This record contains the complete Relational Rank Geometry (RRG) framework, organized as two complementary documents: a formal mathematical core and an empirical domain companion. RRG is a second-order measurement framework designed to certify structural rank collapse in the joint covariance of interacting observers without requiring a parametric model, latent-state assumptions, or predefined ontology. Its central object is the accumulated relational structure: L(t) = ∫ ρab(τ)dτ where relational coherence accumulates through time and is evaluated structurally rather than semantically. Certification is performed through the differential relational operator: dρ = Var(ρab, W) which determines whether the observed accumulation corresponds to genuine structural convergence or stochastic correlation. Document 1 — Formal Core Contains the self-contained mathematical framework of RRG, including the primitive set, Rank-Collapse Theorem, regime conditions, reflexive structure, stability conditions, and the open-boundary formulation. This document is domain-independent and establishes the invariant structural layer of the framework. Document 2 — Domain Companion Contains the empirical calibration protocol, cross-domain seed index (13 substrates across 11 domains), comparative positioning against existing frameworks, and the historical genesis of the model. This companion document serves as the evolving empirical layer through which new domains and substrates can be incorporated and validated. This release formally separates the invariant mathematical core from the expandable empirical record. The formal core is intended to remain structurally stable, while the companion document is designed to evolve as additional relational substrates and domain confirmations emerge. Note:v7 — Formal Core: N-Observer Rank-Collapse incorporated into main body. (Domain companion unchanged).
Jesus David Calderas Cervantes (Wed,) studied this question.