{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UMGZPUVQSDXPCL4LLO52426R4T","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":"b4dbb8e13ebb32c7f686d5a6dd0cda3c56a22c81da1bdba9809bd06a2aa36a5a","cross_cats_sorted":["math.AG","math.FA","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2025-06-02T12:50:06Z","title_canon_sha256":"119a2578957e185ead1c77eed184bc0994083d5e115b21b9d41bd0035094510d"},"schema_version":"1.0","source":{"id":"2506.01610","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01610","created_at":"2026-07-05T11:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01610v1","created_at":"2026-07-05T11:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01610","created_at":"2026-07-05T11:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"UMGZPUVQSDXP","created_at":"2026-07-05T11:14:16Z"},{"alias_kind":"pith_short_16","alias_value":"UMGZPUVQSDXPCL4L","created_at":"2026-07-05T11:14:16Z"},{"alias_kind":"pith_short_8","alias_value":"UMGZPUVQ","created_at":"2026-07-05T11:14:16Z"}],"graph_snapshots":[{"event_id":"sha256:790f45a8056759c966e4ae627c49bf13475aac359754db28f8042228817a6d1a","target":"graph","created_at":"2026-07-05T11:14:16Z","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/2506.01610/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that Toeplitz operators associated with a Bernstein-Markov measure on a compact complex manifold endowed with a big line bundle form an algebra under composition. As an application, we derive a Szeg\\H{o}-type spectral equidistribution result for this class of operators. A key component of our approach is the off-diagonal asymptotic analysis of the Bergman kernel, also known as the Christoffel-Darboux kernel.","authors_text":"Siarhei Finski","cross_cats":["math.AG","math.FA","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2025-06-02T12:50:06Z","title":"Bernstein-Markov measures and Toeplitz theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01610","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:a7fb8c7725d6dba83ebdac82228b2ee37ba075980b9720957204adcead163c58","target":"record","created_at":"2026-07-05T11:14:16Z","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":"b4dbb8e13ebb32c7f686d5a6dd0cda3c56a22c81da1bdba9809bd06a2aa36a5a","cross_cats_sorted":["math.AG","math.FA","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2025-06-02T12:50:06Z","title_canon_sha256":"119a2578957e185ead1c77eed184bc0994083d5e115b21b9d41bd0035094510d"},"schema_version":"1.0","source":{"id":"2506.01610","kind":"arxiv","version":1}},"canonical_sha256":"a30d97d2b090eef12f8b5bbbae6bd1e4e83aaf75d14e79bcecabbf202bc83605","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a30d97d2b090eef12f8b5bbbae6bd1e4e83aaf75d14e79bcecabbf202bc83605","first_computed_at":"2026-07-05T11:14:16.731360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:14:16.731360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B8JimcgFLLWioycvFQLMQ9EJ8qBfTodC66pPLXTvAIlQ8teXlz0yz5RCxMPaglsjPI4hhnnAb3ybPn579dcaAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:14:16.731900Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01610","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7fb8c7725d6dba83ebdac82228b2ee37ba075980b9720957204adcead163c58","sha256:790f45a8056759c966e4ae627c49bf13475aac359754db28f8042228817a6d1a"],"state_sha256":"9c2ce7d88d9d6b781f77215a65be35fe754710be6fa7ceacf953f3f1fd3c83a1"}