{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:S5UKCOIIIUWFTCYKDE7X2ZNJRB","short_pith_number":"pith:S5UKCOII","canonical_record":{"source":{"id":"1311.7523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-11-29T11:23:06Z","cross_cats_sorted":["cs.CC","math.GR"],"title_canon_sha256":"3cee488c25339d0f7118795b6833957ee2e8377ebac5b0b9be39bd478798f1ad","abstract_canon_sha256":"2f82daa53c086fa78a131f423abbff85dd768d378a1da7a242e58c7cf04d5f90"},"schema_version":"1.0"},"canonical_sha256":"9768a13908452c598b0a193f7d65a9887175c7a3b7231480cd59d2e666e3edb5","source":{"kind":"arxiv","id":"1311.7523","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7523","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7523v1","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7523","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"S5UKCOIIIUWF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S5UKCOIIIUWFTCYK","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S5UKCOII","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:S5UKCOIIIUWFTCYKDE7X2ZNJRB","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-11-29T11:23:06Z","cross_cats_sorted":["cs.CC","math.GR"],"title_canon_sha256":"3cee488c25339d0f7118795b6833957ee2e8377ebac5b0b9be39bd478798f1ad","abstract_canon_sha256":"2f82daa53c086fa78a131f423abbff85dd768d378a1da7a242e58c7cf04d5f90"},"schema_version":"1.0"},"canonical_sha256":"9768a13908452c598b0a193f7d65a9887175c7a3b7231480cd59d2e666e3edb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:55.968875Z","signature_b64":"IImZGHRX1ftM2YTrNHXk5l4vK/I5AQcQgNdXYb3Leddu8wJ0zeunJJiwMY5cRk4lP5RhNkop03JnKZHywgFnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9768a13908452c598b0a193f7d65a9887175c7a3b7231480cd59d2e666e3edb5","last_reissued_at":"2026-05-18T03:05:55.968262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:55.968262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7523","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TvP2ugY5ppXR4klIJ/BeAiOpJ43a0imToAJplgh8Aj1z5Bgt+8kb6w4U2e0mH0qtZL95hV8nKKIQ5fyBzrWqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:10:07.316866Z"},"content_sha256":"e310b2059c3c3a7332ce038b3312a765263b7d1e5825c9d8de6a5edee562dd75","schema_version":"1.0","event_id":"sha256:e310b2059c3c3a7332ce038b3312a765263b7d1e5825c9d8de6a5edee562dd75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:S5UKCOIIIUWFTCYKDE7X2ZNJRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The word problem for free adequate semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.GR"],"primary_cat":"math.RA","authors_text":"Alexandr Kazda, Mark Kambites","submitted_at":"2013-11-29T11:23:06Z","abstract_excerpt":"We study the complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids. We present polynomial time (quadratic in the RAM model of computation) algorithms to solve the word problem and compute normal forms in each of these, and hence also to test whether any given identity holds in the classes of left, right and/or two-sided adequate semigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7523","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8DWL6LajZc/K/pHYXBi7VTybZzsHr6QVaKW/xmTrwHANnAvBCecGrs8W0rLfHBAukODrC2Xo9iWSMMvT51bAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:10:07.317211Z"},"content_sha256":"674bcf0aa1496e493974daa01e5b45f957f6739843ec368e1ed244753dd1c582","schema_version":"1.0","event_id":"sha256:674bcf0aa1496e493974daa01e5b45f957f6739843ec368e1ed244753dd1c582"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5UKCOIIIUWFTCYKDE7X2ZNJRB/bundle.json","state_url":"https://pith.science/pith/S5UKCOIIIUWFTCYKDE7X2ZNJRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5UKCOIIIUWFTCYKDE7X2ZNJRB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T04:10:07Z","links":{"resolver":"https://pith.science/pith/S5UKCOIIIUWFTCYKDE7X2ZNJRB","bundle":"https://pith.science/pith/S5UKCOIIIUWFTCYKDE7X2ZNJRB/bundle.json","state":"https://pith.science/pith/S5UKCOIIIUWFTCYKDE7X2ZNJRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5UKCOIIIUWFTCYKDE7X2ZNJRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S5UKCOIIIUWFTCYKDE7X2ZNJRB","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":"2f82daa53c086fa78a131f423abbff85dd768d378a1da7a242e58c7cf04d5f90","cross_cats_sorted":["cs.CC","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-11-29T11:23:06Z","title_canon_sha256":"3cee488c25339d0f7118795b6833957ee2e8377ebac5b0b9be39bd478798f1ad"},"schema_version":"1.0","source":{"id":"1311.7523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7523","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7523v1","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7523","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"S5UKCOIIIUWF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S5UKCOIIIUWFTCYK","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S5UKCOII","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:674bcf0aa1496e493974daa01e5b45f957f6739843ec368e1ed244753dd1c582","target":"graph","created_at":"2026-05-18T03:05:55Z","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 complexity of computation in finitely generated free left, right and two-sided adequate semigroups and monoids. We present polynomial time (quadratic in the RAM model of computation) algorithms to solve the word problem and compute normal forms in each of these, and hence also to test whether any given identity holds in the classes of left, right and/or two-sided adequate semigroups.","authors_text":"Alexandr Kazda, Mark Kambites","cross_cats":["cs.CC","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-11-29T11:23:06Z","title":"The word problem for free adequate semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7523","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:e310b2059c3c3a7332ce038b3312a765263b7d1e5825c9d8de6a5edee562dd75","target":"record","created_at":"2026-05-18T03:05:55Z","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":"2f82daa53c086fa78a131f423abbff85dd768d378a1da7a242e58c7cf04d5f90","cross_cats_sorted":["cs.CC","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-11-29T11:23:06Z","title_canon_sha256":"3cee488c25339d0f7118795b6833957ee2e8377ebac5b0b9be39bd478798f1ad"},"schema_version":"1.0","source":{"id":"1311.7523","kind":"arxiv","version":1}},"canonical_sha256":"9768a13908452c598b0a193f7d65a9887175c7a3b7231480cd59d2e666e3edb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9768a13908452c598b0a193f7d65a9887175c7a3b7231480cd59d2e666e3edb5","first_computed_at":"2026-05-18T03:05:55.968262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:55.968262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IImZGHRX1ftM2YTrNHXk5l4vK/I5AQcQgNdXYb3Leddu8wJ0zeunJJiwMY5cRk4lP5RhNkop03JnKZHywgFnBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:55.968875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e310b2059c3c3a7332ce038b3312a765263b7d1e5825c9d8de6a5edee562dd75","sha256:674bcf0aa1496e493974daa01e5b45f957f6739843ec368e1ed244753dd1c582"],"state_sha256":"c8ce17f1a894910a0c410bcf3bf50fa47b311d81e7bb28ad2b90c566f2e16099"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/sUEHfCxix6HTOkx55gi4rllqRbpup0viei0rC6L+R0HAiRfvK5JiKr43oiNWGfcb4279JDZJ88ia/vgnoNAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:10:07.319337Z","bundle_sha256":"424c8a53186f388e65213ec2b49ee53b6134866f90a1bf9c5d9f61c978fb9de4"}}