Cross-Domain Stability Isomorphism in the Paton System
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901059690037248 |
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| author | Paton, Andrew John |
| author_facet | Paton, Andrew John |
| contents | <p>Stability and collapse phenomena appear across many scientific and computational domains, including physics, computation, organisational systems, and biological processes. These behaviours are typically studied within domain-specific frameworks, leading to the impression that each field possesses distinct mechanisms of stability and failure.</p> <p>This paper introduces a formal structural result within the Paton System framework: the Cross-Domain Stability Isomorphism. Systems are modelled as recursive state transitions governed by domain-specific constraint sets and admissibility conditions. Continuation occurs only when recursive updates remain compatible with governing constraints.</p> <p>The theorem demonstrates that when recursive update structure and admissibility boundaries are preserved under a structure-preserving mapping between domains, continuation and collapse correspond exactly across those domains. Under these conditions, the systems are stability-isomorphic.</p> <p>This result provides a structural explanation for why stability boundaries recur across distinct scientific domains and establishes a formal basis for interpreting stability behaviour through admissibility conditions governing recursive systems.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18910788 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Cross-Domain Stability Isomorphism in the Paton System Paton, Andrew John Paton System System Stability Admissibility Recursive Systems Cross-Domain Isomorphism Constraint Compatibility Structural Stability <p>Stability and collapse phenomena appear across many scientific and computational domains, including physics, computation, organisational systems, and biological processes. These behaviours are typically studied within domain-specific frameworks, leading to the impression that each field possesses distinct mechanisms of stability and failure.</p> <p>This paper introduces a formal structural result within the Paton System framework: the Cross-Domain Stability Isomorphism. Systems are modelled as recursive state transitions governed by domain-specific constraint sets and admissibility conditions. Continuation occurs only when recursive updates remain compatible with governing constraints.</p> <p>The theorem demonstrates that when recursive update structure and admissibility boundaries are preserved under a structure-preserving mapping between domains, continuation and collapse correspond exactly across those domains. Under these conditions, the systems are stability-isomorphic.</p> <p>This result provides a structural explanation for why stability boundaries recur across distinct scientific domains and establishes a formal basis for interpreting stability behaviour through admissibility conditions governing recursive systems.</p> |
| title | Cross-Domain Stability Isomorphism in the Paton System |
| topic | Paton System System Stability Admissibility Recursive Systems Cross-Domain Isomorphism Constraint Compatibility Structural Stability |
| url | https://doi.org/10.5281/zenodo.18910788 |