A Reverse-Construction Route to Structural Unification of Quantum Mechanics and Gravity: Correlation-Causation-Geometry

Preprint, Version 1.0 — 4 October 2026. This manuscript has not been peer reviewed. This work develops an endpoint-first, reverse-construction approach to the structural relationship between quantum mechanics and gravitational spacetime. Rather than beginning with a preferred microscopic ontology, the analysis imposes quantum and relativistic endpoint constraints simultaneously and asks which relational structures survive explicit falsification tests. Phase I finds repeated convergence among quantum correlation, causal accessibility, propagation, effective proximity, and geometry, motivating the proposed Correlation-Causation-Geometry (CCG) architecture. Phase II subjects that architecture to a mathematical stress test. Its principal result is the CCG Rank-Two Compatibility Theorem, which proves the compatibility bound Sρ(a) ≤ 2Gρ(a) throughout the stated normalized rank-two class generated by positive-definite similarity transformations. The result supports structural compatibility within the scope tested. It does not establish structural uniqueness, derive Einstein and quantum-field dynamics from a single microscopic theory, identify a unique substrate, or provide empirical confirmation. Mathematical result, physical interpretation, and speculation are explicitly separated throughout the manuscript. Exact proof-custody materials, verifier scripts, rational certificate tables, audit records, and reproducibility guidance are publicly available in the companion Zenodo record: CCG Rank-Two Compatibility Theorem: Exact Reproducibility and Proof-Custody Archive, Version 1.0, DOI: 10.5281/zenodo.22753799.