{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:U3OWXNZOEEXVELJD6FRRYNM7PC","short_pith_number":"pith:U3OWXNZO","canonical_record":{"source":{"id":"1801.07235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-22T18:34:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6926da9b06d5b11f5ef7df61ea3afdaa74854074f9a91e8f0c11d2d8ca506c64","abstract_canon_sha256":"71362dda7d9fdfbfe01d403884d37e02c326c13413775223367575e9ad7b9a72"},"schema_version":"1.0"},"canonical_sha256":"a6dd6bb72e212f522d23f1631c359f78ac3452d4430fe2bbf2887b906846f2e8","source":{"kind":"arxiv","id":"1801.07235","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07235","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07235v1","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07235","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"U3OWXNZOEEXV","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U3OWXNZOEEXVELJD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U3OWXNZO","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:U3OWXNZOEEXVELJD6FRRYNM7PC","target":"record","payload":{"canonical_record":{"source":{"id":"1801.07235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-22T18:34:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6926da9b06d5b11f5ef7df61ea3afdaa74854074f9a91e8f0c11d2d8ca506c64","abstract_canon_sha256":"71362dda7d9fdfbfe01d403884d37e02c326c13413775223367575e9ad7b9a72"},"schema_version":"1.0"},"canonical_sha256":"a6dd6bb72e212f522d23f1631c359f78ac3452d4430fe2bbf2887b906846f2e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:21.845170Z","signature_b64":"9R0q7NZWZOETQwmHajTmB1ErqGWRdYuKwoqH7rszXbjDhMrObVC+ghTQ5EteiY6bHEnsrfNWe2lVPKeoso9GCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6dd6bb72e212f522d23f1631c359f78ac3452d4430fe2bbf2887b906846f2e8","last_reissued_at":"2026-05-18T00:25:21.844490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:21.844490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.07235","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":"2026-05-18T00:25:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSjZ+PmX7zPzgKo/nxsq/BI0zewbrgPVWvfXZRN3VYn7Ye0lKeR5p2TEC7ZylMfv1tOWpXLrvH5yaMwRoD9kAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T00:22:00.424094Z"},"content_sha256":"f276490ccfe8911d4fb95fdeed39baf35164bbadcab2f93628edcf442bc76317","schema_version":"1.0","event_id":"sha256:f276490ccfe8911d4fb95fdeed39baf35164bbadcab2f93628edcf442bc76317"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:U3OWXNZOEEXVELJD6FRRYNM7PC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The cylinder of a relation and generalized versions of the Nerve Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Elias Gabriel Minian, Ximena Fern\\'andez","submitted_at":"2018-01-22T18:34:44Z","abstract_excerpt":"We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen's Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theorem for posets and simplicial complexes, suitable for covers with not necessarily contractible intersections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07235","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":"2026-05-18T00:25:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUgiAao0977LNUGYtRvwtK2HhqqVP0sTsn/IQldFv/a275z82iPUWz4ENLpJwHH60ztSa+LPRnVLr+0ctGqICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T00:22:00.424460Z"},"content_sha256":"117e2bcb521406f010baa2ece5dc008f38a5c020ea0c946fc4442f4ca640e51e","schema_version":"1.0","event_id":"sha256:117e2bcb521406f010baa2ece5dc008f38a5c020ea0c946fc4442f4ca640e51e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U3OWXNZOEEXVELJD6FRRYNM7PC/bundle.json","state_url":"https://pith.science/pith/U3OWXNZOEEXVELJD6FRRYNM7PC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U3OWXNZOEEXVELJD6FRRYNM7PC/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":"2026-07-04T00:22:00Z","links":{"resolver":"https://pith.science/pith/U3OWXNZOEEXVELJD6FRRYNM7PC","bundle":"https://pith.science/pith/U3OWXNZOEEXVELJD6FRRYNM7PC/bundle.json","state":"https://pith.science/pith/U3OWXNZOEEXVELJD6FRRYNM7PC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U3OWXNZOEEXVELJD6FRRYNM7PC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U3OWXNZOEEXVELJD6FRRYNM7PC","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":"71362dda7d9fdfbfe01d403884d37e02c326c13413775223367575e9ad7b9a72","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-22T18:34:44Z","title_canon_sha256":"6926da9b06d5b11f5ef7df61ea3afdaa74854074f9a91e8f0c11d2d8ca506c64"},"schema_version":"1.0","source":{"id":"1801.07235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07235","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07235v1","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07235","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"U3OWXNZOEEXV","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U3OWXNZOEEXVELJD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U3OWXNZO","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:117e2bcb521406f010baa2ece5dc008f38a5c020ea0c946fc4442f4ca640e51e","target":"graph","created_at":"2026-05-18T00:25:21Z","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":"We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen's Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theorem for posets and simplicial complexes, suitable for covers with not necessarily contractible intersections.","authors_text":"Elias Gabriel Minian, Ximena Fern\\'andez","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-22T18:34:44Z","title":"The cylinder of a relation and generalized versions of the Nerve Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07235","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:f276490ccfe8911d4fb95fdeed39baf35164bbadcab2f93628edcf442bc76317","target":"record","created_at":"2026-05-18T00:25:21Z","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":"71362dda7d9fdfbfe01d403884d37e02c326c13413775223367575e9ad7b9a72","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-22T18:34:44Z","title_canon_sha256":"6926da9b06d5b11f5ef7df61ea3afdaa74854074f9a91e8f0c11d2d8ca506c64"},"schema_version":"1.0","source":{"id":"1801.07235","kind":"arxiv","version":1}},"canonical_sha256":"a6dd6bb72e212f522d23f1631c359f78ac3452d4430fe2bbf2887b906846f2e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6dd6bb72e212f522d23f1631c359f78ac3452d4430fe2bbf2887b906846f2e8","first_computed_at":"2026-05-18T00:25:21.844490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:21.844490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9R0q7NZWZOETQwmHajTmB1ErqGWRdYuKwoqH7rszXbjDhMrObVC+ghTQ5EteiY6bHEnsrfNWe2lVPKeoso9GCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:21.845170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f276490ccfe8911d4fb95fdeed39baf35164bbadcab2f93628edcf442bc76317","sha256:117e2bcb521406f010baa2ece5dc008f38a5c020ea0c946fc4442f4ca640e51e"],"state_sha256":"f8dbfaee3457d453c7a3f0d69bd0caa5237a37f9a91cdd7f5044149383842433"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XryVQlFumH9EV+Bn5oQbAIZkoQKXz1cl79+Drv7P+jV3kiDKxoofS5cs5YhGC3TG7ZNAgePPRbuTWIWParKHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T00:22:00.426388Z","bundle_sha256":"bfddf4a1f7318c7dd8065db613db1fc807bb1562c79939c1bf63f81ebbe5e188"}}