{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OMHGGLK2SWZWJEG7LH4YNR3ZEV","short_pith_number":"pith:OMHGGLK2","canonical_record":{"source":{"id":"1804.07813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-20T20:15:56Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"87d03cbd15e4c2c12d1acbeb559c324b2217f35c9fccd2b1a0fd39f6607ad2b9","abstract_canon_sha256":"b7d2531ab821acc54d346f9d9a7d2f06c13f063b6cd335ab057a6eb66442262a"},"schema_version":"1.0"},"canonical_sha256":"730e632d5a95b36490df59f986c77925662a1f45798d622cca4c3039e4f3edd3","source":{"kind":"arxiv","id":"1804.07813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07813","created_at":"2026-05-18T00:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07813v1","created_at":"2026-05-18T00:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07813","created_at":"2026-05-18T00:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"OMHGGLK2SWZW","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OMHGGLK2SWZWJEG7","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OMHGGLK2","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OMHGGLK2SWZWJEG7LH4YNR3ZEV","target":"record","payload":{"canonical_record":{"source":{"id":"1804.07813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-20T20:15:56Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"87d03cbd15e4c2c12d1acbeb559c324b2217f35c9fccd2b1a0fd39f6607ad2b9","abstract_canon_sha256":"b7d2531ab821acc54d346f9d9a7d2f06c13f063b6cd335ab057a6eb66442262a"},"schema_version":"1.0"},"canonical_sha256":"730e632d5a95b36490df59f986c77925662a1f45798d622cca4c3039e4f3edd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:52.690913Z","signature_b64":"8QVNyRaWIHtB9e7/WvuVlo7Dsy7/A9JTx8NsiBk7n/OLUpsL7wgUUDPBJYcHyGTThUQFYEq9w1x4zoA+II85CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"730e632d5a95b36490df59f986c77925662a1f45798d622cca4c3039e4f3edd3","last_reissued_at":"2026-05-18T00:17:52.690291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:52.690291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.07813","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":"2026-05-18T00:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzGH6+p/VdB/HIzwhhh9w06OtmschkDTiBJcAB2ZPRAuATPBmtnaM/ItPktSm2a2r7cbPn+osf2ffgK8jhVLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:20:08.430904Z"},"content_sha256":"054e694e274dd0e0e1a81a67dbacacb5c8a7ad0f3ce4deba05cb7846f3c1aec0","schema_version":"1.0","event_id":"sha256:054e694e274dd0e0e1a81a67dbacacb5c8a7ad0f3ce4deba05cb7846f3c1aec0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OMHGGLK2SWZWJEG7LH4YNR3ZEV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology change and selection rules for high-dimensional $\\Spin(1, n)_0$-Lorentzian cobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.GT","authors_text":"Gleb Smirnov, Rafael Torres","submitted_at":"2018-04-20T20:15:56Z","abstract_excerpt":"We study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the structure group of the frame bundle of the cobordism is $\\Spin(1, n)_0$. This extends a result of Gibbons-Hawking on $\\Sl(2, \\C)$-Lorentzian cobordisms between 3-manifolds and results of Reinhart and Sorkin on the existence of Lorentzian cobordisms. We compute the $\\Spin(1, n)_0$-Lorentzian cobordism group for several dimensions. Restrictions on the gravitational kink numbers of $\\Spin(1, n)_0$-weak Lorentzian cobordism"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07813","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":"2026-05-18T00:17:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VBEdTJlHFhuOJaZO0cXv42lMwzh3x/PuDASj1W+tk9mj8J1AI1RffJzFREx0C6gIxIgiUBEBkftPFAd0yQnUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:20:08.431243Z"},"content_sha256":"5ad04e9cdeb3a8fb824260a2591095859279cd69118b80a32a07199e5343e61f","schema_version":"1.0","event_id":"sha256:5ad04e9cdeb3a8fb824260a2591095859279cd69118b80a32a07199e5343e61f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMHGGLK2SWZWJEG7LH4YNR3ZEV/bundle.json