{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DSKW4P3ZVDAZP2WC6CJNYAZFLJ","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":"a832c8974f209b97a2e933aef39209ece8a8eb08fb3ee439f89af0297dc356bf","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-23T15:10:14Z","title_canon_sha256":"3807f31f644ad9fb1ccdd5458d957e2991c897fc67d8eccedbc0194353269525"},"schema_version":"1.0","source":{"id":"1611.07830","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07830","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07830v3","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07830","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"DSKW4P3ZVDAZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DSKW4P3ZVDAZP2WC","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DSKW4P3Z","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:83020c389c703ea5c9b95d2411995bad01c8505adfee661dac2b9810e68d02a2","target":"graph","created_at":"2026-05-18T00:48:53Z","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":"In this two-part paper we propose an extension of Connes' notion of even spectral triple to the Lorentzian setting. This extension, which we call a spectral spacetime, is discussed in part II where several natural examples are given which are not covered by the previous approaches to the problem. Part I only deals with the commutative and continuous case of a manifold. It contains all the necessary material for the generalization to come in part II, namely the characterization of the signature of the metric in terms of a time-orientation 1-form and a natural Krein product on spinor fields. It ","authors_text":"Fabien Besnard, Nadir Bizi","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-23T15:10:14Z","title":"On the definition of spacetimes in Noncommutative Geometry, Part I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07830","kind":"arxiv","version":3},"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":"sha256:2ac9faefb789ac6655d6b9d4efc47ddc76dfee3344732402721c3d01b0d724a7","target":"record","created_at":"2026-05-18T00:48:53Z","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":"a832c8974f209b97a2e933aef39209ece8a8eb08fb3ee439f89af0297dc356bf","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-11-23T15:10:14Z","title_canon_sha256":"3807f31f644ad9fb1ccdd5458d957e2991c897fc67d8eccedbc0194353269525"},"schema_version":"1.0","source":{"id":"1611.07830","kind":"arxiv","version":3}},"canonical_sha256":"1c956e3f79a8c197eac2f092dc03255a4161c9390e12026c0077eb984c6692b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c956e3f79a8c197eac2f092dc03255a4161c9390e12026c0077eb984c6692b0","first_computed_at":"2026-05-18T00:48:53.692064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:53.692064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zqUXn56O6xvcG/vI6thavY1O2FTK3YVt1nBQx0ww8GCauv+CBhwqnySOz5NfDnhFL8kJdcXpS4tegC1or1PWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:53.692563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07830","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ac9faefb789ac6655d6b9d4efc47ddc76dfee3344732402721c3d01b0d724a7","sha256:83020c389c703ea5c9b95d2411995bad01c8505adfee661dac2b9810e68d02a2"],"state_sha256":"3742aef287d56e1a42a45dcb0799aedc00008dfd63705f16b08df48c5c0ef204"}