{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3HBQSMJRWPYXKJYVCHX37E2TQV","short_pith_number":"pith:3HBQSMJR","canonical_record":{"source":{"id":"1306.4826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-06-20T11:34:52Z","cross_cats_sorted":[],"title_canon_sha256":"4b4f7cabb64b93bffd60ac561d83b24f14d77d5b1f05f5c6cd3f0a472c686176","abstract_canon_sha256":"ffbddc0f8c24c4237d1a5f070162cb2616eb744a33017681e72fc0571598307a"},"schema_version":"1.0"},"canonical_sha256":"d9c3093131b3f175271511efbf93538566ccce1a413dc637e3ff24435fa78f13","source":{"kind":"arxiv","id":"1306.4826","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4826","created_at":"2026-05-18T03:20:21Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4826v1","created_at":"2026-05-18T03:20:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4826","created_at":"2026-05-18T03:20:21Z"},{"alias_kind":"pith_short_12","alias_value":"3HBQSMJRWPYX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3HBQSMJRWPYXKJYV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3HBQSMJR","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3HBQSMJRWPYXKJYVCHX37E2TQV","target":"record","payload":{"canonical_record":{"source":{"id":"1306.4826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-06-20T11:34:52Z","cross_cats_sorted":[],"title_canon_sha256":"4b4f7cabb64b93bffd60ac561d83b24f14d77d5b1f05f5c6cd3f0a472c686176","abstract_canon_sha256":"ffbddc0f8c24c4237d1a5f070162cb2616eb744a33017681e72fc0571598307a"},"schema_version":"1.0"},"canonical_sha256":"d9c3093131b3f175271511efbf93538566ccce1a413dc637e3ff24435fa78f13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:21.557926Z","signature_b64":"j9S6eUyDghv24hPRPVZvxQkYTv34TbC/eiITf2bBYlJG+s5vKw74bog3jK9Bksh0GC7cfTPAmvFQYNwhHJVEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9c3093131b3f175271511efbf93538566ccce1a413dc637e3ff24435fa78f13","last_reissued_at":"2026-05-18T03:20:21.557202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:21.557202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.4826","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":"2026-05-18T03:20:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2I4QjTkeKTyQeJR4ZSIT2l/iFlV0Q1hunwEMUlCEnGVHQgZROARnwervHgZI0DuqLcZWVP2U4q29aw/Qy34OCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:14:39.944435Z"},"content_sha256":"ecb6c98be335a298b6285d825a791478fc9dcb7a7f780b00d4f69dc2161c05a3","schema_version":"1.0","event_id":"sha256:ecb6c98be335a298b6285d825a791478fc9dcb7a7f780b00d4f69dc2161c05a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3HBQSMJRWPYXKJYVCHX37E2TQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embeddings for solutions of Einstein equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"A.A. Sheykin, S.A. Paston","submitted_at":"2013-06-20T11:34:52Z","abstract_excerpt":"We study isometric embeddings of some solutions of the Einstein equations with suffciently high symmetries into a flat ambient space. We briefly describe a method for constructing surfaces with a given symmetry. We discuss all minimal embeddings of the Schwarzschild metric obtained using this method and show how the method can be used to construct all minimal embeddings for the Friedmann models. We classify all the embeddings in terms of realizations of symmetries of the corresponding solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4826","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":"2026-05-18T03:20:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwKHAidiaPj2DSeIjgVehbSV6laRitWS9viliM4FJ727Zp5LT8bBrPPoMcS72hzwncHrt+j51g2jlgOX9laRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:14:39.944782Z"},"content_sha256":"0b803a147b06bf3a1eab77262fc7fcb66d7bd80da0a07c788c541c08d4a635e6","schema_version":"1.0","event_id":"sha256:0b803a147b06bf3a1eab77262fc7fcb66d7bd80da0a07c788c541c08d4a635e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HBQSMJRWPYXKJYVCHX37E2TQV/bundle.json","state