{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:B3NEWAXO62QJWUY7SXOZTZAXMH","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":"fdb0df26ac62f386b2414d62aabb9778efc4e8c8aadc2f642ecfabc1d7dadc62","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-14T09:50:20Z","title_canon_sha256":"6060953bda6aa05fc93261a80272879daa0801f14591a5872bbac0ca7d4bdde8"},"schema_version":"1.0","source":{"id":"1609.04195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04195","created_at":"2026-05-18T00:01:44Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04195v2","created_at":"2026-05-18T00:01:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04195","created_at":"2026-05-18T00:01:44Z"},{"alias_kind":"pith_short_12","alias_value":"B3NEWAXO62QJ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B3NEWAXO62QJWUY7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B3NEWAXO","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:73f71e3f4d8fe259936cc2f1dae05ca03e8dfc6e1ae7fee5b98a7873aa6b0595","target":"graph","created_at":"2026-05-18T00:01:44Z","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 adapt the arguments of Marcus, Spielman and Srivastava in their proof of the Kadison-Singer problem to prove improved paving estimates. Working with Anderson's paving formulation of Kadison-Singer instead of Weaver's vector balancing version, we show that the machinery of interlacing polyomials due to Marcus, Spielman and Srivastava works in this setting as well. The relevant expected characteristic polynomials turn out to be related to the so called \"mixed determinants\" that have been carefully studied by Borcea and Branden. This technique allows us to show that any projection with diagona","authors_text":"Jonathan Leake, Mohan Ravichandran","cross_cats":["math.CO","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-14T09:50:20Z","title":"Mixed Determinants and the Kadison-Singer problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04195","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":"sha256:2c32a20cdda1bf83e8bdbefb6261785a037019a45a157ed8a9c46d7e82caaabf","target":"record","created_at":"2026-05-18T00:01:44Z","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":"fdb0df26ac62f386b2414d62aabb9778efc4e8c8aadc2f642ecfabc1d7dadc62","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-14T09:50:20Z","title_canon_sha256":"6060953bda6aa05fc93261a80272879daa0801f14591a5872bbac0ca7d4bdde8"},"schema_version":"1.0","source":{"id":"1609.04195","kind":"arxiv","version":2}},"canonical_sha256":"0eda4b02eef6a09b531f95dd99e41761ee3b3e607ce4a3a4aa6c65cc86183a57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0eda4b02eef6a09b531f95dd99e41761ee3b3e607ce4a3a4aa6c65cc86183a57","first_computed_at":"2026-05-18T00:01:44.031200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:44.031200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UzSCqKcZBlYD4GNr4QXe3sGA1tW2DA/W3q8KVcleSz1bl7QV8AVz9ovS7K2OMRqK7gshR0JdIsSkl1NTgVTABg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:44.031899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c32a20cdda1bf83e8bdbefb6261785a037019a45a157ed8a9c46d7e82caaabf","sha256:73f71e3f4d8fe259936cc2f1dae05ca03e8dfc6e1ae7fee5b98a7873aa6b0595"],"state_sha256":"9c95e4bdf9c4f93d7add93fac30d75ba062c9d8be06673acd3395530a6748d42"}