{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HSNZ6NXDQRPVTNWZRVIOBDQ6BE","short_pith_number":"pith:HSNZ6NXD","canonical_record":{"source":{"id":"2505.02051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-04T10:00:04Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"85a1177b4b2427c4989438118b72e32ac77a4c8d06a197053d9b9f1dedb49fbe","abstract_canon_sha256":"bd4ea1a21626d5ed224eb98b154b44143311f8c1bfe0c62a5a1f07abbe9a6835"},"schema_version":"1.0"},"canonical_sha256":"3c9b9f36e3845f59b6d98d50e08e1e0930c540f3f6b0f3dd57a0ea43d1904d7a","source":{"kind":"arxiv","id":"2505.02051","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.02051","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"2505.02051v2","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02051","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"HSNZ6NXDQRPV","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"pith_short_16","alias_value":"HSNZ6NXDQRPVTNWZ","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"pith_short_8","alias_value":"HSNZ6NXD","created_at":"2026-07-05T11:02:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HSNZ6NXDQRPVTNWZRVIOBDQ6BE","target":"record","payload":{"canonical_record":{"source":{"id":"2505.02051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-04T10:00:04Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"85a1177b4b2427c4989438118b72e32ac77a4c8d06a197053d9b9f1dedb49fbe","abstract_canon_sha256":"bd4ea1a21626d5ed224eb98b154b44143311f8c1bfe0c62a5a1f07abbe9a6835"},"schema_version":"1.0"},"canonical_sha256":"3c9b9f36e3845f59b6d98d50e08e1e0930c540f3f6b0f3dd57a0ea43d1904d7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:24.255795Z","signature_b64":"LhZ7QrWUHPDRQRYhen2Ut4NBU+KSnxEkUFdEXEr+/j1T1jDmg3EkDby4VjhzTQ6r21X3YpkWuMh2GqmNUey1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c9b9f36e3845f59b6d98d50e08e1e0930c540f3f6b0f3dd57a0ea43d1904d7a","last_reissued_at":"2026-07-05T11:02:24.255359Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:24.255359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.02051","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":"2026-07-05T11:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mg8LvyTz/WWxxkM/QLKYebDnlosqMTbGMXJ7VfseSUv5M66UYT0rWABCi8dIiPWQZ3MnhnW/fPfeIN4twBEmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T11:23:27.292577Z"},"content_sha256":"0bc80b3c245f7a15365304d0a9987e6eb1adedca9bebce6c9f86c5175ac3471d","schema_version":"1.0","event_id":"sha256:0bc80b3c245f7a15365304d0a9987e6eb1adedca9bebce6c9f86c5175ac3471d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HSNZ6NXDQRPVTNWZRVIOBDQ6BE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyclic polytopes, orientals, and correspondences: some aspects of higher Segal spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Tobias Dyckerhoff","submitted_at":"2025-05-04T10:00:04Z","abstract_excerpt":"We discuss the role of higher Segal spaces at the interface of cyclic polytopes, orientals, and higher correspondences. Along the way we review examples from algebraic K-theory, show how cyclic polytopes provide a geometric model for the definition of orientals, and establish a characterization of higher Segal spaces as lax monadic structures in higher correspondence categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02051","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/2505.02051/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":"2026-07-05T11:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xp+jtCpBdU8o5xRL3OSVSEKcOYaKkK+jpBHRDv2hHriW7qDewGaaQv+NklP84/PiwjHXEZtsAIFGwz3rM1HIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T11:23:27.293093Z"},"content_sha256":"ddad7fb7f26b7dc36b99bcc2233beb967bc3da6e0b358a95a929700b1e10024f","schema_version":"1.0","event_id":"sha256:ddad7fb7f26b7dc36b99bcc2233beb967bc3da6e0b358a95a929700b1e10024f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSNZ6NXDQRPVTNWZRVIOBDQ6BE/bundle.json","state_url":"https://pith.science