{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M7M43H66HBJILNDMCIVEZ7P4HH","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":"9841789e9863709c6fce4b398228a23e4474ea01193fcfd5d06c71f17a925a95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-02-16T11:15:07Z","title_canon_sha256":"4ea600773d18a01f15c378203acac471809668eb6251574c945ee77e995c6899"},"schema_version":"1.0","source":{"id":"1702.04923","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04923","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04923v2","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04923","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"M7M43H66HBJI","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"M7M43H66HBJILNDM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"M7M43H66","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:b963f3733505cd0fa4b685bb3374acaff260f688d62e1767bb2dcb5f54c79310","target":"graph","created_at":"2026-05-18T00:43:45Z","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 present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal equivalence between Minkowski's spacetime and (a region of) the Einstein cylinder is then exploited in order to obtain a knotted, finite energy, radiating solution of the Maxwell equations in flat spacetime. We also discuss similar electromagnetic fields in expanding closed Friedmann models, and compute the matter content of such configurations.","authors_text":"Jaros{\\l}aw Kopi\\'nski, Jos\\'e Nat\\'ario","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-02-16T11:15:07Z","title":"On a remarkable electromagnetic field in the Einstein Universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04923","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":"sha256:6396fd762ed7318773144338e60f31792055899a3cff827a21f864dc4d5ff90e","target":"record","created_at":"2026-05-18T00:43:45Z","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":"9841789e9863709c6fce4b398228a23e4474ea01193fcfd5d06c71f17a925a95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-02-16T11:15:07Z","title_canon_sha256":"4ea600773d18a01f15c378203acac471809668eb6251574c945ee77e995c6899"},"schema_version":"1.0","source":{"id":"1702.04923","kind":"arxiv","version":2}},"canonical_sha256":"67d9cd9fde385285b46c122a4cfdfc39fcc0e723328916608afc0fd68051c460","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67d9cd9fde385285b46c122a4cfdfc39fcc0e723328916608afc0fd68051c460","first_computed_at":"2026-05-18T00:43:45.076080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:45.076080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SgJ9JihQCVLyHiKQ44eqxWW9FsAG7qng9a2NucaLeD7b7O3HbNN5PPBkXpKHel36vjifRnuLLy1qUlM6i6XLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:45.078502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04923","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6396fd762ed7318773144338e60f31792055899a3cff827a21f864dc4d5ff90e","sha256:b963f3733505cd0fa4b685bb3374acaff260f688d62e1767bb2dcb5f54c79310"],"state_sha256":"4a06f3d3aea761ccc62632e7ff9977a0f21c9ca8c981fb6fc6f3e866ba155d48"}