SR103EN Formalization Coherence Cosmology — A Structural Formalization Note

This paper presents a structural formalization note for Coherence Cosmology (SR103EN v1.8). It is situated within the tradition of formal ontology and structural ontology — the project of describing ontological commitments using the tools of formal logic and order theory, rather than deriving physical laws. The core ontological claims of SR103EN — Existence = Coherence, the present as terminal boundary of referenced structure, and the static crystalline nature of the globally coherent whole — are formalized using strict partial orders, antichain conditions, and section theory. The central results are: 1. Theorem 1–3: Existence = Coherence = Unbounded. has no structural exterior — derived from two ontological axioms. 2. Theorem 8: Coherence is preserved across the inter-section order — only coherence transitions to coherence. 3. Definition 11: Mutual recognizability as the formal expression of relative difference-series density. 4. Correspondence Ansatz: Structural correspondence between and the Lorentz factor . 5. Definitions 12–15: Internal structure of — infinite space and infinite field, no first or last section. 6. Definitions 16–19: Quantum mechanical correspondence — probabilistic states as the foundational mode of existence, collapse as crystallized interference. 7. Definition 20: Mutual transformation of patterns — no local structure is isolated within . This paper is a formal ontology note for SR103EN. It does not claim to derive physical laws. The axioms are ontological commitments, not mathematical hypotheses. The correspondences with special relativity and quantum mechanics are proposed as ontological reinterpretations — showing that the structural features of these physical theories are natural consequences of a single ontological ground: the world is already crystallized as a globally coherent static structure.