{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:E32FWMPTUD6TFZEARK6L3LNTLE","short_pith_number":"pith:E32FWMPT","canonical_record":{"source":{"id":"1903.01750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-05T09:56:45Z","cross_cats_sorted":["math.CO","math.CT","math.RA"],"title_canon_sha256":"d3af0cacf8a674a9d8e32785681ccde737c9c22cb2a33cf1438e8a6cdad60168","abstract_canon_sha256":"3fd7a53e04d8b2192146ee25fb8e4d2db35692867fc8b6f4d89db97e2331fd21"},"schema_version":"1.0"},"canonical_sha256":"26f45b31f3a0fd32e4808abcbdadb35902197c1e4ff911ed12359dad71301fe6","source":{"kind":"arxiv","id":"1903.01750","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01750","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01750v1","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01750","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"E32FWMPTUD6T","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"E32FWMPTUD6TFZEA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"E32FWMPT","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:E32FWMPTUD6TFZEARK6L3LNTLE","target":"record","payload":{"canonical_record":{"source":{"id":"1903.01750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-05T09:56:45Z","cross_cats_sorted":["math.CO","math.CT","math.RA"],"title_canon_sha256":"d3af0cacf8a674a9d8e32785681ccde737c9c22cb2a33cf1438e8a6cdad60168","abstract_canon_sha256":"3fd7a53e04d8b2192146ee25fb8e4d2db35692867fc8b6f4d89db97e2331fd21"},"schema_version":"1.0"},"canonical_sha256":"26f45b31f3a0fd32e4808abcbdadb35902197c1e4ff911ed12359dad71301fe6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:59.864534Z","signature_b64":"sqWZDuevlY1B+7XV8HQqYaRrbrdpy8hPOi1yvcJxi91YW/AGHlGPJI4BfAnm94uUMS7KWoTsVt1xRDdWq4xEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26f45b31f3a0fd32e4808abcbdadb35902197c1e4ff911ed12359dad71301fe6","last_reissued_at":"2026-05-17T23:51:59.864151Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:59.864151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.01750","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":"2026-05-17T23:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8gMvwOGVdk26h/ZgeKGgLO6DmFiymnoslAjcFDZL1GQ9QCSl7rwSHruVgoV9S5FzucIR66oI0t+kT1Khk6eBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:57:58.100944Z"},"content_sha256":"2596749feb6f550ed62c276e11371e8c0b4e7dc3b626ba5f8ac964be1729109f","schema_version":"1.0","event_id":"sha256:2596749feb6f550ed62c276e11371e8c0b4e7dc3b626ba5f8ac964be1729109f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:E32FWMPTUD6TFZEARK6L3LNTLE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor product of correspondence functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Jacques Th\\'evenaz, Serge Bouc","submitted_at":"2019-03-05T09:56:45Z","abstract_excerpt":"As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01750","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":"2026-05-17T23:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GlAKnK2fSwsowTm4zMOC5YUZsNsNkCWRNbz2lDmvWDAuzv6Rjjb7ECSlU+5csAUO+1v+llutLG3Op/4XvapqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:57:58.101291Z"},"content_sha256":"8cfca7a0ee91b1decf97baa98c9b9b265ca79bee39ded31fca14e1145cd8996e","schema_version":"1.0","event_id":"sha256:8cfca7a0ee91b1decf97baa98c9b9b265ca79bee39ded31fca14e1145cd8996e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E32FWMPTUD6TFZEARK6L3LNTLE/bundle.json","state_url":"https://pith.science/pith/E32FWMPTUD6TFZEARK6L3LNTLE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E32FWMPTUD6TFZEARK6L3LNTLE/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":"2026-06-23T12:57:58Z","links":{"resolver":"https://pith.science/pith/E32FWMPTUD6TFZEARK6L3LNTLE","bundle":"https://pith.science/pith/E32FWMPTUD6TFZEARK6L3LNTLE/bundle.json","state":"https://pith.science/pith/E32FWMPTUD6TFZEARK6L3LNTLE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E32FWMPTUD6TFZEARK6L3LNTLE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:E32FWMPTUD6TFZEARK6L3LNTLE","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":"3fd7a53e04d8b2192146ee25fb8e4d2db35692867fc8b6f4d89db97e2331fd21","cross_cats_sorted":["math.CO","math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-05T09:56:45Z","title_canon_sha256":"d3af0cacf8a674a9d8e32785681ccde737c9c22cb2a33cf1438e8a6cdad60168"},"schema_version":"1.0","source":{"id":"1903.01750","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01750","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01750v1","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01750","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"E32FWMPTUD6T","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"E32FWMPTUD6TFZEA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"E32FWMPT","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:8cfca7a0ee91b1decf97baa98c9b9b265ca79bee39ded31fca14e1145cd8996e","target":"graph","created_at":"2026-05-17T23:51:59Z","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":"As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors.","authors_text":"Jacques Th\\'evenaz, Serge Bouc","cross_cats":["math.CO","math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-05T09:56:45Z","title":"Tensor product of correspondence functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01750","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":"sha256:2596749feb6f550ed62c276e11371e8c0b4e7dc3b626ba5f8ac964be1729109f","target":"record","created_at":"2026-05-17T23:51:59Z","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":"3fd7a53e04d8b2192146ee25fb8e4d2db35692867fc8b6f4d89db97e2331fd21","cross_cats_sorted":["math.CO","math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-05T09:56:45Z","title_canon_sha256":"d3af0cacf8a674a9d8e32785681ccde737c9c22cb2a33cf1438e8a6cdad60168"},"schema_version":"1.0","source":{"id":"1903.01750","kind":"arxiv","version":1}},"canonical_sha256":"26f45b31f3a0fd32e4808abcbdadb35902197c1e4ff911ed12359dad71301fe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26f45b31f3a0fd32e4808abcbdadb35902197c1e4ff911ed12359dad71301fe6","first_computed_at":"2026-05-17T23:51:59.864151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:59.864151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sqWZDuevlY1B+7XV8HQqYaRrbrdpy8hPOi1yvcJxi91YW/AGHlGPJI4BfAnm94uUMS7KWoTsVt1xRDdWq4xEBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:59.864534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01750","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2596749feb6f550ed62c276e11371e8c0b4e7dc3b626ba5f8ac964be1729109f","sha256:8cfca7a0ee91b1decf97baa98c9b9b265ca79bee39ded31fca14e1145cd8996e"],"state_sha256":"ad3038ed93d69e4f6871829f29db8fbe9fb2391f25b509880d38488d27a9ce66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U2+FHf4gtWkDutEZIBWP3X7jEPWE6UyvNyi7SxLPhrbwtYWUFmtuSKq+rXYlnhSNRLZ2BzkS6Q+WzhMvK+ZeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:57:58.103260Z","bundle_sha256":"328cc33d7aea0ab23dbec9296c476609e88c6a06fb2c229ea2d667ad4913a3c0"}}