{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BWJA3OBOYK5OHK4UU3OGA5NPHX","short_pith_number":"pith:BWJA3OBO","schema_version":"1.0","canonical_sha256":"0d920db82ec2bae3ab94a6dc6075af3dee99f8f0263d25efd7f70942a4d96d47","source":{"kind":"arxiv","id":"1907.07591","version":1},"attestation_state":"computed","paper":{"title":"Defining Functions on Equivalence Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Lawrence C. Paulson","submitted_at":"2019-07-17T15:38:36Z","abstract_excerpt":"A quotient construction defines an abstract type from a concrete type, using an equivalence relation to identify elements of the concrete type that are to be regarded as indistinguishable. The elements of a quotient type are \\emph{equivalence classes}: sets of equivalent concrete values. Simple techniques are presented for defining and reasoning about quotient constructions, based on a general lemma library concerning functions that operate on equivalence classes. The techniques are applied to a definition of the integers from the natural numbers, and then to the definition of a recursive data"},"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":"1907.07591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2019-07-17T15:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"1fb04d9f80ac5f9d5e62aa2add5f934ab714e1ef4a579d81d093674f946592e8","abstract_canon_sha256":"9fd99fe73de277e5df9d397821cef6aea393c44227d55e7688751089d56c4f92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:21.613571Z","signature_b64":"6oVszJrr8LmImJK3BUoJD8qvy/xXWvaQ2y+TzJdhZnxJnn5TIXxGXgCNOuCWyUJBRkx6kQOutUQ4vEXtaJS6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d920db82ec2bae3ab94a6dc6075af3dee99f8f0263d25efd7f70942a4d96d47","last_reissued_at":"2026-05-17T23:40:21.612917Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:21.612917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Defining Functions on Equivalence Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Lawrence C. Paulson","submitted_at":"2019-07-17T15:38:36Z","abstract_excerpt":"A quotient construction defines an abstract type from a concrete type, using an equivalence relation to identify elements of the concrete type that are to be regarded as indistinguishable. The elements of a quotient type are \\emph{equivalence classes}: sets of equivalent concrete values. Simple techniques are presented for defining and reasoning about quotient constructions, based on a general lemma library concerning functions that operate on equivalence classes. The techniques are applied to a definition of the integers from the natural numbers, and then to the definition of a recursive data"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07591","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":"1907.07591","created_at":"2026-05-17T23:40:21.613034+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.07591v1","created_at":"2026-05-17T23:40:21.613034+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07591","created_at":"2026-05-17T23:40:21.613034+00:00"},{"alias_kind":"pith_short_12","alias_value":"BWJA3OBOYK5O","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BWJA3OBOYK5OHK4U","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BWJA3OBO","created_at":"2026-05-18T12:33:12.712433+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/BWJA3OBOYK5OHK4UU3OGA5NPHX","json":"https://pith.science/pith/BWJA3OBOYK5OHK4UU3OGA5NPHX.json","graph_json":"https://pith.science/api/pith-number/BWJA3OBOYK5OHK4UU3OGA5NPHX/graph.json","events_json":"https://pith.science/api/pith-number/BWJA3OBOYK5OHK4UU3OGA5NPHX/events.json","paper":"https://pith.science/paper/BWJA3OBO"},"agent_actions":{"view_html":"https://pith.science/pith/BWJA3OBOYK5OHK4UU3OGA5NPHX","download_json":"https://pith.science/pith/BWJA3OBOYK5OHK4UU3OGA5NPHX.json","view_paper":"https://pith.science/paper/BWJA3OBO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.07591&json=true","fetch_graph":"https://pith.science/api/pith-number/BWJA3OBOYK5OHK4UU3OGA5NPHX/graph.json","fetch_events":"https://pith.science/api/pith-number/BWJA3OBOYK5OHK4UU3OGA5NPHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BWJA3OBOYK5OHK4UU3OGA5NPHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BWJA3OBOYK5OHK4UU3OGA5NPHX/action/storage_attestation","attest_author":"https://pith.science/pith/BWJA3OBOYK5OHK4UU3OGA5NPHX/action/author_attestation","sign_citation":"https://pith.science/pith/BWJA3OBOYK5OHK4UU3OGA5NPHX/action/citation_signature","submit_replication":"https://pith.science/pith/BWJA3OBOYK5OHK4UU3OGA5NPHX/action/replication_record"}},"created_at":"2026-05-17T23:40:21.613034+00:00","updated_at":"2026-05-17T23:40:21.613034+00:00"}