Observability and Stress Monitoring in a Clifford–Thomas Runtime: The χ Trigger Framework
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866902068666564608 |
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| author | García Abad, Rubén |
| author_facet | García Abad, Rubén |
| contents | <p>We develop a complete observability framework for the CT (Clifford–Thomas) runtime operating in Cl(3,0). Five independent measurement channels—commutator defect, Fiedler algebraic connectivity, rotational tension, spectral coherence, and spectral entropy—provide a redundant observability panel without full state reconstruction. A local stress functional χ aggregates these channels into a scalar validity monitor: when χ > χ* = 0.5, the runtime transitions from the fast physical clock t to the structural relaxation clock τ. Empirically, both the Thomas 3D attractor and the Spinor8D attractor produce χ ≈ 0.51, consistent with near-threshold operation at the boundary of continuum validity. We prove 100% contractivity of three runtime maps across 5,000 random pairs each, validate 17/17 unit tests for the new observable functions, and show that the free energy F converges to F ≈ −167 under standard driving. We also introduce a structural conservation law characterising amplitude–structure exchange under bounded resolution.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19202918 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Observability and Stress Monitoring in a Clifford–Thomas Runtime: The χ Trigger Framework García Abad, Rubén Clifford algebra observability dual-clock runtime chi trigger contractivity Hutchinson attractor spectral entropy JAX <p>We develop a complete observability framework for the CT (Clifford–Thomas) runtime operating in Cl(3,0). Five independent measurement channels—commutator defect, Fiedler algebraic connectivity, rotational tension, spectral coherence, and spectral entropy—provide a redundant observability panel without full state reconstruction. A local stress functional χ aggregates these channels into a scalar validity monitor: when χ > χ* = 0.5, the runtime transitions from the fast physical clock t to the structural relaxation clock τ. Empirically, both the Thomas 3D attractor and the Spinor8D attractor produce χ ≈ 0.51, consistent with near-threshold operation at the boundary of continuum validity. We prove 100% contractivity of three runtime maps across 5,000 random pairs each, validate 17/17 unit tests for the new observable functions, and show that the free energy F converges to F ≈ −167 under standard driving. We also introduce a structural conservation law characterising amplitude–structure exchange under bounded resolution.</p> |
| title | Observability and Stress Monitoring in a Clifford–Thomas Runtime: The χ Trigger Framework |
| topic | Clifford algebra observability dual-clock runtime chi trigger contractivity Hutchinson attractor spectral entropy JAX |
| url | https://doi.org/10.5281/zenodo.19202918 |