{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PP4V2J6EKMEA7AZ66PSWARSQIY","short_pith_number":"pith:PP4V2J6E","schema_version":"1.0","canonical_sha256":"7bf95d27c453080f833ef3e56046504620db347f8e11c96472154bc7064cf680","source":{"kind":"arxiv","id":"1611.07842","version":1},"attestation_state":"computed","paper":{"title":"On the definition of spacetimes in Noncommutative Geometry, part II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Fabien Besnard","submitted_at":"2016-11-23T15:28:15Z","abstract_excerpt":"In this second part of the paper, we define spectral spacetimes, a noncommutative generalization of Lorentzian orientable spacetimes of even dimension with a spin structure. There are two main differences with spectral triples: the existence of time-orientation 1-forms and the non-existence of a distinguished C*-structure on the algebra. If a \"reconstructibility condition\" is met, different, yet isomorphic, C*-structures exist. We define a natural notion of stable causality for spectral spacetimes. We give an example of a commutative spectral spacetime which is a Wick rotated version of the sp"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.07842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-23T15:28:15Z","cross_cats_sorted":[],"title_canon_sha256":"7dcbfe2471f71fb220c001fee2eaf282ae71c1f2501423bb1aefca8fd041d5bc","abstract_canon_sha256":"199555fea97896f9f08a4f303a284b9bcfde05c528cc1a13465c97d3162f187a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:59.682531Z","signature_b64":"GrNde79lfOukoL0KRLYsMi3XWjnq5tPHWwL7hIkCcIkf7Lyj3/5uCkv3MBuxWFOEQkbN4fsvn8xvs0XF7JYJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bf95d27c453080f833ef3e56046504620db347f8e11c96472154bc7064cf680","last_reissued_at":"2026-05-18T00:56:59.682128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:59.682128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the definition of spacetimes in Noncommutative Geometry, part II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Fabien Besnard","submitted_at":"2016-11-23T15:28:15Z","abstract_excerpt":"In this second part of the paper, we define spectral spacetimes, a noncommutative generalization of Lorentzian orientable spacetimes of even dimension with a spin structure. There are two main differences with spectral triples: the existence of time-orientation 1-forms and the non-existence of a distinguished C*-structure on the algebra. If a \"reconstructibility condition\" is met, different, yet isomorphic, C*-structures exist. We define a natural notion of stable causality for spectral spacetimes. We give an example of a commutative spectral spacetime which is a Wick rotated version of the sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07842","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.07842","created_at":"2026-05-18T00:56:59.682185+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.07842v1","created_at":"2026-05-18T00:56:59.682185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07842","created_at":"2026-05-18T00:56:59.682185+00:00"},{"alias_kind":"pith_short_12","alias_value":"PP4V2J6EKMEA","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PP4V2J6EKMEA7AZ6","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PP4V2J6E","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY","json":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY.json","graph_json":"https://pith.science/api/pith-number/PP4V2J6EKMEA7AZ66PSWARSQIY/graph.json","events_json":"https://pith.science/api/pith-number/PP4V2J6EKMEA7AZ66PSWARSQIY/events.json","paper":"https://pith.science/paper/PP4V2J6E"},"agent_actions":{"view_html":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY","download_json":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY.json","view_paper":"https://pith.science/paper/PP4V2J6E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.07842&json=true","fetch_graph":"https://pith.science/api/pith-number/PP4V2J6EKMEA7AZ66PSWARSQIY/graph.json","fetch_events":"https://pith.science/api/pith-number/PP4V2J6EKMEA7AZ66PSWARSQIY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY/action/storage_attestation","attest_author":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY/action/author_attestation","sign_citation":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY/action/citation_signature","submit_replication":"https://pith.science/pith/PP4V2J6EKMEA7AZ66PSWARSQIY/action/replication_record"}},"created_at":"2026-05-18T00:56:59.682185+00:00","updated_at":"2026-05-18T00:56:59.682185+00:00"}