{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2E7KLP7ZKUGU7DDLBCFBMF43XS","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":"dbadd5351e64075c7b7e2ea9ea8b6290fd5d8890bb36d5a8e3bfd554c16771c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-17T12:41:01Z","title_canon_sha256":"6b516745a73dd1142294687838c4116c37dee515839588bc389e6f292e3336ee"},"schema_version":"1.0","source":{"id":"1905.07404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07404","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07404v1","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07404","created_at":"2026-05-17T23:45:51Z"},{"alias_kind":"pith_short_12","alias_value":"2E7KLP7ZKUGU","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2E7KLP7ZKUGU7DDL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2E7KLP7Z","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:7ec269cfcb31c43554d5a59f993f455eabbf47aa997c7eaa15b925f76d573a44","target":"graph","created_at":"2026-05-17T23:45:51Z","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":"Let $A=[a_{ij}]\\in O_3(\\mathbb{R})$. We give several different proofs of the fact that the vector $$ V:=\\left[\\begin{array}{ccc} \\displaystyle \\frac{1}{a_{23}+a_{32}} & \\displaystyle \\frac{1}{a_{13}+a_{31}} & \\displaystyle \\frac{1}{a_{12}+a_{21}} \\end{array}\\right]^T, $$ if it exists, is an eigenvector of $A$ corresponding to the eigenvalue $1$.","authors_text":"Amol Sasane, Victor Ufnarovski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-17T12:41:01Z","title":"Eigenvector of a matrix in $SO_3(\\mathbb{R})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07404","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:dc321dc5962c683a6dee831d8dc24bd6a6b5520c499c66b27ee72dc8aabc5d27","target":"record","created_at":"2026-05-17T23:45:51Z","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":"dbadd5351e64075c7b7e2ea9ea8b6290fd5d8890bb36d5a8e3bfd554c16771c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2019-05-17T12:41:01Z","title_canon_sha256":"6b516745a73dd1142294687838c4116c37dee515839588bc389e6f292e3336ee"},"schema_version":"1.0","source":{"id":"1905.07404","kind":"arxiv","version":1}},"canonical_sha256":"d13ea5bff9550d4f8c6b088a16179bbcad1a0a40bfdc8e0c99818bf16a3d2432","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d13ea5bff9550d4f8c6b088a16179bbcad1a0a40bfdc8e0c99818bf16a3d2432","first_computed_at":"2026-05-17T23:45:51.392125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:51.392125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mYlU66oz5XERL89uWdID5b5P+CbkJcgTHhIQJmQIMOsY6xxVi2ws9AwA/QRg7vgOxoRwn1A2ca2PalX7R1EbCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:51.392661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc321dc5962c683a6dee831d8dc24bd6a6b5520c499c66b27ee72dc8aabc5d27","sha256:7ec269cfcb31c43554d5a59f993f455eabbf47aa997c7eaa15b925f76d573a44"],"state_sha256":"85f36b888ee144571bef1d5dca08a7a5dc84b3fcdd77afc9060a3b6ba34d4ddd"}