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PreprintCC BY 4.0Zenodo

The Universal Trajectory Architecture: Continuous Flows, Non-Archimedean Branching, Cauchy–Poisson Spectral Windows, and the Tripartite Index on the Adèle Class Space

  • August Tudor
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Abstract

We present the complete mathematical formulation of the Universal Trajectory Architecture (UTA), an operator-algebraic, spectral-geometric, and topological framework that embeds continuous geometric flows, non-Archimedean arithmetic branching, and non-equilibrium state transitions into a single \theta-twisted algebra \mathcal{A}(\theta) over the global Adèle Class Space: \mathbb{X}_{\mathbb{Q}} \equiv \mathbb{A}_{\mathbb{Q}}/\mathbb{Q}^\times

Physical trajectories are demonstrated to be neither purely smooth classical continuum curves nor disconnected stochastic jumps, but complementary spectral projections of the global infinitesimal scaling generator: \mathbf{H} \equiv x \frac{d}{dx} + \frac{1}{2} = -i \frac{d}{du}, \qquad u \equiv \ln|x|

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Cite

BibTeXRIS
BibTeX
@misc{tudor2026universal,
  title = {{The Universal Trajectory Architecture: Continuous Flows, Non-Archimedean Branching, Cauchy–Poisson Spectral Windows, and the Tripartite Index on the Adèle Class Space}},
  author = {August Tudor},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23547273},
  url = {https://zenodo.org/records/23547273},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Universal Trajectory Architecture: Continuous Flows, Non-Archimedean Branching, Cauchy–Poisson Spectral Windows, and the Tripartite Index on the Adèle Class Space
AU  - August Tudor
PY  - 2026
DA  - 2026/10/21
PB  - Zenodo
DO  - 10.5281/zenodo.23547273
UR  - https://zenodo.org/records/23547273
AB  - We present the complete mathematical formulation of the Universal Trajectory Architecture (UTA), an operator-algebraic, spectral-geometric, and topological framework that embeds continuous geometric flows, non-Archimedean arithmetic branching, and non-equilibrium state transitions into a single \theta-twisted algebra \mathcal{A}(\theta) over the global Adèle Class Space: \mathbb{X}_{\mathbb{Q}} \equiv \mathbb{A}_{\mathbb{Q}}/\mathbb{Q}^\times  Physical trajectories are demonstrated to be neither purely smooth classical continuum curves nor disconnected stochastic jumps, but complementary spectral projections of the global infinitesimal scaling generator: \mathbf{H} \equiv x \frac{d}{dx} + \frac{1}{2} = -i \frac{d}{du}, \qquad u \equiv \ln|x|
ER  -