A Triadic Ontology with SU(3) Invariants A minimal invariant kernel for qutrit-based dynamics
Trent Slade
This paper introduces a triadic ontology grounded in the fundamental representation of SU(3), treating the qutrit as an ontic primitive rather than a semantic metaphor. States are represented as density operators on a three-dimensional Hilbert space, with admissible dynamics given by SU(3) actions. The ontology is triadic at the level of states, operators, and constraints, while preserving SU(3) invariants including unitarity, conjugacy-class structure, and the quadratic and cubic Casimir operators. A mandatory triadic mediation layer is imposed via a discrete ℤ₃ rotation operator, enforcing closure without collapsing the third state. Constraints are formalized as optimization problems over SU(3) orbits, yielding stabilizing states without violating group structure. The framework reduces to a minimal 3–8–2 schema: three basis stances, eight interaction generators, and two conserved classifiers. The paper concludes with an executable research program outlining canonical Hamiltonian families, orbit atlases, invariant-tracking diagnostics, declared non-unitary boundary layers, and extensions to networked systems. The result is a small, invariant, and falsifiable ontic kernel suitable for computational modeling, physical interpretation, and multimodal diagnostics.
•Dec 26, 2025•0 citations