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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.18295 |
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| _version_ | 1866909919555354624 |
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| author | Abishev, Medeu Berkimbayev, Daulet |
| author_facet | Abishev, Medeu Berkimbayev, Daulet |
| contents | Postulating a minimal discrete quantum of action $S=\hbar$ and a simple rule for the growth of an oriented graph, we construct a strict hierarchy of temporal layers $C N$ with discrete periods $τ_N=N\hbar/E$. Each layer is specified by its configuration space, symplectic structure, update rule, and emergent symmetry. At $C1$ the state is represented by a single oriented edge with $U(1)$ phase $e^{i E t/\hbar}$. The transition $C1 \to C2$ splits the edge into two independent flows, which yields canonical pairs $(x_a,p_a)$, local $U(1)$ invariance, and an effective $(2{+}1)$ metric with signature $(+--)$. The closure $C2 \to C3$ produces $SU(3)$ connections and an Einstein-Yang-Mills type action. We show that these structures follow from discrete-action principles, and that stochastic graph growth naturally provides mechanisms for decoherence and spontaneous symmetry breaking. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Discrete Action, Graph Evolution, and the Hierarchy of Symmetries: A Rigorous Construction of Temporal Layers $C1 \to C2 \to C3 \to C4$ Abishev, Medeu Berkimbayev, Daulet General Physics High Energy Physics - Theory Quantum Physics Postulating a minimal discrete quantum of action $S=\hbar$ and a simple rule for the growth of an oriented graph, we construct a strict hierarchy of temporal layers $C N$ with discrete periods $τ_N=N\hbar/E$. Each layer is specified by its configuration space, symplectic structure, update rule, and emergent symmetry. At $C1$ the state is represented by a single oriented edge with $U(1)$ phase $e^{i E t/\hbar}$. The transition $C1 \to C2$ splits the edge into two independent flows, which yields canonical pairs $(x_a,p_a)$, local $U(1)$ invariance, and an effective $(2{+}1)$ metric with signature $(+--)$. The closure $C2 \to C3$ produces $SU(3)$ connections and an Einstein-Yang-Mills type action. We show that these structures follow from discrete-action principles, and that stochastic graph growth naturally provides mechanisms for decoherence and spontaneous symmetry breaking. |
| title | Discrete Action, Graph Evolution, and the Hierarchy of Symmetries: A Rigorous Construction of Temporal Layers $C1 \to C2 \to C3 \to C4$ |
| topic | General Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2511.18295 |