{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:56FRJLU3NTEGSVLRMRFXGAOIHY","short_pith_number":"pith:56FRJLU3","schema_version":"1.0","canonical_sha256":"ef8b14ae9b6cc8695571644b7301c83e1d6aebf6c24c15e1004b70e68c200b88","source":{"kind":"arxiv","id":"0910.5607","version":1},"attestation_state":"computed","paper":{"title":"Characterization of preclones by matrix collections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Erkko Lehtonen","submitted_at":"2009-10-29T10:34:20Z","abstract_excerpt":"Preclones are described as the closed classes of the Galois connection induced by a preservation relation between operations and matrix collections. The Galois closed classes of matrix collections are also described by explicit closure conditions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0910.5607","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-10-29T10:34:20Z","cross_cats_sorted":[],"title_canon_sha256":"d82c6d45725a10df5df1ef74c67c97a11c29119e97791087d576105bc5540b9f","abstract_canon_sha256":"8870a26066eb16008fe58c3ce47db95945c41a3c4f259ef3027eb9de6ba56433"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:38.766830Z","signature_b64":"Qr7gmSU3x0hwhj/UYeOFLsS80bcka0r1ZQs1z5fryqnHOzgA1c7m1otlQDEJYqEfQqkX094ArAKUsMUOcsF7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef8b14ae9b6cc8695571644b7301c83e1d6aebf6c24c15e1004b70e68c200b88","last_reissued_at":"2026-05-18T00:57:38.766222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:38.766222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterization of preclones by matrix collections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Erkko Lehtonen","submitted_at":"2009-10-29T10:34:20Z","abstract_excerpt":"Preclones are described as the closed classes of the Galois connection induced by a preservation relation between operations and matrix collections. The Galois closed classes of matrix collections are also described by explicit closure conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5607","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0910.5607","created_at":"2026-05-18T00:57:38.766350+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.5607v1","created_at":"2026-05-18T00:57:38.766350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5607","created_at":"2026-05-18T00:57:38.766350+00:00"},{"alias_kind":"pith_short_12","alias_value":"56FRJLU3NTEG","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"56FRJLU3NTEGSVLR","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"56FRJLU3","created_at":"2026-05-18T12:25:58.837520+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY","json":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY.json","graph_json":"https://pith.science/api/pith-number/56FRJLU3NTEGSVLRMRFXGAOIHY/graph.json","events_json":"https://pith.science/api/pith-number/56FRJLU3NTEGSVLRMRFXGAOIHY/events.json","paper":"https://pith.science/paper/56FRJLU3"},"agent_actions":{"view_html":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY","download_json":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY.json","view_paper":"https://pith.science/paper/56FRJLU3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.5607&json=true","fetch_graph":"https://pith.science/api/pith-number/56FRJLU3NTEGSVLRMRFXGAOIHY/graph.json","fetch_events":"https://pith.science/api/pith-number/56FRJLU3NTEGSVLRMRFXGAOIHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY/action/storage_attestation","attest_author":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY/action/author_attestation","sign_citation":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY/action/citation_signature","submit_replication":"https://pith.science/pith/56FRJLU3NTEGSVLRMRFXGAOIHY/action/replication_record"}},"created_at":"2026-05-18T00:57:38.766350+00:00","updated_at":"2026-05-18T00:57:38.766350+00:00"}