{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NEKBM4NOQ4QGKALA2EFGCTRCWF","short_pith_number":"pith:NEKBM4NO","canonical_record":{"source":{"id":"1501.04331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-18T18:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"52fec63691f286fdbe918aa2246a4af85235ec82d67cb34d18590d8b943e577c","abstract_canon_sha256":"f72fce66cad40030a45057479165a9985cff3131e19af88a67d88e81a28009f5"},"schema_version":"1.0"},"canonical_sha256":"69141671ae8720650160d10a614e22b15bd69675b20b9e59bffed72b981fa7cd","source":{"kind":"arxiv","id":"1501.04331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04331","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04331v1","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04331","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"pith_short_12","alias_value":"NEKBM4NOQ4QG","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NEKBM4NOQ4QGKALA","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NEKBM4NO","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NEKBM4NOQ4QGKALA2EFGCTRCWF","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-18T18:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"52fec63691f286fdbe918aa2246a4af85235ec82d67cb34d18590d8b943e577c","abstract_canon_sha256":"f72fce66cad40030a45057479165a9985cff3131e19af88a67d88e81a28009f5"},"schema_version":"1.0"},"canonical_sha256":"69141671ae8720650160d10a614e22b15bd69675b20b9e59bffed72b981fa7cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:09.330522Z","signature_b64":"d5x49Yj7oxp+EVcYrvXSSGwrim0gxgzdfGnFBasOsg3jFur7vGNBkCT+swwMscaWADAfkUx43bF4MyKy4p1WBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69141671ae8720650160d10a614e22b15bd69675b20b9e59bffed72b981fa7cd","last_reissued_at":"2026-05-18T02:29:09.329908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:09.329908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04331","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":"2026-05-18T02:29:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MI1JBLaJcSVHJIIMNUvPSoKyn8peRwbyskBkENgUFcopbF8+6rclcmocMTFJPT2YgfqprtCE9CXwhyx1lmRSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:16:08.834287Z"},"content_sha256":"05c0476a3e46f755d509731fe7aadb7a7f408ff74c3096184cbdb4a2b507676d","schema_version":"1.0","event_id":"sha256:05c0476a3e46f755d509731fe7aadb7a7f408ff74c3096184cbdb4a2b507676d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NEKBM4NOQ4QGKALA2EFGCTRCWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commutative, idempotent groupoids and the constraint satisfaction problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Clifford Bergman, David Failing","submitted_at":"2015-01-18T18:13:52Z","abstract_excerpt":"A restatement of the Algebraic Dichotomy Conjecture, due to Maroti and McKenzie, postulates that if a finite algebra A possesses a weak near-unanimity term, then the corresponding constraint satisfaction problem is tractable. A binary operation is weak near-unanimity if and only if it is both commutative and idempotent. Thus if the dichotomy conjecture is true, any finite commutative, idempotent groupoid (CI groupoid) will be tractable. It is known that every semilattice (i.e., an associative CI groupoid) is tractable. A groupoid identity is of Bol-Moufang type if the same three variables appe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04331","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":"2026-05-18T02:29:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUvZOp9XYSd3W2TH+D5/jcg2o8MFKqca5913BPudAKlyaDHaxHChWL6PcrdDnOxFU+EXDht33uD/yEBCyRypAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:16:08.834960Z"},"content_sha256":"4d40f87b5f6fca2403b60aab84751ab9e42142e954a1a3ac131c68f5e0f88c95","schema_version":"1.0","event_id":"sha256:4d40f87b5f6fca2403b60aab84751ab9e42142e954a1a3ac131c68f5e0f88c95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NEKBM4NOQ4QGKALA2EFGCTRCWF/bundle.json","state_url":"https://pith.science/pith/NEKBM4NOQ4QGKALA2EFGCTRCWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NEKBM4NOQ4QGKALA2EFGCTRCWF/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":"2026-06-09T09:16:08Z","links":{"resolver":"https://pith.science/pith/NEKBM4NOQ4QGKALA2EFGCTRCWF","bundle":"https://pith.science/pith/NEKBM4NOQ4QGKALA2EFGCTRCWF/bundle.json","state":"https://pith.science/pith/NEKBM4NOQ4QGKALA2EFGCTRCWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NEKBM4NOQ4QGKALA2EFGCTRCWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NEKBM4NOQ4QGKALA2EFGCTRCWF","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":"f72fce66cad40030a45057479165a9985cff3131e19af88a67d88e81a28009f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-18T18:13:52Z","title_canon_sha256":"52fec63691f286fdbe918aa2246a4af85235ec82d67cb34d18590d8b943e577c"},"schema_version":"1.0","source":{"id":"1501.04331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04331","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04331v1","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04331","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"pith_short_12","alias_value":"NEKBM4NOQ4QG","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NEKBM4NOQ4QGKALA","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NEKBM4NO","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:4d40f87b5f6fca2403b60aab84751ab9e42142e954a1a3ac131c68f5e0f88c95","target":"graph","created_at":"2026-05-18T02:29:09Z","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":"A restatement of the Algebraic Dichotomy Conjecture, due to Maroti and McKenzie, postulates that if a finite algebra A possesses a weak near-unanimity term, then the corresponding constraint satisfaction problem is tractable. A binary operation is weak near-unanimity if and only if it is both commutative and idempotent. Thus if the dichotomy conjecture is true, any finite commutative, idempotent groupoid (CI groupoid) will be tractable. It is known that every semilattice (i.e., an associative CI groupoid) is tractable. A groupoid identity is of Bol-Moufang type if the same three variables appe","authors_text":"Clifford Bergman, David Failing","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-18T18:13:52Z","title":"Commutative, idempotent groupoids and the constraint satisfaction problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04331","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":"sha256:05c0476a3e46f755d509731fe7aadb7a7f408ff74c3096184cbdb4a2b507676d","target":"record","created_at":"2026-05-18T02:29:09Z","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":"f72fce66cad40030a45057479165a9985cff3131e19af88a67d88e81a28009f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-18T18:13:52Z","title_canon_sha256":"52fec63691f286fdbe918aa2246a4af85235ec82d67cb34d18590d8b943e577c"},"schema_version":"1.0","source":{"id":"1501.04331","kind":"arxiv","version":1}},"canonical_sha256":"69141671ae8720650160d10a614e22b15bd69675b20b9e59bffed72b981fa7cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69141671ae8720650160d10a614e22b15bd69675b20b9e59bffed72b981fa7cd","first_computed_at":"2026-05-18T02:29:09.329908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:09.329908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d5x49Yj7oxp+EVcYrvXSSGwrim0gxgzdfGnFBasOsg3jFur7vGNBkCT+swwMscaWADAfkUx43bF4MyKy4p1WBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:09.330522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05c0476a3e46f755d509731fe7aadb7a7f408ff74c3096184cbdb4a2b507676d","sha256:4d40f87b5f6fca2403b60aab84751ab9e42142e954a1a3ac131c68f5e0f88c95"],"state_sha256":"46884c916a21e729a7a5802b9f036287b175d61b5849140b76b314e225245105"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kCuAzW4vKuas/pEW96H6ZNXoeQ+lFUKcdJRD0UVJF1T0haFSOcTE4V7mzeEr3H7ngWD3LJQvDDtEkuslhpDsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:16:08.839438Z","bundle_sha256":"89ba57ab49e0870f0d720f61f3a789f60a5d4bbf84334180471b4bd71c1cb6d0"}}