{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:6XGWCJ3TPAHYH2CFDAOWNLLJLC","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":"4f1699b45d6a43dd3ac5de224a826488b26f39ad43b1100fc5729ccb3f130ec5","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.OA","submitted_at":"2006-04-05T23:26:43Z","title_canon_sha256":"2e2883ab59171be2c874e04870e7f29300d342610479d6da9d6f22e643958392"},"schema_version":"1.0","source":{"id":"math/0604120","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604120","created_at":"2026-07-04T15:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604120v4","created_at":"2026-07-04T15:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604120","created_at":"2026-07-04T15:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"6XGWCJ3TPAHY","created_at":"2026-07-04T15:09:37Z"},{"alias_kind":"pith_short_16","alias_value":"6XGWCJ3TPAHYH2CF","created_at":"2026-07-04T15:09:37Z"},{"alias_kind":"pith_short_8","alias_value":"6XGWCJ3T","created_at":"2026-07-04T15:09:37Z"}],"graph_snapshots":[{"event_id":"sha256:1d94b4e0a8fae81907cf7d05a5913ebd3065f1b2d39b194f8579b77034757c84","target":"graph","created_at":"2026-07-04T15:09:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0604120/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a II$_1$ factor M and a masa A of M, we prove a version of the Schur-Horn Theorem, together with a contractive version. These results are inspired on a recent conjecture of Arveson and Kadison (math.OA/0508482).","authors_text":"M. Argerami, P. Massey","cross_cats":["math.FA"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2006-04-05T23:26:43Z","title":"A Schur-Horn type theorem for II$_1$ factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604120","kind":"arxiv","version":4},"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":"sha256:2ec49d1983c6fb8ed20e74e96ff8adbcd759b39a7e0a5619f108152bbbef982f","target":"record","created_at":"2026-07-04T15:09:37Z","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":"4f1699b45d6a43dd3ac5de224a826488b26f39ad43b1100fc5729ccb3f130ec5","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.OA","submitted_at":"2006-04-05T23:26:43Z","title_canon_sha256":"2e2883ab59171be2c874e04870e7f29300d342610479d6da9d6f22e643958392"},"schema_version":"1.0","source":{"id":"math/0604120","kind":"arxiv","version":4}},"canonical_sha256":"f5cd612773780f83e845181d66ad6958bced1bb9ccd009ee9d36c8b5260110e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5cd612773780f83e845181d66ad6958bced1bb9ccd009ee9d36c8b5260110e5","first_computed_at":"2026-07-04T15:09:37.453912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:09:37.453912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yIODypaPF5M9cfSuXfSKCh3CKjXkZ1YHJCZ0/F5eqXUd6F6+C9/Y9dGX2DSb/GAGcZ2Vux3HXAKWr1/C90UBDg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:09:37.454371Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604120","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ec49d1983c6fb8ed20e74e96ff8adbcd759b39a7e0a5619f108152bbbef982f","sha256:1d94b4e0a8fae81907cf7d05a5913ebd3065f1b2d39b194f8579b77034757c84"],"state_sha256":"490359cf2804511bfe2dbeb2f25a9fb16c97b65769b00966b73aa3914d382a61"}