{"paper":{"title":"Algebraic Semantics of Governed Execution: Monoidal Categories, Effect Algebras, and Coterminous Boundaries","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Governance is defined so that it exactly coincides with what programs can express using four basic constructors.","cross_cats":["cs.LO","cs.PL"],"primary_cat":"cs.AI","authors_text":"Alan L. McCann","submitted_at":"2026-05-01T18:59:01Z","abstract_excerpt":"We present an algebraic semantics for governed execution in which governance is axiomatized, compositional, and coterminous with expressibility. The framework, mechanized in 32 Rocq modules (~12,000 lines, 454 theorems, 0 admitted), is built on interaction trees and parameterized coinduction. A three-axiom GovernanceAlgebra record (safety, transparency, properness) induces a symmetric monoidal category with verified pentagon, triangle, and hexagon coherence, where every tensor composition preserves governance. An algebraic effect system constrains the handler algebra so that only governance-pr"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The capstone result is the coterminous boundary: within our formal model, every program expressible via the four primitive morphism constructors is governed under interpretation, and every governed program is the image of such a program.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The three-axiom GovernanceAlgebra record (safety, transparency, properness) induces a symmetric monoidal category with verified coherence where every tensor composition preserves governance.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Governed execution is defined via a three-axiom GovernanceAlgebra that induces a symmetric monoidal category where expressible programs are exactly the governed ones, with all properties machine-checked in Rocq.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Governance is defined so that it exactly coincides with what programs can express using four basic constructors.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0274147c685b7f51d1f35a1532b4837d5d32dbfa4c8de9f283418eeef4a77b50"},"source":{"id":"2605.01032","kind":"arxiv","version":3},"verdict":{"id":"26af4df0-1332-4e99-b120-e3071e160674","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T19:19:21.711160Z","strongest_claim":"The capstone result is the coterminous boundary: within our formal model, every program expressible via the four primitive morphism constructors is governed under interpretation, and every governed program is the image of such a program.","one_line_summary":"Governed execution is defined via a three-axiom GovernanceAlgebra that induces a symmetric monoidal category where expressible programs are exactly the governed ones, with all properties machine-checked in Rocq.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The three-axiom GovernanceAlgebra record (safety, transparency, properness) induces a symmetric monoidal category with verified coherence where every tensor composition preserves governance.","pith_extraction_headline":"Governance is defined so that it exactly coincides with what programs can express using four basic constructors."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01032/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T18:39:33.750737Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:41:11.822503Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b90c2662598ea019658b906fafac34f819544644a4a6c539a3c68a9f9faa1c1c"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}