{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T7IGZKDUEKB6M5HAF2LN7U6I3I","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":"8484b09cdc0bddf3a2083cc43af3e324c96beb22dd5f8b94a47889210e445bcf","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-12T13:37:14Z","title_canon_sha256":"681c34d33ce4de4721bd159d95ce50330b8a8ec91287b49107392b9f7bba3b2c"},"schema_version":"1.0","source":{"id":"1710.04512","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04512","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04512v2","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04512","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"T7IGZKDUEKB6","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T7IGZKDUEKB6M5HA","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T7IGZKDU","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:1e0f6f7e0d456ab8e7368028ac8e6f000ab8cd3cf13392aa863a99eacc62d7ac","target":"graph","created_at":"2026-05-18T00:18:25Z","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 review some recent results on geometric equations on Lorentzian manifolds such as the wave and Dirac equations. This includes well-posedness and stability for various initial value problems, as well as results on the structure of these equations on black-hole spacetimes (in particular, on the Kerr solution), the index theorem for hyperbolic Dirac operators and properties of the class of Green-hyperbolic operators.","authors_text":"Christian Baer, Lars Andersson","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-12T13:37:14Z","title":"Wave and Dirac equations on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04512","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:c34702c5ce94be5b971a6b3562f5cceed9e63a6f8e4f39588f2f46d1e0b64260","target":"record","created_at":"2026-05-18T00:18:25Z","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":"8484b09cdc0bddf3a2083cc43af3e324c96beb22dd5f8b94a47889210e445bcf","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-12T13:37:14Z","title_canon_sha256":"681c34d33ce4de4721bd159d95ce50330b8a8ec91287b49107392b9f7bba3b2c"},"schema_version":"1.0","source":{"id":"1710.04512","kind":"arxiv","version":2}},"canonical_sha256":"9fd06ca8742283e674e02e96dfd3c8da32bd8d8724f0000c381f049157ac4fb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fd06ca8742283e674e02e96dfd3c8da32bd8d8724f0000c381f049157ac4fb3","first_computed_at":"2026-05-18T00:18:25.621121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:25.621121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CBIhIDuDfeZeRpGPEdJQeOymZlWwVb6pBn3wN4ysii+IsgFlqNbJjkzBoNnJl4ot+G0u/Z7/j6gTDLNdp+e/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:25.621630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.04512","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c34702c5ce94be5b971a6b3562f5cceed9e63a6f8e4f39588f2f46d1e0b64260","sha256:1e0f6f7e0d456ab8e7368028ac8e6f000ab8cd3cf13392aa863a99eacc62d7ac"],"state_sha256":"36fa6f36f74c1789c358692f6838504dfdf446289345311ce4200b571cf5a6d1"}