_url":"https://pith.science/pith/3HBQSMJRWPYXKJYVCHX37E2TQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HBQSMJRWPYXKJYVCHX37E2TQV/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":"2026-05-28T14:14:39Z","links":{"resolver":"https://pith.science/pith/3HBQSMJRWPYXKJYVCHX37E2TQV","bundle":"https://pith.science/pith/3HBQSMJRWPYXKJYVCHX37E2TQV/bundle.json","state":"https://pith.science/pith/3HBQSMJRWPYXKJYVCHX37E2TQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HBQSMJRWPYXKJYVCHX37E2TQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3HBQSMJRWPYXKJYVCHX37E2TQV","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":"ffbddc0f8c24c4237d1a5f070162cb2616eb744a33017681e72fc0571598307a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-06-20T11:34:52Z","title_canon_sha256":"4b4f7cabb64b93bffd60ac561d83b24f14d77d5b1f05f5c6cd3f0a472c686176"},"schema_version":"1.0","source":{"id":"1306.4826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4826","created_at":"2026-05-18T03:20:21Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4826v1","created_at":"2026-05-18T03:20:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4826","created_at":"2026-05-18T03:20:21Z"},{"alias_kind":"pith_short_12","alias_value":"3HBQSMJRWPYX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3HBQSMJRWPYXKJYV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3HBQSMJR","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:0b803a147b06bf3a1eab77262fc7fcb66d7bd80da0a07c788c541c08d4a635e6","target":"graph","created_at":"2026-05-18T03:20:21Z","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 study isometric embeddings of some solutions of the Einstein equations with suffciently high symmetries into a flat ambient space. We briefly describe a method for constructing surfaces with a given symmetry. We discuss all minimal embeddings of the Schwarzschild metric obtained using this method and show how the method can be used to construct all minimal embeddings for the Friedmann models. We classify all the embeddings in terms of realizations of symmetries of the corresponding solutions.","authors_text":"A.A. Sheykin, S.A. Paston","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-06-20T11:34:52Z","title":"Embeddings for solutions of Einstein equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4826","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:ecb6c98be335a298b6285d825a791478fc9dcb7a7f780b00d4f69dc2161c05a3","target":"record","created_at":"2026-05-18T03:20:21Z","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":"ffbddc0f8c24c4237d1a5f070162cb2616eb744a33017681e72fc0571598307a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-06-20T11:34:52Z","title_canon_sha256":"4b4f7cabb64b93bffd60ac561d83b24f14d77d5b1f05f5c6cd3f0a472c686176"},"schema_version":"1.0","source":{"id":"1306.4826","kind":"arxiv","version":1}},"canonical_sha256":"d9c3093131b3f175271511efbf93538566ccce1a413dc637e3ff24435fa78f13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9c3093131b3f175271511efbf93538566ccce1a413dc637e3ff24435fa78f13","first_computed_at":"2026-05-18T03:20:21.557202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:21.557202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9S6eUyDghv24hPRPVZvxQkYTv34TbC/eiITf2bBYlJG+s5vKw74bog3jK9Bksh0GC7cfTPAmvFQYNwhHJVEAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:21.557926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecb6c98be335a298b6285d825a791478fc9dcb7a7f780b00d4f69dc2161c05a3","sha256:0b803a147b06bf3a1eab77262fc7fcb66d7bd80da0a07c788c541c08d4a635e6"],"state_sha256":"1998f03838ca54608e9f4573e87a1807a2e0796dcc3e4b7aeac6cb028bb74664"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LEtOg2MCkuSlCLV8sw8dv3rzZ6lPGkxx56UgFWQT2oaG+cXmnoRd6CRCzCau1BDN000oJwyxTNyAQujQgOvBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:14:39.946856Z","bundle_sha256":"02fb7709248b9fdc5f1e6041b21a8dd5d00869a90a50c86833d3d68cd83a61a0"}}