Generative Structural Theory v1.0: From Difference-Like Processes to Selected Stable Structure

Most formal and physical theories begin from elements that are already constituted: objects, points, space, time, or physical quantities. The question of how such elements come to be available is then placed outside the theory. Generative Structural Theory (GST) v1.0 takes a different starting layer. It adopts as primitive a difference-like process equipped with formal compositional boundary labels, and assumes no primitive objects, points, space, time, distance, or physical magnitude. On this basis, the paper defines a compatibility relation, a partial composition operation with conditional associativity, a coherence functional, a compositional closure operator, an abstract structural update operator, criteria separating fixedness from local stability, and a selection functional that adjudicates candidate sectors. The endpoint of GST v1.0 is a selected stable sector: a structure that is closed, coherent, fixed under the update operator, robust under small perturbations, and selected against degenerate alternatives. Such a sector supports an object-like external description without being a primitive object. A minimal finite toy model is computed in full. It exhibits monotone coherence increase, vanishing closure defect, convergence of the update sequence, three emergent idempotents, and explicit rejection of degenerate candidates. The accompanying verification artifact reproduces every numerical claim in Appendix B, including the compatibility matrix, update sequence, selection results, truncated-closure sizes, and exhaustive enumeration of all 512 configurations of the label square. Claim boundary GST v1.0 does not derive topology, open sets, continuity, geometry, metric structure, distance, dimension, spacetime, matter, interaction, gravity, cosmology, life, cognition, or any empirical physical realization. No later layer shown in the research roadmap is derived or validated here. The mathematical resources employed—including partial composition, associativity, semicategories, fixed-point methods, contraction mappings, idempotents, and the Karoubi envelope—are established mathematics and are not claimed as new. The proposed contribution is their architecture, ordering, and formal integration within a restricted process-first generative framework. Any assessment of novelty relative to the literature requires a separate comprehensive prior-art review. Record contents • GST_v1.0_Okino_Generative_Structural_Theory.pdf — Preprint, A4, 29 pages, including Figures 1–12. • gst_v1.0_appendixB_verification.py — Formal verification artifact using only the Python standard library. • expected_output.txt — Canonical 51-line output for byte-level comparison. • README.md — Contents, reproduction instructions, checksums, claim boundary, and citation information. • CITATION.cff — Machine-readable citation metadata. • LICENSE — CC BY 4.0 licence for the paper and Figures 1–12. • LICENSE-CODE — MIT licence for the verification script. The paper and Figures 1–12 are released under CC BY 4.0. The verification script is separately released under the MIT Licence.