Triadic Closure and Oriented Triple Systems: A Minimal Generative Interpretation of Octonionic Multiplication
| Τίτλος: | Triadic Closure and Oriented Triple Systems: A Minimal Generative Interpretation of Octonionic Multiplication |
|---|---|
| Συγγραφείς: | Kornhaus, Devin |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Zenodo, 2026. |
| Έτος έκδοσης: | 2026 |
| Θεματικοί όροι: | Finite Geometry, Octonions, Algebraic Structures, Higher Algebra, Non-commutative Algebra, Fano Plane, Algebraic Systems, Symmetry Structures, Triple Systems, Combinatorial Design, Algebraic Topology, Recursive Structures, FOS: Mathematics, Alternativity, Division Algebras, Non-associative Algebra, Algebraic Geometry, Steiner Triple System, Moufang Identities, Mathematical Physics, Abstract Algebra |
| Περιγραφή: | We introduce a minimal triadic closure rule on a three-element system and show that its nontrivial extension yields an oriented triple system isomorphic to the Fano plane. This structure reproduces the multiplication of imaginary octonion units. Within this framework, octonionic non-associativity is interpreted as dependence on the order of pairwise closure operations. We further show that the resulting system is minimal for supporting non-associative behavior and inherits key algebraic identities, including alternativity and the Moufang identities. This provides a compact generative formulation of octonionic multiplication.*This paper has been submitted for Peer Review |
| DOI: | 10.5281/zenodo.19635023 |
| Rights: | CC BY |
| Αριθμός Καταχώρησης: | edsair.doi...........457574d2705e238d3e4a984cf3cfab74 |
| Βάση Δεδομένων: | OpenAIRE |
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