Proposal: Paper admission audit of three complete original-theta mechanisms: auxiliary heat-source control, complete modular-duplication sector positivity, and direct contour analysis of k=C/M. Record their outcomes and the conditional finite falsification edge for an uncancelled original quotient pole. No scan.
Shared-input group: ZERO-GEOMETRY, closest NS100/101 and PR76-78. Status: frozen. Thaw requires original arithmetic absent from applicable controls and a concrete estimating step with complete transfer. No thaw is claimed. Auxiliary Gaussian heat here is not the original nonlinear Jacobi clock or NS52’s same-test spectral transport comparison.
Arithmetic input beyond the functional equation: Complete integer-square theta series and original polynomial completion; exact half-integer/alternating parity coefficients under duplication; original n=1 complex saddle and complete n>=2 lattice gaps. These justify the exact completed sector identities and uniform horizontal quotient tails. No signed lower estimate is inferred from those identities alone.
Dependency edge and arithmetic use (before any new candidate computation): Heat: Q_0=G_AQ_A-2 int_0^A G_aS_a da, A=1/8, with Q=L1[H], S=L1[H’]. The source-to-endpoint comparison is unestimated; assuming it restates Q_0>=0. Duplication: the complete Hermitian sector matrix is indefinite wherever original X!=0; correcting its phase part leaves exactly L1[X] A A*. Contour positivity: a pole-free shift leaves the same unestimated Fourier sign. All domains, mixed terms and zeros are retained. Separate falsification implication, now independently checked: original M(z0)=0, C(z0)!=0, abs(Im z0)<pi/4 => nonremovable k pole => a lowest-height nonzero-frequency residue sum forces sign changes of K => k is not positive definite. Complete strip tails and all pole orders are accounted for. This rejects a sufficient mechanism only: signed K can still give L1[X]=(1/pi) int X(r-xi/2)^2 K(xi) dxi>=0. No implication to failure of J, RH or G2. No original pole location or certificate is supplied.
Control screen (actual candidate, before proof/certification): Davenport-Heilbronn: no literal original theta coefficients/completion; its own analytic strip must be established before numerical transplantation. Generic contour or heat identities alone are not an arithmetic distinction. NS100 log-concave order-2: rejects slice positivity, not these full integrals. NS101 reciprocal dilation: shares generic heat/quotient/contour algebra; changes the original lattice and Jacobi IVP. Its known negative L1 forces non-PD quotient but does not say poles cause that failure. No pole search on this control is presumed to succeed; no hypothesis mismatch is a pass. Additional controls: exact polynomial forward-heat example rejects generic Laguerre-cone preservation. Exact cosh-denominator pole example checks residue sign/scaling; entire Gaussian-polynomial example shows that no poles does not imply positive Fourier density. Future locator must check both M=z^4+1,C=1 and C=M*exp(-z^2), detecting cancellation in the latter. These are analytic controls, not original theta data or a completed pipeline. NS74/83 concern NB targets and dyadic rates, absent here. Command/artifact, precision, sample domain, values/residuals: Paper identities only in reviews/01-06; no controls command or numerical precision applies. No sampled sign or zero claim, no actual scan performed. Full-scope obstruction: stated unrestricted duplication matrix is indefinite on original X!=0. Any uncancelled interior quotient pole would exclude k-PD, but existence has not been established. No general heat, duplication or contour no-go.
Wall check: Same open gap. Closest result: NS100/101, PR76-78. What changes: a scoped sector-cone rejection and a complete quotient-pole falsification edge; no original arithmetic sign bound. A later instantiated locator would be a Distinct test of general k-PD, beyond PR78’s mixture.
What success changes: a certified original uncancelled pole would reject the general quotient-PD certificate. A genuine source or recurrence bound would need its full comparison and could address first Laguerre only. What failure changes: no pole found in a finite region is inconclusive; no positivity claim, wider automatic search or manuscript version follows. Budget: current six paper reviews and one audit PR, zero scans/certificates. Possible separate locator: one fixed rectangle Re z in [1/8,2], Im z in [1/8,5/8]; at most 9x9 grid, four cells and twelve refinement steps per cell; 90 minutes including controls. Evaluator, selection and complete-error rules must be preregistered before running. A found box could receive at most two initial hours of Arb certification with complete tails and two precisions. Disposition before claim: stop the three unestimated/rejected sign proposals; retain a bounded falsification protocol as a useful next proposal, not a run already approved by this audit. External candidate box is optional, not an AGENTS requirement. No research row is claimed. Version bump expected: no. Audit only; unchanged manuscript.