Classification: exact identities and a scoped control; no new arithmetic positivity estimate. The feasibility attempt reached its stop.
The actual Jacobi completion gives the usual autocorrelation of the tilted theta kernel. The kernel required by the growth criterion is its parameter derivative, a difference of two positive definite kernels. The comparison between those terms remains unproved.
A concrete reciprocal-theta control preserves positive Gaussian mixtures, the reciprocal identity, a positive even differential kernel, order one, and the critical-strip zero bound, while adding explicit off-axis zeros. It changes the original single-lattice coefficients and does not assert monotonicity, log-concavity or all modular transformations. It therefore does not exclude a proof using those additional original properties.
Direct absolute unfolding only works beyond the classical convergence boundary. At the boundary each Gaussian summand integrates to zero but the complete kernel integrates to 1/4. This forbids that interchange, not correlated resummation or the desired sign for the original function.
argument.tex: self-contained completion, factorization attempt, control
and complete integration-domain calculation.checks.mac, checks-output.txt: 20 exact algebra checks. These check
identities, not the unproved sign or all analytic steps.turn-review.json: all 104 conclusion records reviewed, provenance,
scope and Wall checks.sources.json: primary sources and an expanded, nonexhaustive literature
screen; reported external blockwise claims are not imported as proofs.self-review.json, validation.json, inventory.json: audit and checks.Run maxima --very-quiet -b evidence/ns101_theta_factorization/checks.mac.
There are no approximate numerical proof gates, cutoff experiments or new
Python files in this task. No manuscript version or theorem node is added.
Both missing-original evidence groups remain OPEN. RH and G2 remain open.