{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4GOLEPDFRKWYXVSMJBC3CPWFGS","short_pith_number":"pith:4GOLEPDF","canonical_record":{"source":{"id":"1902.05444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-13T14:25:15Z","cross_cats_sorted":["math.CO","math.CT","math.GR"],"title_canon_sha256":"28c585d4f3598fe0bbc703703010e86b13be5a832dcbc9475b4dd2c1bb294b89","abstract_canon_sha256":"e7218befeb2f7514c2928e014d4494a0504d57312ef31a63d0a1c079fbfdab0b"},"schema_version":"1.0"},"canonical_sha256":"e19cb23c658aad8bd64c4845b13ec534b0f065a79ef1c139ebe3f55b141b6a2f","source":{"kind":"arxiv","id":"1902.05444","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05444","created_at":"2026-05-17T23:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05444v1","created_at":"2026-05-17T23:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05444","created_at":"2026-05-17T23:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"4GOLEPDFRKWY","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4GOLEPDFRKWYXVSM","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4GOLEPDF","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4GOLEPDFRKWYXVSMJBC3CPWFGS","target":"record","payload":{"canonical_record":{"source":{"id":"1902.05444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-13T14:25:15Z","cross_cats_sorted":["math.CO","math.CT","math.GR"],"title_canon_sha256":"28c585d4f3598fe0bbc703703010e86b13be5a832dcbc9475b4dd2c1bb294b89","abstract_canon_sha256":"e7218befeb2f7514c2928e014d4494a0504d57312ef31a63d0a1c079fbfdab0b"},"schema_version":"1.0"},"canonical_sha256":"e19cb23c658aad8bd64c4845b13ec534b0f065a79ef1c139ebe3f55b141b6a2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:00.747807Z","signature_b64":"7LaiPLh2Nro0WO4bldocyb1gRumgbN0Rl50mGoZAG32+E635UASLMF5Zmv+3irRh+AGqCsyYV18+ZVolGEH9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e19cb23c658aad8bd64c4845b13ec534b0f065a79ef1c139ebe3f55b141b6a2f","last_reissued_at":"2026-05-17T23:54:00.747204Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:00.747204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.05444","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":"2026-05-17T23:54:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tMcQ8OLn6/ONWzJ7/65oK+3pq676y0/6dPDkgOtASa8lox2kp1KOENGUtzqs6CDEvsuHUtqAowAsedsnvFRTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T11:02:58.317469Z"},"content_sha256":"eee091a5646d5e883212cf43ccd35b1a02f2d6a44136ebcd7079a64e16623911","schema_version":"1.0","event_id":"sha256:eee091a5646d5e883212cf43ccd35b1a02f2d6a44136ebcd7079a64e16623911"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4GOLEPDFRKWYXVSMJBC3CPWFGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Correspondence functors and lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CT","math.GR"],"primary_cat":"math.RT","authors_text":"Jacques Th\\'evenaz, Serge Bouc (LAMFA)","submitted_at":"2019-02-13T14:25:15Z","abstract_excerpt":"A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated to any finite lattice T. We prove for instance that this functor is projective if and only if the lattice T is distributive. Moreover, it has quotients which play a crucial role in the analysis of simple functors. The special case of total orders yields some more specific and complete results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05444","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":"2026-05-17T23:54:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pRbqMG0NdV+zQxX/rSgEq/37W/YfPHmwe2W0I1Wq7jEafShTdVub7uYHrvIfyDp+bbV/OPMewIqc2drz/B6oBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T11:02:58.317813Z"},"content_sha256":"197e284eabc30a05cbfe3275b5c5df3b81d2cbbbb77ffb2e7a956d6ee0d63765","schema_version":"1.0","event_id":"sha256:197e284eabc30a05cbfe3275b5c5df3b81d2cbbbb77ffb2e7a956d6ee0d63765"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GOLEPDFRKWYXVSMJBC3CPWFGS/bundle.json","state_url":"https://pith.science/pith/4GOLEPDFRKWYXVSMJBC3CPWFGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GOLEPDFRKWYXVSMJBC3CPWFGS/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":"2026-06-23T11:02:58Z","links":{"resolver":"https://pith.science/pith/4GOLEPDFRKWYXVSMJBC3CPWFGS","bundle":"https://pith.science/pith/4GOLEPDFRKWYXVSMJBC3CPWFGS/bundle.json","state":"https://pith.science/pith/4GOLEPDFRKWYXVSMJBC3CPWFGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GOLEPDFRKWYXVSMJBC3CPWFGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4GOLEPDFRKWYXVSMJBC3CPWFGS","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":"e7218befeb2f7514c2928e014d4494a0504d57312ef31a63d0a1c079fbfdab0b","cross_cats_sorted":["math.CO","math.CT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-13T14:25:15Z","title_canon_sha256":"28c585d4f3598fe0bbc703703010e86b13be5a832dcbc9475b4dd2c1bb294b89"},"schema_version":"1.0","source":{"id":"1902.05444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05444","created_at":"2026-05-17T23:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05444v1","created_at":"2026-05-17T23:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05444","created_at":"2026-05-17T23:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"4GOLEPDFRKWY","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4GOLEPDFRKWYXVSM","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4GOLEPDF","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:197e284eabc30a05cbfe3275b5c5df3b81d2cbbbb77ffb2e7a956d6ee0d63765","target":"graph","created_at":"2026-05-17T23:54:00Z","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 correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commu-tative ring. A main tool for this study is the construction of a correspondence functor associated to any finite lattice T. We prove for instance that this functor is projective if and only if the lattice T is distributive. Moreover, it has quotients which play a crucial role in the analysis of simple functors. The special case of total orders yields some more specific and complete results.","authors_text":"Jacques Th\\'evenaz, Serge Bouc (LAMFA)","cross_cats":["math.CO","math.CT","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-13T14:25:15Z","title":"Correspondence functors and lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05444","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:eee091a5646d5e883212cf43ccd35b1a02f2d6a44136ebcd7079a64e16623911","target":"record","created_at":"2026-05-17T23:54:00Z","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":"e7218befeb2f7514c2928e014d4494a0504d57312ef31a63d0a1c079fbfdab0b","cross_cats_sorted":["math.CO","math.CT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-13T14:25:15Z","title_canon_sha256":"28c585d4f3598fe0bbc703703010e86b13be5a832dcbc9475b4dd2c1bb294b89"},"schema_version":"1.0","source":{"id":"1902.05444","kind":"arxiv","version":1}},"canonical_sha256":"e19cb23c658aad8bd64c4845b13ec534b0f065a79ef1c139ebe3f55b141b6a2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e19cb23c658aad8bd64c4845b13ec534b0f065a79ef1c139ebe3f55b141b6a2f","first_computed_at":"2026-05-17T23:54:00.747204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:00.747204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7LaiPLh2Nro0WO4bldocyb1gRumgbN0Rl50mGoZAG32+E635UASLMF5Zmv+3irRh+AGqCsyYV18+ZVolGEH9Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:00.747807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eee091a5646d5e883212cf43ccd35b1a02f2d6a44136ebcd7079a64e16623911","sha256:197e284eabc30a05cbfe3275b5c5df3b81d2cbbbb77ffb2e7a956d6ee0d63765"],"state_sha256":"9ff17679ee461c228a002d8b134513931066b982997a357216dc0ffd6e0a3ce6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"feR1U6aL9qdpLYLElxpQZuOLJBWpRQ6Vkrc+ah3Oxadt7bfrVejbJBNi/M2vrVDMFyJHpcRU9lX82GEqMdMSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T11:02:58.319804Z","bundle_sha256":"77f91b884ae60c38e9d17c6c937554ffb24db7ce1824dc7fb143811570a7c743"}}