Obstructions to Fourfold Aggregation of Prime Phases

We examine whether independently defined aggregates of logarithmic prime phases can realize the equal-amplitude four-phase geometry of a repeated projection model. Positive prime and von Mangoldt weighted phase measures fail the stated quartet criterion at every finite cutoff containing 2, 3 and 5, and the prime number theorem gives a strictly positive limiting defect in the open critical strip at fixed height. A local interval computation isolates one simple zeta zero and excludes exact cancellation of four raw samples at radius one tenth. Version 2 adds a logarithmic-derivative contour-centroid computation that recovers the isolated zero coordinate from its divisor count and first moment, together with a Lean 4.19.0 proof of the bounded algebraic recovery theorem under an explicit moment interface. The numerical contour evaluations are COMPUTED; the local interval input is VERIFIED within its stated software boundary; the Lean algebra is PROVED_LOCAL_KERNEL. The analytic specialization of the moment interface to zeta, a prime-only four-phase construction, exclusion of off-critical-line zeros, and the Riemann hypothesis remain OPEN.