{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZCON5TPDPJYCKSP7MJIOAQ6CZP","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":"a0d007dd8bddb2ca8d314b55587dba14ee78c724f8ba31599d134de27d7286c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-20T15:42:21Z","title_canon_sha256":"42f1903ea20deb49e5dc5e4c1a0f22c02c91bd1204ef61821fd01cf7f377fc03"},"schema_version":"1.0","source":{"id":"1402.5046","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5046","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5046v2","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5046","created_at":"2026-05-18T02:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZCON5TPDPJYC","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCON5TPDPJYCKSP7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCON5TPD","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:0491c5d75ce7fe0d248ec6d11b5672d10fb9bffc323b787b1cc167162a9b03e9","target":"graph","created_at":"2026-05-18T02:57:25Z","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":"For operators on Hilbert spaces of any dimension, we show that equivalence after extension coincides with equivalence after one-sided extension, thus obtaining a proof of their coincidence with Schur coupling. We also provide a concrete description of this equivalence relation in several cases, in particular for compact operators.","authors_text":"Dan Timotin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-20T15:42:21Z","title":"Schur coupling and related equivalence relations for operators on a Hilbert space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5046","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":"sha256:34984ebcc436bf1b89e6a8deb746a04a271e2a19e05092076a7945bd04091c71","target":"record","created_at":"2026-05-18T02:57:25Z","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":"a0d007dd8bddb2ca8d314b55587dba14ee78c724f8ba31599d134de27d7286c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-02-20T15:42:21Z","title_canon_sha256":"42f1903ea20deb49e5dc5e4c1a0f22c02c91bd1204ef61821fd01cf7f377fc03"},"schema_version":"1.0","source":{"id":"1402.5046","kind":"arxiv","version":2}},"canonical_sha256":"c89cdecde37a702549ff6250e043c2cbe84798acd975f9d30d455e7a8f4f7376","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c89cdecde37a702549ff6250e043c2cbe84798acd975f9d30d455e7a8f4f7376","first_computed_at":"2026-05-18T02:57:25.979044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:25.979044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ivKGxXIctQDLG+qAN6eN56D69VNkRJPnVsPWkcLyRY4C/0H749HdZwokXOOL+soCRumhKkiv3Kh6iPkYIzu4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:25.979749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5046","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34984ebcc436bf1b89e6a8deb746a04a271e2a19e05092076a7945bd04091c71","sha256:0491c5d75ce7fe0d248ec6d11b5672d10fb9bffc323b787b1cc167162a9b03e9"],"state_sha256":"0320fac241e3576190cf6561baefec217cdc1023b890760340d6fa0581dcf750"}