","state_url":"https://pith.science/pith/OMHGGLK2SWZWJEG7LH4YNR3ZEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMHGGLK2SWZWJEG7LH4YNR3ZEV/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":"2026-06-27T19:20:08Z","links":{"resolver":"https://pith.science/pith/OMHGGLK2SWZWJEG7LH4YNR3ZEV","bundle":"https://pith.science/pith/OMHGGLK2SWZWJEG7LH4YNR3ZEV/bundle.json","state":"https://pith.science/pith/OMHGGLK2SWZWJEG7LH4YNR3ZEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMHGGLK2SWZWJEG7LH4YNR3ZEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OMHGGLK2SWZWJEG7LH4YNR3ZEV","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":"b7d2531ab821acc54d346f9d9a7d2f06c13f063b6cd335ab057a6eb66442262a","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-20T20:15:56Z","title_canon_sha256":"87d03cbd15e4c2c12d1acbeb559c324b2217f35c9fccd2b1a0fd39f6607ad2b9"},"schema_version":"1.0","source":{"id":"1804.07813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07813","created_at":"2026-05-18T00:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07813v1","created_at":"2026-05-18T00:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07813","created_at":"2026-05-18T00:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"OMHGGLK2SWZW","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OMHGGLK2SWZWJEG7","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OMHGGLK2","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:5ad04e9cdeb3a8fb824260a2591095859279cd69118b80a32a07199e5343e61f","target":"graph","created_at":"2026-05-18T00:17:52Z","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 study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the structure group of the frame bundle of the cobordism is $\\Spin(1, n)_0$. This extends a result of Gibbons-Hawking on $\\Sl(2, \\C)$-Lorentzian cobordisms between 3-manifolds and results of Reinhart and Sorkin on the existence of Lorentzian cobordisms. We compute the $\\Spin(1, n)_0$-Lorentzian cobordism group for several dimensions. Restrictions on the gravitational kink numbers of $\\Spin(1, n)_0$-weak Lorentzian cobordism","authors_text":"Gleb Smirnov, Rafael Torres","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-20T20:15:56Z","title":"Topology change and selection rules for high-dimensional $\\Spin(1, n)_0$-Lorentzian cobordisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07813","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":"sha256:054e694e274dd0e0e1a81a67dbacacb5c8a7ad0f3ce4deba05cb7846f3c1aec0","target":"record","created_at":"2026-05-18T00:17:52Z","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":"b7d2531ab821acc54d346f9d9a7d2f06c13f063b6cd335ab057a6eb66442262a","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-20T20:15:56Z","title_canon_sha256":"87d03cbd15e4c2c12d1acbeb559c324b2217f35c9fccd2b1a0fd39f6607ad2b9"},"schema_version":"1.0","source":{"id":"1804.07813","kind":"arxiv","version":1}},"canonical_sha256":"730e632d5a95b36490df59f986c77925662a1f45798d622cca4c3039e4f3edd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"730e632d5a95b36490df59f986c77925662a1f45798d622cca4c3039e4f3edd3","first_computed_at":"2026-05-18T00:17:52.690291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:52.690291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8QVNyRaWIHtB9e7/WvuVlo7Dsy7/A9JTx8NsiBk7n/OLUpsL7wgUUDPBJYcHyGTThUQFYEq9w1x4zoA+II85CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:52.690913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:054e694e274dd0e0e1a81a67dbacacb5c8a7ad0f3ce4deba05cb7846f3c1aec0","sha256:5ad04e9cdeb3a8fb824260a2591095859279cd69118b80a32a07199e5343e61f"],"state_sha256":"9c0f6cd5d1f06d02f5d7e0ff3a79c4afefba5e4a5f0c50a6981f3fea0f0dcba6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkXqc5HdAblCxEjF95vFjhP3zok2kN44u92JwkfWof+WjSxIB2rotuEkLuSxNaBkCaOCixw8jQIRNffzacmdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T19:20:08.436330Z","bundle_sha256":"5e41e3a0c554bd67798627330ab63a553dfa5b776db9ad0638ab18e73e4c5c21"}}