SGOED Exploratory Notes: STF Connection & K-Analogue Program

Abstract

TOY-LEVEL EXPLORATORY NOTES - NOT PEER-REVIEWED PHYSICS. This record groups five working notes produced during the SGOED program, covering the conceptual connection between SGOED and the Structural Time Framework (STF), the K-analogue ordering mechanism, the time-vs-order-of-change distinction, and a bounded numerical test of emergent spacetime from matrices. Included File: 1_SGOED_exploratory_notes.pdf: A single combined document with a warning abstract, containing all five notes as appendices (A-E). Individual source files are kept under appendix/ for provenance. Contents: Appendix A - SGOED to STF Connection Note: Records the design intent that SGOED targets STF's Level A, separating connections with genuine structural substance from terminological similarity. Observation note, not derived. Appendix B - K-Analogue Design (antisymmetric-driven ordering): Designs and tests an orientation function driven by the antisymmetric part of the G-matrix. First-pass prototype exists: creates per-collision ordering but does not amplify. Design + completed prototype. Appendix C - K-Analogue Program: Summary: Overview of the K-analogue research program results. Working summary. Appendix D - Time vs Order of Change: Conceptual Separation: Separates the notion of time from the atemporal order of change. Conceptual note. Appendix E - Emergent-Spacetime Test (exploration, not a claim): Bounded numerical exploration of whether a matrix formalism can support emergent spacetime. Result: not confirmed within the current formalism. Negative result recorded so it is not re-claimed without a real construction. Related Records: Record A (main SGOED manuscript): 10.5281/zenodo.21786260 - this record references A via the "references" relation; it is not part of the main manuscript. Record B (analysis scripts): 10.5281/zenodo.21786190 - the K-analogue scripts referenced in Appendices B and C (sgoed_k_analogue_prototype.py, sgoed_k_analogue_relative.py, sgoed_k_analogue_non_iid.py, sgoed_k_analogue_extref.py, sgoed_k_analogue_extended.py) are published in record B. Structural Time Framework (STF): 10.5281/zenodo.20752981 - the STF preprint these notes connect to. Please note: these are toy-level exploratory notes, not peer-reviewed physics, and they do not modify the tested Phase 1-2 content. They must not be cited as evidence for any empirically verified physics.