/pith/HSNZ6NXDQRPVTNWZRVIOBDQ6BE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSNZ6NXDQRPVTNWZRVIOBDQ6BE/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":"2026-08-09T11:23:27Z","links":{"resolver":"https://pith.science/pith/HSNZ6NXDQRPVTNWZRVIOBDQ6BE","bundle":"https://pith.science/pith/HSNZ6NXDQRPVTNWZRVIOBDQ6BE/bundle.json","state":"https://pith.science/pith/HSNZ6NXDQRPVTNWZRVIOBDQ6BE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSNZ6NXDQRPVTNWZRVIOBDQ6BE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HSNZ6NXDQRPVTNWZRVIOBDQ6BE","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":"bd4ea1a21626d5ed224eb98b154b44143311f8c1bfe0c62a5a1f07abbe9a6835","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-04T10:00:04Z","title_canon_sha256":"85a1177b4b2427c4989438118b72e32ac77a4c8d06a197053d9b9f1dedb49fbe"},"schema_version":"1.0","source":{"id":"2505.02051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.02051","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"2505.02051v2","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02051","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"HSNZ6NXDQRPV","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"pith_short_16","alias_value":"HSNZ6NXDQRPVTNWZ","created_at":"2026-07-05T11:02:24Z"},{"alias_kind":"pith_short_8","alias_value":"HSNZ6NXD","created_at":"2026-07-05T11:02:24Z"}],"graph_snapshots":[{"event_id":"sha256:ddad7fb7f26b7dc36b99bcc2233beb967bc3da6e0b358a95a929700b1e10024f","target":"graph","created_at":"2026-07-05T11:02:24Z","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/2505.02051/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss the role of higher Segal spaces at the interface of cyclic polytopes, orientals, and higher correspondences. Along the way we review examples from algebraic K-theory, show how cyclic polytopes provide a geometric model for the definition of orientals, and establish a characterization of higher Segal spaces as lax monadic structures in higher correspondence categories.","authors_text":"Tobias Dyckerhoff","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-04T10:00:04Z","title":"Cyclic polytopes, orientals, and correspondences: some aspects of higher Segal spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02051","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":"sha256:0bc80b3c245f7a15365304d0a9987e6eb1adedca9bebce6c9f86c5175ac3471d","target":"record","created_at":"2026-07-05T11:02:24Z","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":"bd4ea1a21626d5ed224eb98b154b44143311f8c1bfe0c62a5a1f07abbe9a6835","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-05-04T10:00:04Z","title_canon_sha256":"85a1177b4b2427c4989438118b72e32ac77a4c8d06a197053d9b9f1dedb49fbe"},"schema_version":"1.0","source":{"id":"2505.02051","kind":"arxiv","version":2}},"canonical_sha256":"3c9b9f36e3845f59b6d98d50e08e1e0930c540f3f6b0f3dd57a0ea43d1904d7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c9b9f36e3845f59b6d98d50e08e1e0930c540f3f6b0f3dd57a0ea43d1904d7a","first_computed_at":"2026-07-05T11:02:24.255359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:02:24.255359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LhZ7QrWUHPDRQRYhen2Ut4NBU+KSnxEkUFdEXEr+/j1T1jDmg3EkDby4VjhzTQ6r21X3YpkWuMh2GqmNUey1Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:02:24.255795Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.02051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bc80b3c245f7a15365304d0a9987e6eb1adedca9bebce6c9f86c5175ac3471d","sha256:ddad7fb7f26b7dc36b99bcc2233beb967bc3da6e0b358a95a929700b1e10024f"],"state_sha256":"4714c52126df281ad50f48c6679616a56b7a33193f1baa62dc74657fed55c5cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EHfZ7Lj8d/Tm5S3hiDxhaYTlDbq2Wy8telpbQttdKP/FlIY0vc2al38XAyVKxLNEmUfNpx6d1mlkjHJRTrdUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T11:23:27.298267Z","bundle_sha256":"4e247f83171a8c3bfe65efdd4a9353e47be773ba2d7904cd6b90736d6f404048"}}