{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BFVTTWHXH2K2VTUETBRZNWMUTK","short_pith_number":"pith:BFVTTWHX","canonical_record":{"source":{"id":"1403.5799","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-23T20:47:56Z","cross_cats_sorted":[],"title_canon_sha256":"14fcfdd89853d4a09668d9f09434306405e056dbeb7087b8900d2323e74d9a7c","abstract_canon_sha256":"fe32e8774c247821eaad669aa181df60eb4c13f42ffc7faedffa7d3efc79b4e7"},"schema_version":"1.0"},"canonical_sha256":"096b39d8f73e95aace84986396d9949aa337bd4b7d8ec925191bc76f378d9491","source":{"kind":"arxiv","id":"1403.5799","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5799","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5799v2","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5799","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"BFVTTWHXH2K2","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"pith_short_16","alias_value":"BFVTTWHXH2K2VTUE","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"pith_short_8","alias_value":"BFVTTWHX","created_at":"2026-07-05T02:44:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BFVTTWHXH2K2VTUETBRZNWMUTK","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5799","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-23T20:47:56Z","cross_cats_sorted":[],"title_canon_sha256":"14fcfdd89853d4a09668d9f09434306405e056dbeb7087b8900d2323e74d9a7c","abstract_canon_sha256":"fe32e8774c247821eaad669aa181df60eb4c13f42ffc7faedffa7d3efc79b4e7"},"schema_version":"1.0"},"canonical_sha256":"096b39d8f73e95aace84986396d9949aa337bd4b7d8ec925191bc76f378d9491","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:44:13.826079Z","signature_b64":"/GKQ16ohrS4b5Dg3LPY/yOKUQTJEyxgIjlkDIQRM0cPLt2DWAXHD1gANSLG6Ssip7+KdEnG8wr8HmoQ3G1ZaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"096b39d8f73e95aace84986396d9949aa337bd4b7d8ec925191bc76f378d9491","last_reissued_at":"2026-07-05T02:44:13.825672Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:44:13.825672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5799","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:44:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7JrGlVve7cfWeOG81WRCMCUgSnNzLm7bc7rW1rJ9G8XFYfRIiO8qCn/PS4W0Yki3m/b7JO3b2IZVQUl/e+WtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:48:04.585967Z"},"content_sha256":"0db618551fc3dcfd6dd3416d8f9080d3e12efd475d23e181484cf0b89cdd60ed","schema_version":"1.0","event_id":"sha256:0db618551fc3dcfd6dd3416d8f9080d3e12efd475d23e181484cf0b89cdd60ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BFVTTWHXH2K2VTUETBRZNWMUTK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Crossed simplicial groups and structured surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mikhail Kapranov, Tobias Dyckerhoff","submitted_at":"2014-03-23T20:47:56Z","abstract_excerpt":"We propose a generalization of the concept of a Ribbon graph suitable to provide combinatorial models for marked surfaces equipped with a G-structure. Our main insight is that the necessary combinatorics is neatly captured in the concept of a crossed simplicial group as introduced, independently, by Krasauskas and Fiedorowicz-Loday. In this context, Connes' cyclic category leads to Ribbon graphs while other crossed simplicial groups naturally yield different notions of structured graphs which model unoriented, N-spin, framed, etc, surfaces. Our main result is that structured graphs provide orb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5799","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1403.5799/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:44:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZPqSR4vVJFt+3VywC9aAQY/vczftchTSqwvHwtghtulpxXTAY1ma/NzbRsLl/S0EFk91BM1d6a6R5XZhS9maCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:48:04.586702Z"},"content_sha256":"1974a09bd7e013a9bcecef0b045ca08f69e85546b2824a168954b9bff697119a","schema_version":"1.0","event_id":"sha256:1974a09bd7e013a9bcecef0b045ca08f69e85546b2824a168954b9bff697119a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFVTTWHXH2K2VTUETBRZNWMUTK/bundle.json","state_url":"https://pith.science/pith/BFVTTWHXH2K2VTUETBRZNWMUTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFVTTWHXH2K2VTUETBRZNWMUTK/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":"2026-08-16T15:48:04Z","links":{"resolver":"https://pith.science/pith/BFVTTWHXH2K2VTUETBRZNWMUTK","bundle":"https://pith.science/pith/BFVTTWHXH2K2VTUETBRZNWMUTK/bundle.json","state":"https://pith.science/pith/BFVTTWHXH2K2VTUETBRZNWMUTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFVTTWHXH2K2VTUETBRZNWMUTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BFVTTWHXH2K2VTUETBRZNWMUTK","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":"fe32e8774c247821eaad669aa181df60eb4c13f42ffc7faedffa7d3efc79b4e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-23T20:47:56Z","title_canon_sha256":"14fcfdd89853d4a09668d9f09434306405e056dbeb7087b8900d2323e74d9a7c"},"schema_version":"1.0","source":{"id":"1403.5799","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5799","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5799v2","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5799","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"BFVTTWHXH2K2","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"pith_short_16","alias_value":"BFVTTWHXH2K2VTUE","created_at":"2026-07-05T02:44:13Z"},{"alias_kind":"pith_short_8","alias_value":"BFVTTWHX","created_at":"2026-07-05T02:44:13Z"}],"graph_snapshots":[{"event_id":"sha256:1974a09bd7e013a9bcecef0b045ca08f69e85546b2824a168954b9bff697119a","target":"graph","created_at":"2026-07-05T02:44:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1403.5799/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a generalization of the concept of a Ribbon graph suitable to provide combinatorial models for marked surfaces equipped with a G-structure. Our main insight is that the necessary combinatorics is neatly captured in the concept of a crossed simplicial group as introduced, independently, by Krasauskas and Fiedorowicz-Loday. In this context, Connes' cyclic category leads to Ribbon graphs while other crossed simplicial groups naturally yield different notions of structured graphs which model unoriented, N-spin, framed, etc, surfaces. Our main result is that structured graphs provide orb","authors_text":"Mikhail Kapranov, Tobias Dyckerhoff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-23T20:47:56Z","title":"Crossed simplicial groups and structured surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5799","kind":"arxiv","version":2},"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":"sha256:0db618551fc3dcfd6dd3416d8f9080d3e12efd475d23e181484cf0b89cdd60ed","target":"record","created_at":"2026-07-05T02:44:13Z","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":"fe32e8774c247821eaad669aa181df60eb4c13f42ffc7faedffa7d3efc79b4e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-23T20:47:56Z","title_canon_sha256":"14fcfdd89853d4a09668d9f09434306405e056dbeb7087b8900d2323e74d9a7c"},"schema_version":"1.0","source":{"id":"1403.5799","kind":"arxiv","version":2}},"canonical_sha256":"096b39d8f73e95aace84986396d9949aa337bd4b7d8ec925191bc76f378d9491","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"096b39d8f73e95aace84986396d9949aa337bd4b7d8ec925191bc76f378d9491","first_computed_at":"2026-07-05T02:44:13.825672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:44:13.825672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/GKQ16ohrS4b5Dg3LPY/yOKUQTJEyxgIjlkDIQRM0cPLt2DWAXHD1gANSLG6Ssip7+KdEnG8wr8HmoQ3G1ZaCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:44:13.826079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5799","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db618551fc3dcfd6dd3416d8f9080d3e12efd475d23e181484cf0b89cdd60ed","sha256:1974a09bd7e013a9bcecef0b045ca08f69e85546b2824a168954b9bff697119a"],"state_sha256":"be6faf199d70cf47db94373b2cdcbbb880824dd7003f6bcfe325cb899fb3d140"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DWlE7oHdIwph+TzczpJCA0MUpedRp+vm1z3bMnS30tmjMRoUtovye3OL844DcT5xdxAlH8M5ucGT/ZjLPYOqCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:48:04.591845Z","bundle_sha256":"7ec365461563dcf2d5a63a32e59cfcefcb414b0e8f2686f8fbb84cec483a6ff7"}}