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This study explores whether a Clifford algebra-based runtime can express different computational regimes and if topological observables can quantify those differences.

March 24, 2026Open Access

Regimes, Soliton Structure, and Inter-Grade Modulation in a Clifford–Thomas Runtime

Key Points

This study explores whether a Clifford algebra-based runtime can express different computational regimes and if topological observables can quantify those differences.
Utilized an 8-component multivector field driven by two chaotic attractors of varying complexity.
Examined the output of Thomas 3D and SpinorAttractor 8D families under structured dynamics.
Measured vortex-type defects as a primary observable to differentiate computational regimes.
The 8D attractor showed a significant vortex-persistence gap of Δf_vortex = 0.2917 compared to the 3D baseline.
Results were consistent across two independent random seeds.
Differences in field configurations were reliably measurable by the fraction of steps containing vortex defects.

Abstract

We ask whether a field runtime based on Clifford algebra Cl (3, 0) can express structurally distinct computational regimes, and whether topological observables can reliably measure that distinction. We drive an 8-component multivector field with two chaotic attractor families of different complexity (Thomas 3D and SpinorAttractor 8D) and show that under structured dynamics the two families produce measurably different field configurations. The discriminating observable is the fraction of time steps containing at least one vortex-type topological defect (|Q|≥1): the 8D attractor yields a vortex-persistence gap Δfᵥortex = 0. 2917 over the 3D baseline, stable across two independent seeds. Builds on P01 (DOI: 10. 5281/zenodo. 18995428). All results reproducible from ods-unified-v2 (390 tests passing).

Regimes, Soliton Structure, and Inter-Grade Modulation in a Clifford–Thomas Runtime

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