Compatibility Filtering - Selective Persistence Among Composite Relations - Paper 1f

Bloggs, Joe

doi:10.5281/zenodo.18924947

Published March 9, 2026 | Version v1

Preprint Open

Compatibility Filtering - Selective Persistence Among Composite Relations - Paper 1f

Bloggs, Joe (Researcher)

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.

Abstract (English)

Description

Paper 1f introduces the first structural reduction mechanism within the FRC framework.

Primitive 0 establishes finite realisation and excludes operational infinities.

Primitive 1 establishes closure as a requirement for realised systems.

Paper 1a defined the Zerofield boundary representing the absence of relational structure.

Paper 1b introduced distinction as the minimal relational contrast.

Paper 1c stabilised distinction through relational independence.

Paper 1d introduced orthogonality as the simplest uncoupled geometric representation of independence.

Paper 1e introduced composite relations arising from simultaneous variation along independent directions.

These steps generate a large number of possible relational configurations.

However, observed systems do not retain all possible configurations. Instead they exhibit selective persistence.

Compatibility filtering describes this behaviour.

Possible relational configurations are reduced to a smaller set of surviving relations according to structural compatibility conditions.

Conceptually this process can be represented as;

possible relations -> selective persistence -> surviving relations

Compatibility conditions represent structural constraints that determine whether a configuration can remain self-consistent.

Examples of such conditions include;-

boundary compatibility in standing wave systems
geometric compatibility in crystal lattice structures
dynamical compatibility in orbital resonances
structural compatibility in molecular bonding arrangements

Configurations that violate compatibility conditions tend to dissolve or transform, while configurations satisfying these conditions persist.

Compatibility filtering therefore reduces the set of possible relations to a smaller set of surviving relations.

This reduction creates the conditions under which self-consistent relational loops may later appear.

Closure relations therefore emerge only within the subset of relations that survive compatibility filtering.

The structural ladder of the programme therefore becomes;-

Primitive 0 — Finite Realisation
Primitive 1 — Primitive Closure

Paper 1a — Zerofield Boundary
Absence of relational structure

Paper 1b — Distinction
Minimal relational difference

Paper 1c — Independence
Stabilisation of distinction

Paper 1d — Orthogonality
Uncoupled geometric representation

Paper 1e — Composite (Diagonal) Relations
First composite relational magnitudes

Paper 1f — Compatibility Filtering
Selective persistence among configurations

The next paper examines how surviving relations form self-consistent relational loops.

Paper 1g — Closure Relations

This paper forms part of the Finite Reversible Closure (FRC) research programme (Papers 0–20) describing the emergence of physical structure from finite relational closure.

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