The Schimmel Prime-Compression Operator: A Frozen Recursive Specification

Abstract

This paper defines the frozen Kevin Schimmel Prime Compression (KSPC) operator, a deterministic recursive transformation of ordered prime sequences. The operator searches according to its fixed block-selection rule, replaces an eligible consecutive block whose sum is prime by that prime sum, preserves the remaining sequence order, and recursively applies the same procedure until no eligible block remains. The document distinguishes the operator’s exact definition from computational observations and unproved conjectures concerning persistence, terminal survivors, and the associated Omega lineage. It is intended to establish a stable, citable specification for independent implementation, reproduction, testing, and future mathematical investigation. The KSPC operator, its research direction, and the associated conjectural framework were formulated by Kevin Mark Schimmel. No claim is made that finite computational evidence proves infinite continuation or unbounded terminal-survivor growth.