{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5XAT4WL7JQDMBYYWCQD4UFHWSR","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":"ee714e72606aea7f76a03916d2286857fe13424d4417639396be3cbdefc020d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-28T21:31:18Z","title_canon_sha256":"749c8e631368b68688abfe14a67115e864e98ede7e879a087388a0c4bb9448f2"},"schema_version":"1.0","source":{"id":"1508.07353","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07353","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07353v2","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07353","created_at":"2026-05-18T01:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"5XAT4WL7JQDM","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5XAT4WL7JQDMBYYW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5XAT4WL7","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:bfe1a437a721b4d72da3859c4accff711709e325677eab4997ed2d3e6037099a","target":"graph","created_at":"2026-05-18T01:12:19Z","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":"We sharpen the constant in the $KS_2$ conjecture of Weaver \\cite{We}, which was validated by Marcus, Spielman, and Srivastava \\cite{MSS} in their solution of the Kadison--Singer problem. We then apply this result to prove optimal asymptotic bounds on the size of partitions in the Feichtinger conjecture.","authors_text":"Adam W. Marcus, Darrin Speegle, Marcin Bownik, Peter G. Casazza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-28T21:31:18Z","title":"Improved bounds in Weaver and Feichtinger Conjectures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07353","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":"sha256:2af2c65e74f902b32b205cd142ea9bcfa7fbd3573c53058774a77c028f1a9e4f","target":"record","created_at":"2026-05-18T01:12:19Z","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":"ee714e72606aea7f76a03916d2286857fe13424d4417639396be3cbdefc020d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-28T21:31:18Z","title_canon_sha256":"749c8e631368b68688abfe14a67115e864e98ede7e879a087388a0c4bb9448f2"},"schema_version":"1.0","source":{"id":"1508.07353","kind":"arxiv","version":2}},"canonical_sha256":"edc13e597f4c06c0e3161407ca14f6947148099c8e84cdac9f167343b3fbb9f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edc13e597f4c06c0e3161407ca14f6947148099c8e84cdac9f167343b3fbb9f4","first_computed_at":"2026-05-18T01:12:19.985082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:19.985082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bUEad2BSpJ51hoB9ASBws6vE6RivQhupZefBUKKl9NcgyS8U9Oblvibl7Zn/pCUamCMGYJ9yzK4IVOADf2y/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:19.985484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07353","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2af2c65e74f902b32b205cd142ea9bcfa7fbd3573c53058774a77c028f1a9e4f","sha256:bfe1a437a721b4d72da3859c4accff711709e325677eab4997ed2d3e6037099a"],"state_sha256":"5aafb40ddea23558fff46adc480183e5d85948213eed7e28fc37bcfc8feba0c8"}