This preprint develops an exact finite packet-sieve framework for symmetric diagonal affine systems. It merges the local residue-cloud obstruction structure of the previous finite local sieve draft with finite packet-survivor counts, survivor convolutions, admissible-state decompositions, rectangle counts, and fiber-moment identities over squarefree moduli. The paper is part of the MSI survivor-envelope program. Its purpose is to organize finite congruence data attached to prime-constraint systems before any analytic or asymptotic prime-distribution input is introduced. Classical sieve theory, Hardy--Littlewood-type products, Bateman--Horn-type local factors, and related analytic theories are used only as external comparison and calibration points, not as ingredients in the proofs. This version substantially revises and consolidates the previous Zenodo preprint “Exact Finite Local Sieve Structures for Symmetric Diagonal Affine Systems”:https://zenodo.org/records/20447546 It is also a companion continuation of:“Additive Encoding of Primality Constraints and Local Obstruction Structure in a Symmetric Affine System”https://zenodo.org/records/20259817 The present preprint does not claim to prove Goldbach, Hardy--Littlewood, Bateman--Horn, Dickson-type, twin-prime-type, or general prime-distribution conjectures. It proves exact finite congruence, survivor-fiber, convolution, and moment identities that are intended to support later global/windowed survivor-envelope investigations.
Gabriel Dorel Dura (Fri,) studied this question.