{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XXVO2COWQXMTNIPFQV75RRUBXB","short_pith_number":"pith:XXVO2COW","canonical_record":{"source":{"id":"1407.0512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-07-02T10:36:20Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"727a1785db0dff2fc473de080355c090bc9824fe8866f36f22aa8c4fb9686b4c","abstract_canon_sha256":"857d5255507b1e60c3542987b6a22e3d24caf6973df5fb9ba282516cdabe7a17"},"schema_version":"1.0"},"canonical_sha256":"bdeaed09d685d936a1e5857fd8c681b87d2abff37216f2b26636c672e099061f","source":{"kind":"arxiv","id":"1407.0512","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0512","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0512v1","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0512","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"XXVO2COWQXMT","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XXVO2COWQXMTNIPF","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XXVO2COW","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XXVO2COWQXMTNIPFQV75RRUBXB","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-07-02T10:36:20Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"727a1785db0dff2fc473de080355c090bc9824fe8866f36f22aa8c4fb9686b4c","abstract_canon_sha256":"857d5255507b1e60c3542987b6a22e3d24caf6973df5fb9ba282516cdabe7a17"},"schema_version":"1.0"},"canonical_sha256":"bdeaed09d685d936a1e5857fd8c681b87d2abff37216f2b26636c672e099061f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:26.715305Z","signature_b64":"k1vbrLDAhirXBsnAeb0XrPDJbtOzOLlp7lQfVRCW2rwjrh7WCYUklvwu6VPmLljPWGDFNgs+TFFHrDX0OCS/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdeaed09d685d936a1e5857fd8c681b87d2abff37216f2b26636c672e099061f","last_reissued_at":"2026-05-18T02:48:26.714866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:26.714866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0512","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":"2026-05-18T02:48:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b2q9xcXiknENX6x210ohwPBeen8bcxWMd7Mse6r1P4hT/zFRKFO6MuBlbWLkckDjA9yVq823dg+D2WUgBLh/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:38:39.482250Z"},"content_sha256":"54f11e834a87a90bc617245db8fb65f42d4496626aaf3586ed898d3cb995e6a1","schema_version":"1.0","event_id":"sha256:54f11e834a87a90bc617245db8fb65f42d4496626aaf3586ed898d3cb995e6a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XXVO2COWQXMTNIPFQV75RRUBXB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categories of contexts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CT","authors_text":"Marcel Ern\\'e","submitted_at":"2014-07-02T10:36:20Z","abstract_excerpt":"Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we show that the category CLc of complete lattices with complete homomorphisms is (up to a natural isomorphism) a full reflective subcategory of the category of contexts with so-called conceptual morphisms; the reflector associates with each context its concept lattice. On the other hand, we obtain a dual adjunction between CLc and the category of contexts with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0512","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":"2026-05-18T02:48:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZPOcr8+9ohmKOaAptANvrrwWzEo4lyxsRFp6y+TTJPyIcpruQKCgnszHhumbnpyjBDS/YUnBKIjWEgKKW1WDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T10:38:39.482616Z"},"content_sha256":"525d1facd9af407e32b6ce894ba51d002a4ec64eb14e9a1fd9d38f09d3cecbae","schema_version":"1.0","event_id":"sha256:525d1facd9af407e32b6ce894ba51d002a4ec64eb14e9a1fd9d38f09d3cecbae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XXVO2COWQXMTNIPFQV75RRUBXB/bundle.json","state_url":"https://pith.science/pith/XXVO2COWQXMTNIPFQV75RRUBXB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XXVO2COWQXMTNIPFQV75RRUBXB/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":"2026-06-03T10:38:39Z","links":{"resolver":"https://pith.science/pith/XXVO2COWQXMTNIPFQV75RRUBXB","bundle":"https://pith.science/pith/XXVO2COWQXMTNIPFQV75RRUBXB/bundle.json","state":"https://pith.science/pith/XXVO2COWQXMTNIPFQV75RRUBXB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XXVO2COWQXMTNIPFQV75RRUBXB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XXVO2COWQXMTNIPFQV75RRUBXB","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":"857d5255507b1e60c3542987b6a22e3d24caf6973df5fb9ba282516cdabe7a17","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-07-02T10:36:20Z","title_canon_sha256":"727a1785db0dff2fc473de080355c090bc9824fe8866f36f22aa8c4fb9686b4c"},"schema_version":"1.0","source":{"id":"1407.0512","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0512","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0512v1","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0512","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"XXVO2COWQXMT","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XXVO2COWQXMTNIPF","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XXVO2COW","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:525d1facd9af407e32b6ce894ba51d002a4ec64eb14e9a1fd9d38f09d3cecbae","target":"graph","created_at":"2026-05-18T02:48:26Z","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":"Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we show that the category CLc of complete lattices with complete homomorphisms is (up to a natural isomorphism) a full reflective subcategory of the category of contexts with so-called conceptual morphisms; the reflector associates with each context its concept lattice. On the other hand, we obtain a dual adjunction between CLc and the category of contexts with ","authors_text":"Marcel Ern\\'e","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-07-02T10:36:20Z","title":"Categories of contexts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0512","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":"sha256:54f11e834a87a90bc617245db8fb65f42d4496626aaf3586ed898d3cb995e6a1","target":"record","created_at":"2026-05-18T02:48:26Z","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":"857d5255507b1e60c3542987b6a22e3d24caf6973df5fb9ba282516cdabe7a17","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-07-02T10:36:20Z","title_canon_sha256":"727a1785db0dff2fc473de080355c090bc9824fe8866f36f22aa8c4fb9686b4c"},"schema_version":"1.0","source":{"id":"1407.0512","kind":"arxiv","version":1}},"canonical_sha256":"bdeaed09d685d936a1e5857fd8c681b87d2abff37216f2b26636c672e099061f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdeaed09d685d936a1e5857fd8c681b87d2abff37216f2b26636c672e099061f","first_computed_at":"2026-05-18T02:48:26.714866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:26.714866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k1vbrLDAhirXBsnAeb0XrPDJbtOzOLlp7lQfVRCW2rwjrh7WCYUklvwu6VPmLljPWGDFNgs+TFFHrDX0OCS/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:26.715305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0512","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54f11e834a87a90bc617245db8fb65f42d4496626aaf3586ed898d3cb995e6a1","sha256:525d1facd9af407e32b6ce894ba51d002a4ec64eb14e9a1fd9d38f09d3cecbae"],"state_sha256":"9657d792a23bce656ac3fa9d2088425ff40dc5478e0951ff4485e745c1101115"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LV7HjcKEIkpVPoexUUzAw62y1OMUj06Znw4tEbDLOXVDwo70ju+BcL2F/dFpVrN9jAx7YxXW2M4q0OaWnXByDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T10:38:39.484562Z","bundle_sha256":"f024c5d05f349e6845f382ab312a3045e0251dff432061fdcdbcde074442882b"}}