{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:JOZCO3FDIHORGLZV6KQP44JOJR","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":"c5358cb7cec6a0fc9699d8e2e0d05ebed5840011aaebc617c7cd41e63d1cc6e8","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2005-04-29T03:41:44Z","title_canon_sha256":"b2089cae26fb9db8dad74c0795487bea2effebaa08bea3c32138b98353249a2c"},"schema_version":"1.0","source":{"id":"gr-qc/0504142","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0504142","created_at":"2026-07-04T16:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0504142v2","created_at":"2026-07-04T16:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0504142","created_at":"2026-07-04T16:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"JOZCO3FDIHOR","created_at":"2026-07-04T16:55:13Z"},{"alias_kind":"pith_short_16","alias_value":"JOZCO3FDIHORGLZV","created_at":"2026-07-04T16:55:13Z"},{"alias_kind":"pith_short_8","alias_value":"JOZCO3FD","created_at":"2026-07-04T16:55:13Z"}],"graph_snapshots":[{"event_id":"sha256:d8666562b769c6d37e53392b420f8dd0d9351826f5ef05c46091365fc18f2993","target":"graph","created_at":"2026-07-04T16:55:13Z","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/gr-qc/0504142/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The conformal thin sandwich (CTS) equations are a set of four of the Einstein equations, which generalize the Laplace-Poisson equation of Newton's theory. We examine numerically solutions of the CTS equations describing perturbed Minkowski space, and find only one solution. However, we find {\\em two} distinct solutions, one even containing a black hole, when the lapse is determined by a fifth elliptic equation through specification of the mean curvature. While the relationship of the two systems and their solutions is a fundamental property of general relativity, this fairly simple example of ","authors_text":"Harald P. Pfeiffer (Caltech), James W. York (Cornell)","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2005-04-29T03:41:44Z","title":"Uniqueness and Non-uniqueness in the Einstein Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0504142","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":"sha256:28bbf1b95a9c090451d44674a238e2107ad7fa2929ef729618ba842216e326da","target":"record","created_at":"2026-07-04T16:55:13Z","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":"c5358cb7cec6a0fc9699d8e2e0d05ebed5840011aaebc617c7cd41e63d1cc6e8","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2005-04-29T03:41:44Z","title_canon_sha256":"b2089cae26fb9db8dad74c0795487bea2effebaa08bea3c32138b98353249a2c"},"schema_version":"1.0","source":{"id":"gr-qc/0504142","kind":"arxiv","version":2}},"canonical_sha256":"4bb2276ca341dd132f35f2a0fe712e4c4d2d21d853a88e281fe25fdc9afc412a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bb2276ca341dd132f35f2a0fe712e4c4d2d21d853a88e281fe25fdc9afc412a","first_computed_at":"2026-07-04T16:55:13.429051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:55:13.429051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ff3EA1HoIhx35WqR1cQTlKf6rigqIQogXr2sfmF+vf5uZqGzwn8KvCveMC5feL9ZzvM6HZx2UUEH4mZF0sGzBg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:55:13.429444Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0504142","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28bbf1b95a9c090451d44674a238e2107ad7fa2929ef729618ba842216e326da","sha256:d8666562b769c6d37e53392b420f8dd0d9351826f5ef05c46091365fc18f2993"],"state_sha256":"549bf13931643afc3176d438268ea75bf145b51c6b57ed4bfadee21c1cd7a9cc"}