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2026
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| Online Access: | https://doi.org/10.5281/zenodo.18393190 |
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| _version_ | 1866901493661040640 |
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| author | Kelly Rhys |
| author_facet | Kelly Rhys |
| contents | <p>This note extends the structural diagnostics introduced in <em>The Rhys Canon</em> by formalizing the conditions under which a dynamical process may be lawfully incomplete. Central to this is the notion of <strong>Ω-completion</strong>—a boundary framework for evaluating whether a process that resists continuation does so within admissible structural constraints, rather than due to model insufficiency or unbounded divergence.</p> <p>The text defines admissibility criteria for process refusal, introducing a refined ontology where certain terminations or non-resumptions are not anomalies but structurally encoded limits. The work also examines the morphism space between potential continuations and identifies lawful refusal as a nontrivial selection process orthogonal to classical determinacy or randomness.</p> <p>This contribution informs mathematical logic, process ontology, systems theory, and foundational physics—particularly in contexts where scale divergence, renormalization failure, or symbolic undecidability prohibit canonical completion. It offers a new lexicon for diagnosing where systems may cease to evolve coherently and yet do so in structural fidelity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18393190 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Tone Science: Admissible Continuation, Ω-Completion, and the Lawful Refusal of Processes Kelly Rhys <p>This note extends the structural diagnostics introduced in <em>The Rhys Canon</em> by formalizing the conditions under which a dynamical process may be lawfully incomplete. Central to this is the notion of <strong>Ω-completion</strong>—a boundary framework for evaluating whether a process that resists continuation does so within admissible structural constraints, rather than due to model insufficiency or unbounded divergence.</p> <p>The text defines admissibility criteria for process refusal, introducing a refined ontology where certain terminations or non-resumptions are not anomalies but structurally encoded limits. The work also examines the morphism space between potential continuations and identifies lawful refusal as a nontrivial selection process orthogonal to classical determinacy or randomness.</p> <p>This contribution informs mathematical logic, process ontology, systems theory, and foundational physics—particularly in contexts where scale divergence, renormalization failure, or symbolic undecidability prohibit canonical completion. It offers a new lexicon for diagnosing where systems may cease to evolve coherently and yet do so in structural fidelity.</p> |
| title | Tone Science: Admissible Continuation, Ω-Completion, and the Lawful Refusal of Processes |
| url | https://doi.org/10.5281/zenodo.18393190 |