{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WNU4UEP4IEGLYLGM3JEWJRYPCZ","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":"cf9d34c86c34709aef6b2a203c70c3f8099b25197722ac912cc86a9ef0f3d3f9","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-22T11:12:23Z","title_canon_sha256":"c2d187bf9c2ed0f9862da8efb58b28a3b3c39f84ea17e2d154f5ec35e37d18c4"},"schema_version":"1.0","source":{"id":"1812.09503","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09503","created_at":"2026-05-17T23:46:29Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09503v2","created_at":"2026-05-17T23:46:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09503","created_at":"2026-05-17T23:46:29Z"},{"alias_kind":"pith_short_12","alias_value":"WNU4UEP4IEGL","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WNU4UEP4IEGLYLGM","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WNU4UEP4","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:67d2a7f7caa46745fe06bc1078b0df83770c6f9f02ca8653baf8a7e9fb258b15","target":"graph","created_at":"2026-05-17T23:46:29Z","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":"In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian-Wachs conjecture, which links the Stanley-Stembridge conjecture in combinatorics to the geometry of Hessenberg varieties through Tymoczko's permutation group action on the cohomology ring of regular semisimple Hessenberg varieties. In previous work, the authors exploited this connection to prove a refined (graded) version of the Stanley-Stembridge conjecture in a special case. In this manuscript, we derive a new set of linear relations satisfied by the multiplicities of certain permutation representations in Tymocz","authors_text":"Martha Precup, Megumi Harada","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-22T11:12:23Z","title":"Upper-triangular linear relations on multiplicities and the Stanley-Stembridge conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09503","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":"sha256:25238e52d9103e1f05f60759afc6d844a350f7a03cc7db6bdde1a351b567b954","target":"record","created_at":"2026-05-17T23:46:29Z","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":"cf9d34c86c34709aef6b2a203c70c3f8099b25197722ac912cc86a9ef0f3d3f9","cross_cats_sorted":["math.AG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-22T11:12:23Z","title_canon_sha256":"c2d187bf9c2ed0f9862da8efb58b28a3b3c39f84ea17e2d154f5ec35e37d18c4"},"schema_version":"1.0","source":{"id":"1812.09503","kind":"arxiv","version":2}},"canonical_sha256":"b369ca11fc410cbc2cccda4964c70f1660c7ffca30d15f05b1bd1eec5735ab09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b369ca11fc410cbc2cccda4964c70f1660c7ffca30d15f05b1bd1eec5735ab09","first_computed_at":"2026-05-17T23:46:29.227002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:29.227002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WAfWwhLS5YpSYGZfWA63hSnn+F+lHzDINrWN97A8riizGt+OYrF4MMhKFhCBiO0WeLNVAzB2Az6CmHAOYLFhAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:29.227647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09503","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25238e52d9103e1f05f60759afc6d844a350f7a03cc7db6bdde1a351b567b954","sha256:67d2a7f7caa46745fe06bc1078b0df83770c6f9f02ca8653baf8a7e9fb258b15"],"state_sha256":"9e7fd9d2a598cb411d359e32fc64c2d4ab9b4f75c99a0233b49292ee7e213674"}