{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6TFOSXIVYSYYA6DJEQKHCWQDXI","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":"61a66303267dc480f8e7644e3c3e8661bef3c9cd08cff7b13fac605c9f100124","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-08T20:10:34Z","title_canon_sha256":"b7656bac284194efa2f832b0478979b65c2ee092e11db61b4c3e04a0af47758d"},"schema_version":"1.0","source":{"id":"1612.02791","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02791","created_at":"2026-05-18T00:26:18Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02791v2","created_at":"2026-05-18T00:26:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02791","created_at":"2026-05-18T00:26:18Z"},{"alias_kind":"pith_short_12","alias_value":"6TFOSXIVYSYY","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6TFOSXIVYSYYA6DJ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6TFOSXIV","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:e49fd50e8e99fefc4fc3e7850d1455e5bb318629c3798308bae009c422f930cd","target":"graph","created_at":"2026-05-18T00:26:18Z","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 unitary correlation sets defined by the first author in conjunction with tensor products of $\\mathcal{U}_{nc}(n)$ are further studied. We show that Connes' embedding problem is equivalent to deciding whether or not two smaller versions of the unitary correlation sets are equal. Moreover, we obtain the result that Connes' embedding problem is equivalent to deciding whether or not two cross norms on $M_n \\otimes M_n$ are equal for all $n \\geq 2$.","authors_text":"Samuel J. Harris, Vern I. Paulsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-08T20:10:34Z","title":"Unitary Correlation Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02791","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":"sha256:4741164173c24e182212099d8c56078fcb73c5426015ea97cbf0a0f6dd88b735","target":"record","created_at":"2026-05-18T00:26:18Z","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":"61a66303267dc480f8e7644e3c3e8661bef3c9cd08cff7b13fac605c9f100124","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-08T20:10:34Z","title_canon_sha256":"b7656bac284194efa2f832b0478979b65c2ee092e11db61b4c3e04a0af47758d"},"schema_version":"1.0","source":{"id":"1612.02791","kind":"arxiv","version":2}},"canonical_sha256":"f4cae95d15c4b18078692414715a03ba07578f8048da3e8d60ecde45b6c99eec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4cae95d15c4b18078692414715a03ba07578f8048da3e8d60ecde45b6c99eec","first_computed_at":"2026-05-18T00:26:18.436959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:18.436959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"55gTzMHE5FjG5gU/Rm8Z5EXMTbemFMQoM42QaEeeimgkP2OfoUbIKhe6VK9okQxlHg8n/eJNKbY6Ax3fVVJPAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:18.437571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02791","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4741164173c24e182212099d8c56078fcb73c5426015ea97cbf0a0f6dd88b735","sha256:e49fd50e8e99fefc4fc3e7850d1455e5bb318629c3798308bae009c422f930cd"],"state_sha256":"7f57cb1a18c569c7f8b7689830b1c308ad3ad130aba89b29bbcdcc8be207a9d8"}