Mathematical Foundations of an Emergent Constant: An Axiom-Theorem System for Constraint Network Dynamics
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| Format: | Recurso digital |
| Language: | English |
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2026
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| _version_ | 1866901888035717120 |
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| author | Yu, Menggang |
| author_facet | Yu, Menggang |
| contents | <p>We construct a deterministic discrete dynamical system—the Constraint Network<br>Model—defined by three axioms: energy units move at constant speed, upon<br>encounter they undergo symmetric collision, and in asymmetric encounters a<br>residual unit may merge if directional alignment occurs. The system is fully<br>formalizable in ZF set theory. We prove eight theorems: the evolution is<br>well-posed and total energy is conserved; merging is irreversible and the<br>maximum aggregate number is non-decreasing; the system must converge to a<br>steady state in finite time; the aggregate number of a saturated sealed node<br>is bounded by a sphere-covering problem; the aggregate number of a sealed<br>node must be even, and this emergent constant is uniquely determined by the<br>system parameters; an odd neighbor inevitably appears adjacent to a sealed<br>node, with conditional stability depending on the existence of a chain; the<br>sealed node is a global attractor; multiple sealed nodes can coexist, each<br>locked at the same emergent constant, connected by chains into a stable<br>network. The specific numerical value of the emergent constant is not given<br>in this paper. Its determination is deferred to subsequent work.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20349678 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Mathematical Foundations of an Emergent Constant: An Axiom-Theorem System for Constraint Network Dynamics Yu, Menggang Constraint Network Model, emergent constant, discrete dynamical system, sphere covering, parity constraint, global attractor, mathematical foundations <p>We construct a deterministic discrete dynamical system—the Constraint Network<br>Model—defined by three axioms: energy units move at constant speed, upon<br>encounter they undergo symmetric collision, and in asymmetric encounters a<br>residual unit may merge if directional alignment occurs. The system is fully<br>formalizable in ZF set theory. We prove eight theorems: the evolution is<br>well-posed and total energy is conserved; merging is irreversible and the<br>maximum aggregate number is non-decreasing; the system must converge to a<br>steady state in finite time; the aggregate number of a saturated sealed node<br>is bounded by a sphere-covering problem; the aggregate number of a sealed<br>node must be even, and this emergent constant is uniquely determined by the<br>system parameters; an odd neighbor inevitably appears adjacent to a sealed<br>node, with conditional stability depending on the existence of a chain; the<br>sealed node is a global attractor; multiple sealed nodes can coexist, each<br>locked at the same emergent constant, connected by chains into a stable<br>network. The specific numerical value of the emergent constant is not given<br>in this paper. Its determination is deferred to subsequent work.</p> |
| title | Mathematical Foundations of an Emergent Constant: An Axiom-Theorem System for Constraint Network Dynamics |
| topic | Constraint Network Model, emergent constant, discrete dynamical system, sphere covering, parity constraint, global attractor, mathematical foundations |
| url | https://doi.org/10.5281/zenodo.20349678 |