A Finite-Count Search for a Morphology-Structured Projection Ridge Near 2.75 in Riemann-Zero Gap Coordinates

We report a finite-count empirical search for localized enrichment near 2.75 in unfolded Riemann zeta-zero gap coordinates. The tested coordinate is motivated by a geometric search prior derived from the N = 2 state of Euler’s finite-step complex approximation and a half-step phase identity involving the circle remainder Pr = π − 3. Across 22 support-filtered zero-height sample blocks, where support-filtering requires adequate finite-count support for both the active marker and its control, the frozen-design active marker exceeded its sign-reversed control in 22/22 cases. The combined primary ledger produced 736 observed hits against 218 random-surrogate hits, for cumulative enrichment 3.376×. The combined Fisher-method sign-control statistic gives p = 1.86 × 10−21, while the primary affinity-vs-random evaluation gives p = 4.17 × 10−56. A subsequent coordinate-locality validation scan, R142A, evaluated the same frozen grammar over a coordinate grid and showed that the original active marker lies inside a broader enriched shelf spanning approximately 2.70–2.81, rather than at a unique isolated maximum. This conditional test complements rather than challenges the standard pair-correlation/GUE baseline for unfolded zero statistics. We interpret the result as a finite-count empirical observation of conditional localized enrichment across sampled zero-height blocks under the frozen grammar and operational surrogate. It is not presented as a proof of analytic necessity or a theorem about prime counting.