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2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.19983043 |
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| _version_ | 1866902265885884416 |
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| author | Ellington, Micheal |
| author_facet | Ellington, Micheal |
| contents | <p>This paper formalizes Coh as a category whose morphisms are not arbitrary transitions, but certified admissible traces. A basic transition becomes a CohBit only when it carries explicit resource data and satisfies both an envelope condition and a commit inequality.</p> <p>The central object is a certified morphism b = (R, s, d, x, y), where R : x ⇝ y is an observable trace from state x to state y, s is transition spend, d is admitted defect, d ≥ δ(R), and V(y) + s ≤ V(x) + d.</p> <p>Under trace closure, identity, additive bookkeeping, and an oplax defect envelope law δ(R_g ∘ R_f) ≤ δ(R_f) + δ(R_g), these certified transitions form a category Coh_δ.</p> <p>This v2 refinement upgrades the earlier Coh Category formulation by internalizing spend, admitted defect, source, target, and envelope/resource witnesses directly into the morphism itself. The construction separates the base category of admissible change from later compression layers such as PhaseLoom, which is interpreted as a quotient or compression functor from raw admissible paths into certified summary representatives.</p> <p>The guiding principle is: change is not primitive; admissible change is primitive.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19983043 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Coh Category: Certified Admissible Change as a Category of Proof-Carrying Traces Ellington, Micheal <p>This paper formalizes Coh as a category whose morphisms are not arbitrary transitions, but certified admissible traces. A basic transition becomes a CohBit only when it carries explicit resource data and satisfies both an envelope condition and a commit inequality.</p> <p>The central object is a certified morphism b = (R, s, d, x, y), where R : x ⇝ y is an observable trace from state x to state y, s is transition spend, d is admitted defect, d ≥ δ(R), and V(y) + s ≤ V(x) + d.</p> <p>Under trace closure, identity, additive bookkeeping, and an oplax defect envelope law δ(R_g ∘ R_f) ≤ δ(R_f) + δ(R_g), these certified transitions form a category Coh_δ.</p> <p>This v2 refinement upgrades the earlier Coh Category formulation by internalizing spend, admitted defect, source, target, and envelope/resource witnesses directly into the morphism itself. The construction separates the base category of admissible change from later compression layers such as PhaseLoom, which is interpreted as a quotient or compression functor from raw admissible paths into certified summary representatives.</p> <p>The guiding principle is: change is not primitive; admissible change is primitive.</p> |
| title | Coh Category: Certified Admissible Change as a Category of Proof-Carrying Traces |
| url | https://doi.org/10.5281/zenodo.19983043 |