Governed Relational Geometry: A Formal Model for Evidence, Context and Valid Transformation

Governed Relational Geometry develops the public formal layer of the Geometry Intelligence framework established in Paper 1. It models entities, claims, evidence, contexts, authorities, constraints and validation states as governed objects whose meaning depends on structured position, typed relationships and permissible transformation.

The paper defines a policy-indexed governed relational geometry; separates content equivalence from governed equivalence; distinguishes declared context from evaluation context; and formalizes identity preservation, provenance continuity, constraint handling, authority boundedness, contextual transport, contradiction containment, noninterference under irrelevant change and responsiveness to material change.

A transformation loss record makes authorized information loss explicit. Under stated compatibility and monotonicity assumptions, valid transformations compose. Provenance continuity is proved by induction over finite transformation chains. A complete worked example demonstrates entity disambiguation, evidence admission, conflict classification, bounded derivation, supersession and context transport.

The model is implementation-neutral. It does not prescribe or disclose an implementation-specific coordinate representation, metric, algorithm, storage architecture or deployment procedure.

This is Paper 2 of the Geometry Intelligence Foundational Series. Paper 1 established the field definition; Paper 2 supplies the formal model; Paper 3 is intended to translate the resulting invariants into external Machine Entity Comprehension conformance profiles.

Final Manuscript 1.0. Published by KTS Global. Licensed under CC BY 4.0.