2. With numerator1 it flagged a candidate needing certification;
with numerator (z^4+1)*exp(-z^2) it did not flag an uncancelled pole.
The removable toy therefore tests the important cancellation distinction.
Neither synthetic control supplies original-theta evidence. DH, NS100/101,
NS74/83 hypothesis matches/mismatches are explicit in the
filled proposal and independent protocol review.
Evidence: diagnostic record, full original output, controls.
Six assigned roles: evaluator, locator/controls, mathematical protocol,
independent endpoint integration, code/results, final admission.
Reviews and final verification are recorded in review-record.json.
A separate direct-term theta implementation with 256-bit adaptive tanh-sinh integration, 36 lattice terms and real cutoff5 checked the four existing endpoints, including the analytic normalized derivative. It did not search for roots or evaluate a new domain. Largest relative differences from the Gauss-Legendre replay were below8.374e-29 for M,1.404e-26 for C and1.048e-26 for normalized M’. These are observed discrepancies, not error enclosures. The four sampled values are stable across these methods; no certification candidate results. Replay archive.