{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DWXLOWE53EL5ETLNLTECZPYCJ7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"81bf62c0c95866a69fc4213ae26fcbc4f15c3cc0646becbe1a08781b79d329e8","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-19T23:12:00Z","title_canon_sha256":"45e9c3a5c2b132761fc3f06eaf779678570b8a7619db39c8f0a61f60ead7f587"},"schema_version":"1.0","source":{"id":"1408.4498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4498","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4498v1","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4498","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"pith_short_12","alias_value":"DWXLOWE53EL5","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DWXLOWE53EL5ETLN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DWXLOWE5","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:c38f2fe116c6b1d388be7766b3cf52121133a1db710a67161b46a49efe7ebc66","target":"graph","created_at":"2026-05-18T02:44:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, {\\em if-then-else} and {\\em while-do} defined in terms of a Boolean algebra of conditions. It has previously been shown that there is no finite axiomatisation of algebras of partial functions under these operations alone, and this holds even if one restricts attention to transformations (representing halting programs) rather than partial functions, and omits {\\em while-do} from the s","authors_text":"Marcel Jackson, Tim Stokes","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-19T23:12:00Z","title":"Monoids with tests and the algebra of possibly non-halting programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4498","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8c450a2f466b012378329622216e2e1520518117ff12da4e282b55b8878e6d29","target":"record","created_at":"2026-05-18T02:44:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"81bf62c0c95866a69fc4213ae26fcbc4f15c3cc0646becbe1a08781b79d329e8","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-19T23:12:00Z","title_canon_sha256":"45e9c3a5c2b132761fc3f06eaf779678570b8a7619db39c8f0a61f60ead7f587"},"schema_version":"1.0","source":{"id":"1408.4498","kind":"arxiv","version":1}},"canonical_sha256":"1daeb7589dd917d24d6d5cc82cbf024fd0f56dd9878a563080b2df95bf0297a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1daeb7589dd917d24d6d5cc82cbf024fd0f56dd9878a563080b2df95bf0297a3","first_computed_at":"2026-05-18T02:44:55.113110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:55.113110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TomrJI1c0cI6zUl0c6khuR8ASguI6RbAJu5WyryVYsfaGuuwuoHHcJykwD7iPuW6NpegbVwOhvx3NFELPpQlBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:55.113610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c450a2f466b012378329622216e2e1520518117ff12da4e282b55b8878e6d29","sha256:c38f2fe116c6b1d388be7766b3cf52121133a1db710a67161b46a49efe7ebc66"],"state_sha256":"1d55e4365b393bbdde77308b0e334cc8df473ee860aee76f4f8c9e3ec5f710ce"}