{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Z5654JFO6Z6Y7E2HP5PBALTIQR","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":"6b7887e13ca871749f34e3c335d89c376f62cf008e5542fb0b645d0c623082fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-20T14:17:56Z","title_canon_sha256":"7a3c16d59e5f3cf0aa50d74f481d5592f33d4445194c1996d2daafc19eeeb411"},"schema_version":"1.0","source":{"id":"2606.22058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22058","created_at":"2026-06-23T02:13:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22058v1","created_at":"2026-06-23T02:13:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22058","created_at":"2026-06-23T02:13:06Z"},{"alias_kind":"pith_short_12","alias_value":"Z5654JFO6Z6Y","created_at":"2026-06-23T02:13:06Z"},{"alias_kind":"pith_short_16","alias_value":"Z5654JFO6Z6Y7E2H","created_at":"2026-06-23T02:13:06Z"},{"alias_kind":"pith_short_8","alias_value":"Z5654JFO","created_at":"2026-06-23T02:13:06Z"}],"graph_snapshots":[{"event_id":"sha256:f66b9f0b730182afb94fefb70b046b6bf44a77ab537c82b4596eafc587d8e350","target":"graph","created_at":"2026-06-23T02:13:06Z","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/2606.22058/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The recent work of Greaves, Jing, and Zhu gives an operator construction for the $t$-Schur functions and the $t$-Schur measure. Motivated by their construction, we consider the same type of vertex operator on the odd power-sum ring. Its Fourier modes generate a family of symmetric functions indexed by strict partitions, which we call shifted $t$-Schur functions. These functions specialize to Schur $Q$-functions at $t=0$. We derive a two-row formula, a Pfaffian Giambelli formula, a Cauchy identity, and a finite shifted Gessel-type formula. This note is intended as a first step toward further st","authors_text":"S.-J. Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-20T14:17:56Z","title":"A Modified Greaves--Jing--Zhu Operator and a Shifted $t$-Gessel Formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22058","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":"sha256:15364ac22593d9b0a87933d9fade22ae9dd3ffe76fcd3b68aaed27cdbf27f4f8","target":"record","created_at":"2026-06-23T02:13:06Z","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":"6b7887e13ca871749f34e3c335d89c376f62cf008e5542fb0b645d0c623082fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-20T14:17:56Z","title_canon_sha256":"7a3c16d59e5f3cf0aa50d74f481d5592f33d4445194c1996d2daafc19eeeb411"},"schema_version":"1.0","source":{"id":"2606.22058","kind":"arxiv","version":1}},"canonical_sha256":"cf7dde24aef67d8f93477f5e102e688462ed02eb4879441aaed2ec5b8a5c2af1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf7dde24aef67d8f93477f5e102e688462ed02eb4879441aaed2ec5b8a5c2af1","first_computed_at":"2026-06-23T02:13:06.653342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:06.653342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z6qbBK6N8JAYfUKJZHj4B3o9ncLNftpkKfGvdQryxy2pSdHVjO/EagWm+y7bQ2gwmgDZcu3MGPaeSl7oEwJcBQ==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:06.653727Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15364ac22593d9b0a87933d9fade22ae9dd3ffe76fcd3b68aaed27cdbf27f4f8","sha256:f66b9f0b730182afb94fefb70b046b6bf44a77ab537c82b4596eafc587d8e350"],"state_sha256":"f107dd2600ead35a1c92f62721eff856557a4190c2c8b97057365cbb10bf8966"}