SGOED: An Atemporal Matrix Formalism for Stability-Gated Crystallization and Aggregation (Phase 1-2)

This record contains the main SGOED manuscript in publication-ready format, together with its two technical appendices. SGOED (Structural Gradient Ontology & Equilibrium Dynamics) is a toy-level mathematical formalism exploring how stable structures emerge from matrix chaos without requiring a fundamental time dimension. Included Files: Main Manuscript (1_SGOED_manuscript.pdf): Presents the derived components — a stability criterion fixed by Bendixson's theorem, a Fermi-Dirac nucleation probability, a two-gate structure, and a kinetic stability-gated aggregation model with analytic characterization — along with an honest statement of boundaries. Appendix 1 (2_SGOED_v2_revision.pdf): Detailed derivation record (v2 revision). Appendix 2 (3_SGOED_phase2_artifact_tests.pdf): Artifact-test supplementary record, with script-to-section mapping. Related Code & Record: The analysis scripts backing all numbers are published separately as Record B: DOI: 10.5281/zenodo.21786191 Concept DOI: 10.5281/zenodo.21786190 Please note: this work represents a theoretical/conceptual framework and does not claim empirically verified physics.