{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LFU4AYEHJMG7BYI6KGCUYOFFQO","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":"2acc01761dd20e3f842ca832f31f8b4b99f51e7f8c1e5e9f2cb0e6e4daf41260","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-24T10:14:14Z","title_canon_sha256":"fb2ca3ba6c174cf8291e17da514c945a0278700e21ba070d2aeeff2ebf48c44f"},"schema_version":"1.0","source":{"id":"2605.24976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24976","created_at":"2026-05-26T01:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24976v1","created_at":"2026-05-26T01:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24976","created_at":"2026-05-26T01:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"LFU4AYEHJMG7","created_at":"2026-05-26T01:04:08Z"},{"alias_kind":"pith_short_16","alias_value":"LFU4AYEHJMG7BYI6","created_at":"2026-05-26T01:04:08Z"},{"alias_kind":"pith_short_8","alias_value":"LFU4AYEH","created_at":"2026-05-26T01:04:08Z"}],"graph_snapshots":[{"event_id":"sha256:4ba288fb3059af157afe63816a1883b04adbaf91675f74284d0c4233c031ca77","target":"graph","created_at":"2026-05-26T01:04:08Z","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/2605.24976/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a Fredholm determinantal identity for the tilted Toeplitz minor $$ D_{N}^{\\xi,\\theta}(\\varphi):= \\det\\bigl[(\\theta_{i}\\xi_{j}\\varphi)_{i-j}\\bigr]_{i,j=1}^{N}, $$ generalizing the Borodin-Okounkov-Geronimo-Case (BOGC) identity to oblique splittings of the Hardy space. The tilts $\\xi_{j},\\theta_{i}$ enter only through an oblique projection that multiplies the trace-class kernel $K$ inside the Fredholm determinant; the BOGC operator $A=I-K$ constructed from $\\varphi$ is unchanged.\n  Baik-Liao-Liu (arXiv:2603.01964) and Liu-Tripathi (arXiv:2604.24747) have recently shown that the same til","authors_text":"Leonid Petrov","cross_cats":["math.CA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-24T10:14:14Z","title":"A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24976","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":"sha256:75ad98a9498825c5274f398571b08d79cf0bb5080a4ed91ad0142dbe5832ecb0","target":"record","created_at":"2026-05-26T01:04:08Z","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":"2acc01761dd20e3f842ca832f31f8b4b99f51e7f8c1e5e9f2cb0e6e4daf41260","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-24T10:14:14Z","title_canon_sha256":"fb2ca3ba6c174cf8291e17da514c945a0278700e21ba070d2aeeff2ebf48c44f"},"schema_version":"1.0","source":{"id":"2605.24976","kind":"arxiv","version":1}},"canonical_sha256":"5969c060874b0df0e11e51854c38a5838c7b2ab3ad2e57b5a0a737db3b6a2053","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5969c060874b0df0e11e51854c38a5838c7b2ab3ad2e57b5a0a737db3b6a2053","first_computed_at":"2026-05-26T01:04:08.937130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:04:08.937130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8I4NzvbxPFkaMYXgFXO9po3qlrJYvUFhCq8fN4CpJCVGCGhwCsw5Pz4oJAGF9YtpF2qlXe9DNhCwZoZArydpDw==","signature_status":"signed_v1","signed_at":"2026-05-26T01:04:08.937907Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75ad98a9498825c5274f398571b08d79cf0bb5080a4ed91ad0142dbe5832ecb0","sha256:4ba288fb3059af157afe63816a1883b04adbaf91675f74284d0c4233c031ca77"],"state_sha256":"3690fd52e8faf47b7b31906f6b28170fe25ba1308ac5d93d3ac4d887276f3cbc"}