{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:T6PNFHMPJEBWHULTLMO2MOKCVS","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":"c3cd158a79179261b5df27df37264aea3c06cce476954cd075d984614e277ba9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-02T12:43:05Z","title_canon_sha256":"12036f84020e7661c63c3c06ff30b28c235b7f6b8bab817b03c40a160d98b4ae"},"schema_version":"1.0","source":{"id":"2607.02108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02108","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02108v1","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02108","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_12","alias_value":"T6PNFHMPJEBW","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_16","alias_value":"T6PNFHMPJEBWHULT","created_at":"2026-07-03T01:17:42Z"},{"alias_kind":"pith_short_8","alias_value":"T6PNFHMP","created_at":"2026-07-03T01:17:42Z"}],"graph_snapshots":[{"event_id":"sha256:2b2ae1c7dc3671f719100dbb6bd00dcb42c5adec6e99ab591724573b486ff713","target":"graph","created_at":"2026-07-03T01:17:42Z","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/2607.02108/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"At the specialization $t=-q$, $q\\geq0$, the shifted $t$-Schur function associated with the modified odd Greaves--Jing--Zhu operator is $Q_\\lambda[X+qX]$. Instead of merging the two alphabets $X$ and $qX$, we insert an intermediate strict partition between the two corresponding half-vertex operators. This gives a two-color lift of the shifted Schur measure on pairs $\\mu\\subseteq\\lambda$ with weight \\[\n  Q_\\mu(qX)Q_{\\lambda/\\mu}(X)P_\\lambda(Y). \\] We compute the normalization and both marginals, identify an explicit Markov transition kernel, prove a semigroup property, and show that the two colo","authors_text":"S.-J. Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-02T12:43:05Z","title":"A Two-Color Lift of the Shifted $t$-Schur Measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02108","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":"sha256:543415d50d90331bf43b7cbe68609c682fd5aad6a6badca39089270cd26b1b83","target":"record","created_at":"2026-07-03T01:17:42Z","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":"c3cd158a79179261b5df27df37264aea3c06cce476954cd075d984614e277ba9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-02T12:43:05Z","title_canon_sha256":"12036f84020e7661c63c3c06ff30b28c235b7f6b8bab817b03c40a160d98b4ae"},"schema_version":"1.0","source":{"id":"2607.02108","kind":"arxiv","version":1}},"canonical_sha256":"9f9ed29d8f490363d1735b1da63942ac99ec61787271f1478f2b254a03895804","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f9ed29d8f490363d1735b1da63942ac99ec61787271f1478f2b254a03895804","first_computed_at":"2026-07-03T01:17:42.453142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:42.453142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ut2qPp/gh8t4jtUHX+qeREKOUg9/tXVTC2riNAnoANxKzdgDeGFHuElPq0e8kyzgyqbe3XIdboQVcCLKs8eKCA==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:42.453523Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:543415d50d90331bf43b7cbe68609c682fd5aad6a6badca39089270cd26b1b83","sha256:2b2ae1c7dc3671f719100dbb6bd00dcb42c5adec6e99ab591724573b486ff713"],"state_sha256":"f75d3b9511558fd768160c1f098394d9c13b6e1065e95e54e93b88a65401454f"}