{"paper":{"title":"Mechanized Foundations of Structural Governance: Machine-Checked Proofs for Governed Intelligence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Four atomic primitives suffice to express and govern any discrete intelligent system, as shown by machine-checked theorems.","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Alan L. McCann","submitted_at":"2026-04-30T01:03:15Z","abstract_excerpt":"We present five results in the theory of structural governance for cognitive workflow systems. Three are mechanized in Coq 8.19 using the Interaction Trees library with parameterized coinduction; two are proved on paper with explicit reductions. The Coinductive Safety Predicate (gov_safe) is a coinductive property that captures governance safety for infinite program behaviors, indexed by a boolean permission flag that is provably false for ungoverned I/O and true for governed interpretations (mechanized). The Governance Invariance Theorem establishes that governance is uniform across the meta-"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The Sufficiency Theorem proves that four atomic primitives (code, reason, memory, call) are expressively complete for any discrete intelligent system, formalized as compositional closure of a Kleisli category (mechanized).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the four primitives suffice for any discrete intelligent system and that property-based testing on 70,000 random directive sequences is sufficient to validate the BEAM runtime specification against all possible behaviors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Coq-mechanized proofs establish a coinductive governance safety predicate, invariance across recursion levels, sufficiency of four primitives for any discrete intelligent system, necessity of semantic judgment via Rice's theorem, and a verified BEAM interpreter spec with zero disagreements on 70k+随机","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Four atomic primitives suffice to express and govern any discrete intelligent system, as shown by machine-checked theorems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c94919bf5d19f8522f497fbf41b71b24664eadd83311ae9c43090c60ce68d22a"},"source":{"id":"2604.27289","kind":"arxiv","version":3},"verdict":{"id":"3ab36a6f-8dd7-40c8-be4c-9844d0573c6d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T09:50:14.543580Z","strongest_claim":"The Sufficiency Theorem proves that four atomic primitives (code, reason, memory, call) are expressively complete for any discrete intelligent system, formalized as compositional closure of a Kleisli category (mechanized).","one_line_summary":"Coq-mechanized proofs establish a coinductive governance safety predicate, invariance across recursion levels, sufficiency of four primitives for any discrete intelligent system, necessity of semantic judgment via Rice's theorem, and a verified BEAM interpreter spec with zero disagreements on 70k+随机","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the four primitives suffice for any discrete intelligent system and that property-based testing on 70,000 random directive sequences is sufficient to validate the BEAM runtime specification against all possible behaviors.","pith_extraction_headline":"Four atomic primitives suffice to express and govern any discrete intelligent system, as shown by machine-checked theorems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.27289/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T22:40:29.629531Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:24:40.184347Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6d5d0078ed0c11713ddcc5eaeef1371dda7d01a4fba2321219ad5303fb9e10ba"},"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"}