Interactive Proof Dynamics Theory: A Continuous-State Framework for Proofs as Stable Dynamical Systems
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| Format: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866902325669396480 |
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| author | Zhang, Jincheng |
| author_facet | Zhang, Jincheng |
| contents | <p><span>This paper proposes a novel formal system: the theory of interactive proof dynamics (IPDT). In this theory, proofs are no longer static objects or discrete sequences, but are defined as continuous dynamical systems evolving within a "semantic constraint space." The validity of a proof is no longer determined by single-step derivation rules, but by stability conditions in an "interactive consistency field." We introduce a proof state space, a semantic potential function, a verifier-builder coupling operator, and define a new correctness criterion: a proof is a convergent trajectory on a doubly constrained manifold, rather than a checkable string. This framework unifies logical reasoning, verifiable computation, and interactive processes, and provides a novel mathematical foundation for the concept that "proof is a dynamically stable point."</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20046585 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Interactive Proof Dynamics Theory: A Continuous-State Framework for Proofs as Stable Dynamical Systems Zhang, Jincheng <p><span>This paper proposes a novel formal system: the theory of interactive proof dynamics (IPDT). In this theory, proofs are no longer static objects or discrete sequences, but are defined as continuous dynamical systems evolving within a "semantic constraint space." The validity of a proof is no longer determined by single-step derivation rules, but by stability conditions in an "interactive consistency field." We introduce a proof state space, a semantic potential function, a verifier-builder coupling operator, and define a new correctness criterion: a proof is a convergent trajectory on a doubly constrained manifold, rather than a checkable string. This framework unifies logical reasoning, verifiable computation, and interactive processes, and provides a novel mathematical foundation for the concept that "proof is a dynamically stable point."</span></p> |
| title | Interactive Proof Dynamics Theory: A Continuous-State Framework for Proofs as Stable Dynamical Systems |
| url | https://doi.org/10.5281/zenodo.20046585 |