Compatibility Filtering - Selective Persistence Among Composite Relations - Paper 1f Abstract Papers 1a through 1e established the emergence of relational structure through the steps of distinction, independence, orthogonality and composite relations between independent directions. These steps introduce a large set of possible relational configurations. Observed physical systems demonstrate that not all possible configurations persist. Instead, systems exhibit selective persistence; some relations remain stable while others dissolve, transform or decay. This paper introduces compatibility filtering as the minimal structural description of this selective persistence. Compatibility filtering does not itself create closure or discrete structural units. Instead it describes the process by which incompatible relations fail to persist, leaving a reduced set of surviving relations. Within this reduced set of surviving relations, self-consistent relational loops may later form. Compatibility filtering therefore represents the structural reduction step that precedes closure in the Finite Reversible Closure (FRC) framework. Introduction Paper 1a defined the Zerofield as the absence of realised relational structure. Paper 1b introduced distinction between relational states. Paper 1c established independence as the condition preventing relational collapse. Paper 1d introduced orthogonality as the simplest uncoupled geometric representation of independence. Paper 1e established composite relations that arise when variation occurs simultaneously along independent directions. These steps significantly increase the number of possible relational configurations within the system. However, observed physical systems do not maintain all possible configurations. Instead, systems demonstrate selective persistence. Some configurations remain stable while others dissipate or transform. Examples of such behaviour appear across many physical contexts, including resonant modes in wave systems, stable lattice geometries in crystals, molecular bonding arrangements and orbital resonances in gravitational systems. The purpose of this paper is therefore to introduce the minimal structural principle that explains why only some configurations persist. This principle is compatibility filtering. Compatibility filtering describes the process by which incompatible relations fail to persist while compatible relations remain.
Joe Bloggs (Mon,) studied this question.