{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4L6HPVJA4EVRU4EP5SCOIECB3A","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":"89d4655ddac11abb4fcaff7c3b52cd0c4fd855c6ab20ace24e00cc79e3d6642b","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-04-12T01:23:25Z","title_canon_sha256":"a523219671cf963e91bd1e55ff8fd5ce8639ba63d61cf854095efc9f80b9c87e"},"schema_version":"1.0","source":{"id":"math/0604265","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604265","created_at":"2026-05-18T03:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604265v2","created_at":"2026-05-18T03:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604265","created_at":"2026-05-18T03:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"4L6HPVJA4EVR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"4L6HPVJA4EVRU4EP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"4L6HPVJA","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:becfac341df5e82d82606409f60173e44e6a5722ff8c63fb46190e65b45be51c","target":"graph","created_at":"2026-05-18T03:01:36Z","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":"The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic spacetimes, (2) the relativistic initial value problem, (3) constant mean curvature surfaces, (4) singularity theorems, (5) cosmic censorship and Penrose inequality, (6) spinors and holonomy.","authors_text":"Miguel S\\'anchez, Olaf M\\\"uller","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-04-12T01:23:25Z","title":"An Invitation to Lorentzian Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604265","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:bbd1847421d79b542e9b0d71158af09a35a9a6fe45790ac37f5014b8b16c7276","target":"record","created_at":"2026-05-18T03:01:36Z","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":"89d4655ddac11abb4fcaff7c3b52cd0c4fd855c6ab20ace24e00cc79e3d6642b","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-04-12T01:23:25Z","title_canon_sha256":"a523219671cf963e91bd1e55ff8fd5ce8639ba63d61cf854095efc9f80b9c87e"},"schema_version":"1.0","source":{"id":"math/0604265","kind":"arxiv","version":2}},"canonical_sha256":"e2fc77d520e12b1a708fec84e41041d83880b8e6935b5252ecc143fa3c0dcb2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2fc77d520e12b1a708fec84e41041d83880b8e6935b5252ecc143fa3c0dcb2e","first_computed_at":"2026-05-18T03:01:36.334667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:36.334667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9z3Lb/LVpE44JhWgD+EPaQeWudbX6TMZgMzL/kK5BdGGQCs0tX53pUAAvaShAi12LEKmHGvkc/Ja59tBCTUhAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:36.335210Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604265","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbd1847421d79b542e9b0d71158af09a35a9a6fe45790ac37f5014b8b16c7276","sha256:becfac341df5e82d82606409f60173e44e6a5722ff8c63fb46190e65b45be51c"],"state_sha256":"fcd897ea05ef3aa973651ed4a48785a166480d7c30c6e7284d92b64c48fa33bd"}