{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CWNWHUKY7IOMTCW2NE34L6BKTV","short_pith_number":"pith:CWNWHUKY","schema_version":"1.0","canonical_sha256":"159b63d158fa1cc98ada6937c5f82a9d5b5862692194c64436107f6fb5413ab6","source":{"kind":"arxiv","id":"1802.00118","version":1},"attestation_state":"computed","paper":{"title":"Continuous frames and the Kadison-Singer problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marcin Bownik","submitted_at":"2018-02-01T01:32:58Z","abstract_excerpt":"In this paper we survey a recent progress on continuous frames inspired by the solution of the Kadison-Singer problem by Marcus, Spielman, and Srivastava. We present an extension of Lyapunov's theorem for discrete frames due to Akemann and Weaver and a similar extension for continuous frames by the author. We also outline a solution of the discretization problem, which was originally posed by Ali, Antoine, and Gazeau, and recently solved by Freeman and Speegle."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1802.00118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-01T01:32:58Z","cross_cats_sorted":[],"title_canon_sha256":"91ebf0b5c1ab845a5dcc80207e794f0d9f276b7f120a86ca9c73a9b6d352fe37","abstract_canon_sha256":"45a4c3d0c2fbc8bc045f1c22120a5d9d71b70f3892c11834718c96aa1f5f48e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:36.749856Z","signature_b64":"c4YAe8dRKq29WWSt1kKkKU2kfG2Y1IEwwPSe9T1I9VgcZpBRp+ddKQKbRaJldOqCFdh4n7K8GNbEDCtKcOdwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"159b63d158fa1cc98ada6937c5f82a9d5b5862692194c64436107f6fb5413ab6","last_reissued_at":"2026-05-18T00:24:36.749394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:36.749394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuous frames and the Kadison-Singer problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marcin Bownik","submitted_at":"2018-02-01T01:32:58Z","abstract_excerpt":"In this paper we survey a recent progress on continuous frames inspired by the solution of the Kadison-Singer problem by Marcus, Spielman, and Srivastava. We present an extension of Lyapunov's theorem for discrete frames due to Akemann and Weaver and a similar extension for continuous frames by the author. We also outline a solution of the discretization problem, which was originally posed by Ali, Antoine, and Gazeau, and recently solved by Freeman and Speegle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00118","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1802.00118","created_at":"2026-05-18T00:24:36.749474+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.00118v1","created_at":"2026-05-18T00:24:36.749474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00118","created_at":"2026-05-18T00:24:36.749474+00:00"},{"alias_kind":"pith_short_12","alias_value":"CWNWHUKY7IOM","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"CWNWHUKY7IOMTCW2","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"CWNWHUKY","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV","json":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV.json","graph_json":"https://pith.science/api/pith-number/CWNWHUKY7IOMTCW2NE34L6BKTV/graph.json","events_json":"https://pith.science/api/pith-number/CWNWHUKY7IOMTCW2NE34L6BKTV/events.json","paper":"https://pith.science/paper/CWNWHUKY"},"agent_actions":{"view_html":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV","download_json":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV.json","view_paper":"https://pith.science/paper/CWNWHUKY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.00118&json=true","fetch_graph":"https://pith.science/api/pith-number/CWNWHUKY7IOMTCW2NE34L6BKTV/graph.json","fetch_events":"https://pith.science/api/pith-number/CWNWHUKY7IOMTCW2NE34L6BKTV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV/action/storage_attestation","attest_author":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV/action/author_attestation","sign_citation":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV/action/citation_signature","submit_replication":"https://pith.science/pith/CWNWHUKY7IOMTCW2NE34L6BKTV/action/replication_record"}},"created_at":"2026-05-18T00:24:36.749474+00:00","updated_at":"2026-05-18T00:24:36.749474+00:00"}