{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JKIVJP62ZZKAFVJMPPZLKKMZYS","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":"710ac0c0482c9789f1e968ba9dd6f1bc60f7c92938ef7b903e4c1fc219fb9986","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-11T20:16:37Z","title_canon_sha256":"733150260716e0e5d868056ef7f915530120ea5abcdf575294cb6f0e63f93c59"},"schema_version":"1.0","source":{"id":"1007.1797","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1797","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1797v2","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1797","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"JKIVJP62ZZKA","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JKIVJP62ZZKAFVJM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JKIVJP62","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:fccaade9f8b58a3544327f8b3b387ad38ebc91ed8d6c1be012d5e7a452f1a548","target":"graph","created_at":"2026-05-18T03:14:17Z","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 prove an extension to R^n, endowed with a suitable metric, of the relation between the Einstein-Hilbert action and the Dirac operator which holds on closed spin manifolds. By means of complex powers, we first define the regularised Wodzicki Residue for a class of operators globally defined on R^n. The result is then obtained by using the properties of heat kernels and generalised Laplacians.","authors_text":"S. Coriasco, U. Battisti","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-11T20:16:37Z","title":"A Note on the Einstein-Hilbert action and the Dirac operator on R^n"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1797","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":"sha256:230640a01f432573afa51d3764d3c20e4e9ebc5252e03eba461f5d7ef928fcfb","target":"record","created_at":"2026-05-18T03:14:17Z","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":"710ac0c0482c9789f1e968ba9dd6f1bc60f7c92938ef7b903e4c1fc219fb9986","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-11T20:16:37Z","title_canon_sha256":"733150260716e0e5d868056ef7f915530120ea5abcdf575294cb6f0e63f93c59"},"schema_version":"1.0","source":{"id":"1007.1797","kind":"arxiv","version":2}},"canonical_sha256":"4a9154bfdace5402d52c7bf2b52999c4b8d93e0d78ccf8dd02e126e4bb278df8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a9154bfdace5402d52c7bf2b52999c4b8d93e0d78ccf8dd02e126e4bb278df8","first_computed_at":"2026-05-18T03:14:17.873264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:17.873264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+xYCi+0XCSJxDLy4ZrR/Va3i7rNalz0oGraVLuzT8y2Ek4t9n6P0HTQ5pXeCkYI5RLnUUz9Jy6v3Y7vOUyDaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:17.873864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1797","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:230640a01f432573afa51d3764d3c20e4e9ebc5252e03eba461f5d7ef928fcfb","sha256:fccaade9f8b58a3544327f8b3b387ad38ebc91ed8d6c1be012d5e7a452f1a548"],"state_sha256":"710745f30d1f1c6f420de18d9f97e01db398e50aa1ca1bb82b09829f494c5bfe"}