Simple critical zeros in short intervals: stability, pressure, and parity

We study proportions of simple and distinct nontrivial zeros of the Riemann zeta function in short intervals. The finite stable Hilbert rank-trace method and Wang's fixed-test short-interval input are retained with their stated assumptions. An odd-multiplicity parity transfer combines a fixed classical positive density of distinct odd-multiplicity critical zeros with the multiplicity excess in the finite inequality. For every fixed exponent theta in (0.51,1), this gives a simple-critical lower bound max{0,c(theta),(c(theta)+2 kappa)/3}, where c(theta)=2-theta/2-cot(theta/sqrt(2))/sqrt(2) and kappa is one fixed positive classical density constant. Consequently some fixed theta below Wang's cosine positivity root has positive simple-critical density; a separate identity gives a distinct-zero proportion greater than one half at another exponent below that root. The new exponent and kappa are intentionally left unquantified. The same finite method is strengthened by an odd-frame pressure transfer. At theta=3/4, a certified two-variable interval certificate with 16,797 nodes and zero unresolved cells gives simple-critical lower bound 0.419087888170111727959091183775 and distinct companion 0.709543944085055863979545591888. Construction and a separate sinc-Taylor replay pass under the declared rational parameters. The parity census and arithmetic controls are reproducible from the accompanying CAOS Research repository. The scientific proof and imported analytic interfaces were independently audited within the project; this is a self-published preprint and has not received external peer review or end-to-end formal verification. The work does not prove the Riemann hypothesis, establish a new global record, provide an effective starting height, or claim a numerical improvement to the positivity exponent.