CDT: The Critical Distinction Trichotomy
Fuente:
Zenodo
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Recurso digital |
| Lingua: | inglese |
| Pubblicazione: |
Zenodo
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866902211178528768 |
|---|---|
| author | Allen, Kearon |
| author_facet | Allen, Kearon |
| contents | <p>This paper proves the <strong>Critical Distinction Trichotomy (CDT)</strong>, a structural classification theorem for anchor-free unary distinctions on finite relational structures. Two admissibility models are treated independently and in full detail: <strong>parameter free first order definability at bounded quantifier rank</strong> and <strong>automorphism-invariant distinctions</strong> under group actions. In each model, any nontrivial admissible distinction is shown to fall into exactly one of three regimes: <strong>melting</strong>, where symmetry or indistinguishability forces triviality; <strong>global support</strong>, where the absence of rare intrinsic classes enforces a quadratic lower bound on witness mass; or <strong>internal anchor defect</strong>, where a small parameter-free definable exceptional class permits subquadratic distinction. All derivations are explicit and non-compressed. The results are pre-identity in nature and characterize the existence and cost of invariant distinction without assuming identity persistence, temporal order, or physical interpretation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18283538 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | CDT: The Critical Distinction Trichotomy Allen, Kearon Critical Distinction Trichotomy Anchor Free Finite Graph Automorphism Invariance Witness Mass Symmetry Breaking Finite Model Theory First Order Logic Bonded Quantifier Rank Pre Identity Law <p>This paper proves the <strong>Critical Distinction Trichotomy (CDT)</strong>, a structural classification theorem for anchor-free unary distinctions on finite relational structures. Two admissibility models are treated independently and in full detail: <strong>parameter free first order definability at bounded quantifier rank</strong> and <strong>automorphism-invariant distinctions</strong> under group actions. In each model, any nontrivial admissible distinction is shown to fall into exactly one of three regimes: <strong>melting</strong>, where symmetry or indistinguishability forces triviality; <strong>global support</strong>, where the absence of rare intrinsic classes enforces a quadratic lower bound on witness mass; or <strong>internal anchor defect</strong>, where a small parameter-free definable exceptional class permits subquadratic distinction. All derivations are explicit and non-compressed. The results are pre-identity in nature and characterize the existence and cost of invariant distinction without assuming identity persistence, temporal order, or physical interpretation.</p> |
| title | CDT: The Critical Distinction Trichotomy |
| topic | Critical Distinction Trichotomy Anchor Free Finite Graph Automorphism Invariance Witness Mass Symmetry Breaking Finite Model Theory First Order Logic Bonded Quantifier Rank Pre Identity Law |
| url | https://doi.org/10.5281/zenodo.18283538 |