{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:UPV5WAYHEVFKNOH5ET7VYLOE6N","short_pith_number":"pith:UPV5WAYH","canonical_record":{"source":{"id":"0706.3055","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-06-20T20:17:24Z","cross_cats_sorted":[],"title_canon_sha256":"48bbc3a389dec508ea56445952d6710880dae9f9b9b3493f99117458714449f8","abstract_canon_sha256":"12d459c29aeb2ff818626000b7bea83b7ecfdd23266f57762a841ff42ddd46b3"},"schema_version":"1.0"},"canonical_sha256":"a3ebdb0307254aa6b8fd24ff5c2dc4f367dcf2c96dba3b341f7bd63426a548b4","source":{"kind":"arxiv","id":"0706.3055","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3055","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3055v1","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3055","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"pith_short_12","alias_value":"UPV5WAYHEVFK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UPV5WAYHEVFKNOH5","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UPV5WAYH","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:UPV5WAYHEVFKNOH5ET7VYLOE6N","target":"record","payload":{"canonical_record":{"source":{"id":"0706.3055","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-06-20T20:17:24Z","cross_cats_sorted":[],"title_canon_sha256":"48bbc3a389dec508ea56445952d6710880dae9f9b9b3493f99117458714449f8","abstract_canon_sha256":"12d459c29aeb2ff818626000b7bea83b7ecfdd23266f57762a841ff42ddd46b3"},"schema_version":"1.0"},"canonical_sha256":"a3ebdb0307254aa6b8fd24ff5c2dc4f367dcf2c96dba3b341f7bd63426a548b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:35.123822Z","signature_b64":"pWZhCWZ7hY4v5STX5pIiqW5qfe3yftt2cYZVqPuVzWeEiofZnlpr5TwSFIWvCqHxcvFug5mNteU150VgzcsaBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3ebdb0307254aa6b8fd24ff5c2dc4f367dcf2c96dba3b341f7bd63426a548b4","last_reissued_at":"2026-05-18T04:18:35.123228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:35.123228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.3055","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eONdUaHm3zAksZBk93xMn0GEevwoBI1vwndilfz5vd7ifvT2r4imT24tlMcX3mtkZKnWFhA2Md8/mUOCYtsyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:45:04.981304Z"},"content_sha256":"651bf4daf9344c977f6b4209437bbe6964de5011dfe35eba79a897101e1143b8","schema_version":"1.0","event_id":"sha256:651bf4daf9344c977f6b4209437bbe6964de5011dfe35eba79a897101e1143b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:UPV5WAYHEVFKNOH5ET7VYLOE6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A primer on the (2+1) Einstein universe","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Karin Melnick, Thierry Barbot, Todd Drumm, Virginie Charette, William M. Goldman","submitted_at":"2007-06-20T20:17:24Z","abstract_excerpt":"The Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is to develop the synthetic geometry of the Einstein universe in terms of its homogeneous submanifolds and causal structure, with particular emphasis on dimension $2 + 1$, in which there is a rich interplay with symplectic geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3055","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g65DP7Xijz3iF4EwfrTsDXoPDq7iP9ufkCvgTiGY99ETvkOyKR6R5sFlvh529fHUbUtyVjKCl/JR/w7w83OGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:45:04.981658Z"},"content_sha256":"d6920032edf4dd6736dc721d26763c092b02541c6108a9c37809e326cdcca8f8","schema_version":"1.0","event_id":"sha256:d6920032edf4dd6736dc721d26763c092b02541c6108a9c37809e326cdcca8f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPV5WAYHEVFKNOH5ET7VYLOE6N/bundle.json","state_url":"https://pith.science/pith/UPV5WAYHEVFKNOH5ET7VYLOE6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPV5WAYHEVFKNOH5ET7VYLOE6N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T17:45:04Z","links":{"resolver":"https://pith.science/pith/UPV5WAYHEVFKNOH5ET7VYLOE6N","bundle":"https://pith.science/pith/UPV5WAYHEVFKNOH5ET7VYLOE6N/bundle.json","state":"https://pith.science/pith/UPV5WAYHEVFKNOH5ET7VYLOE6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPV5WAYHEVFKNOH5ET7VYLOE6N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UPV5WAYHEVFKNOH5ET7VYLOE6N","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":"12d459c29aeb2ff818626000b7bea83b7ecfdd23266f57762a841ff42ddd46b3","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-06-20T20:17:24Z","title_canon_sha256":"48bbc3a389dec508ea56445952d6710880dae9f9b9b3493f99117458714449f8"},"schema_version":"1.0","source":{"id":"0706.3055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3055","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3055v1","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3055","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"pith_short_12","alias_value":"UPV5WAYHEVFK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UPV5WAYHEVFKNOH5","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UPV5WAYH","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d6920032edf4dd6736dc721d26763c092b02541c6108a9c37809e326cdcca8f8","target":"graph","created_at":"2026-05-18T04:18:35Z","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 Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is to develop the synthetic geometry of the Einstein universe in terms of its homogeneous submanifolds and causal structure, with particular emphasis on dimension $2 + 1$, in which there is a rich interplay with symplectic geometry.","authors_text":"Karin Melnick, Thierry Barbot, Todd Drumm, Virginie Charette, William M. Goldman","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-06-20T20:17:24Z","title":"A primer on the (2+1) Einstein universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3055","kind":"arxiv","version":1},"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":"sha256:651bf4daf9344c977f6b4209437bbe6964de5011dfe35eba79a897101e1143b8","target":"record","created_at":"2026-05-18T04:18:35Z","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":"12d459c29aeb2ff818626000b7bea83b7ecfdd23266f57762a841ff42ddd46b3","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-06-20T20:17:24Z","title_canon_sha256":"48bbc3a389dec508ea56445952d6710880dae9f9b9b3493f99117458714449f8"},"schema_version":"1.0","source":{"id":"0706.3055","kind":"arxiv","version":1}},"canonical_sha256":"a3ebdb0307254aa6b8fd24ff5c2dc4f367dcf2c96dba3b341f7bd63426a548b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3ebdb0307254aa6b8fd24ff5c2dc4f367dcf2c96dba3b341f7bd63426a548b4","first_computed_at":"2026-05-18T04:18:35.123228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:35.123228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pWZhCWZ7hY4v5STX5pIiqW5qfe3yftt2cYZVqPuVzWeEiofZnlpr5TwSFIWvCqHxcvFug5mNteU150VgzcsaBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:35.123822Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.3055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:651bf4daf9344c977f6b4209437bbe6964de5011dfe35eba79a897101e1143b8","sha256:d6920032edf4dd6736dc721d26763c092b02541c6108a9c37809e326cdcca8f8"],"state_sha256":"4f19ce3f5d7f703e73903f47b506198ba4112691f0b687d3193cb1d3c98128d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HnsG6boAWsGXAdEhH0OF1ibj7ZlEd9GDFcnvDRNkzy0CjrWv0MsdU78oqxXYNz5jJc63V7TeBO98oqi9FAuBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:45:04.983632Z","bundle_sha256":"fbb3ecc1e4d6ff53eb2f88b7a44b3a036ecadcff17f1e043445f5b9d62634ef8"}}