{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SZEWZS767G7JX3OBARCULX4TX5","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":"19a127729956ddf3580baadda86bb2c784c8c6d9bcdd285cd9b1de9b1b7912e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-09T20:55:54Z","title_canon_sha256":"92430d9c6efdba5b2ef7d7bbe699b1518c3f7caf6df289dfb5ba34b5bffcea0f"},"schema_version":"1.0","source":{"id":"1807.03384","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03384","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03384v1","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03384","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"SZEWZS767G7J","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SZEWZS767G7JX3OB","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SZEWZS76","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:d4a87e9d8695df9fa4f59d9cb6f104cc246fb299bdc032fe60b11ecf6180f8be","target":"graph","created_at":"2026-05-18T00:11:10Z","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 give local axioms that uniquely characterize the crystal-like structure on shifted tableaux developed in a previous paper by Gillespie, Levinson, and Purbhoo. These axioms closely resemble those developed by Stembridge for type A tableau crystals. This axiomatic characterization gives rise to a new method for proving and understanding Schur $Q$-positive expansions in symmetric function theory, just as the Stembridge axiomatic structure provides for ordinary Schur positivity.","authors_text":"Jake Levinson, Maria Gillespie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-09T20:55:54Z","title":"Axioms for shifted tableau crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03384","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":"sha256:73af2b7c7bf1537aa83d744d2cba90027c537dacdca33d5ea46a422afd5da156","target":"record","created_at":"2026-05-18T00:11:10Z","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":"19a127729956ddf3580baadda86bb2c784c8c6d9bcdd285cd9b1de9b1b7912e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-09T20:55:54Z","title_canon_sha256":"92430d9c6efdba5b2ef7d7bbe699b1518c3f7caf6df289dfb5ba34b5bffcea0f"},"schema_version":"1.0","source":{"id":"1807.03384","kind":"arxiv","version":1}},"canonical_sha256":"96496ccbfef9be9bedc1044545df93bf52609fcce87b02a428fba9a73cb0ea9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96496ccbfef9be9bedc1044545df93bf52609fcce87b02a428fba9a73cb0ea9e","first_computed_at":"2026-05-18T00:11:10.597450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:10.597450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WdM+q5majDI1airrexgmi7g0Dt3u8IFdtf/f5u1p1PxwuyvzdC82ofUuUbNBgrNM+GQj/hrnlcLwUhGJ7+zdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:10.598204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73af2b7c7bf1537aa83d744d2cba90027c537dacdca33d5ea46a422afd5da156","sha256:d4a87e9d8695df9fa4f59d9cb6f104cc246fb299bdc032fe60b11ecf6180f8be"],"state_sha256":"70b6be8caadde5cddc4d7c112801b6325966e045bc50d2b7dce724a8839f7cef"}