{"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"}