{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:B2IQHMZE6BAJ6YDKGQWJKSQJS7","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":"95553d6fe68628cc7f8916ff990f33f6c31bfaab859877bb06c5d785524fb673","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-08T01:59:10Z","title_canon_sha256":"9c2416f108f94ea92058009ce437faeef1095fab891eef0d3cfd61df008760f3"},"schema_version":"1.0","source":{"id":"2211.03953","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.03953","created_at":"2026-07-05T05:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"2211.03953v2","created_at":"2026-07-05T05:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.03953","created_at":"2026-07-05T05:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"B2IQHMZE6BAJ","created_at":"2026-07-05T05:14:37Z"},{"alias_kind":"pith_short_16","alias_value":"B2IQHMZE6BAJ6YDK","created_at":"2026-07-05T05:14:37Z"},{"alias_kind":"pith_short_8","alias_value":"B2IQHMZE","created_at":"2026-07-05T05:14:37Z"}],"graph_snapshots":[{"event_id":"sha256:3f55c0f4e1a7953a51811de0375eb3f24b1ce2d253163c09178ad8322b0c2012","target":"graph","created_at":"2026-07-05T05:14:37Z","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/2211.03953/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a $(3+1)$-free poset $P$, we define a hybrid of $P$-tableaux and cylindric tableaux called cylindric $P$-tableaux. We introduce $P$-analogs of cylindric Schur functions, defined by a determinantal formula, and prove that they are the weight generating functions of cylindric $P$-tableaux. We deduce that certain sums of the $e$-expansion coefficients of the chromatic symmetric function $X_{inc(P)}$ are positive. This improves on Gasharov's theorem on the Schur positivity of $X_{inc(P)}$ and gives further evidence for the Stanley-Stembridge conjecture.","authors_text":"Isaiah Siegl","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-08T01:59:10Z","title":"Cylindric $P$-Tableaux for (3+1)-Free Posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.03953","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:f13f0907ee99b34ac47f4db48de2f381d4097cfa19ea3ece9b14242110429d75","target":"record","created_at":"2026-07-05T05:14:37Z","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":"95553d6fe68628cc7f8916ff990f33f6c31bfaab859877bb06c5d785524fb673","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2022-11-08T01:59:10Z","title_canon_sha256":"9c2416f108f94ea92058009ce437faeef1095fab891eef0d3cfd61df008760f3"},"schema_version":"1.0","source":{"id":"2211.03953","kind":"arxiv","version":2}},"canonical_sha256":"0e9103b324f0409f606a342c954a0997cbfe1c60bcbdb217456b37115eb0ead2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e9103b324f0409f606a342c954a0997cbfe1c60bcbdb217456b37115eb0ead2","first_computed_at":"2026-07-05T05:14:37.840095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:14:37.840095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"edhlUo/PWFe9LJJzaUc5j1pz1Ena2qJoj6FE+n8BSjV0Ye4lEhV10JdhYanp0Hi4M8jcozEXDz3HYXwj1ExZDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:14:37.840642Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.03953","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f13f0907ee99b34ac47f4db48de2f381d4097cfa19ea3ece9b14242110429d75","sha256:3f55c0f4e1a7953a51811de0375eb3f24b1ce2d253163c09178ad8322b0c2012"],"state_sha256":"87650793ed4d57b9fd2b1324203d922246d45ebe970275a84ae5ad54c4deb849"}