{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GCQOJZY7IVTIG7QOLTP6VBC5TK","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":"4f219d40feafa308b7f8ade57397470d76ffbc4e435d8c7ca72ac380cace67ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-04-12T08:17:45Z","title_canon_sha256":"519981b783e6518330800dccbe43f861fdfcca208987722bc60bcb4adee0ac03"},"schema_version":"1.0","source":{"id":"2504.09123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09123","created_at":"2026-07-05T10:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09123v1","created_at":"2026-07-05T10:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09123","created_at":"2026-07-05T10:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"GCQOJZY7IVTI","created_at":"2026-07-05T10:48:04Z"},{"alias_kind":"pith_short_16","alias_value":"GCQOJZY7IVTIG7QO","created_at":"2026-07-05T10:48:04Z"},{"alias_kind":"pith_short_8","alias_value":"GCQOJZY7","created_at":"2026-07-05T10:48:04Z"}],"graph_snapshots":[{"event_id":"sha256:1c2aea1f1acd2a628581c017bfcdd5ff6d150b37f92ebb3dffdde78554dee674","target":"graph","created_at":"2026-07-05T10:48:04Z","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/2504.09123/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the symmetric functions \\( g_{\\mm,k}(x;q) \\), introduced by\n  Abreu and Nigro for a Hessenberg function \\( \\mm \\) and a positive\n  integer \\( k \\), which refine the chromatic symmetric function.\n  Building on Hikita's recent breakthrough on the Stanley--Stembridge\n  conjecture, we prove the \\( e \\)-positivity of \\( g_{\\mm,k}(x;1) \\),\n  refining Hikita's result. We also provide a Schur expansion of the\n  sum \\( \\sum_{k=1}^n e_k(x) g_{\\mm,n-k}(x;q) \\) in terms of\n  \\( P \\)-tableaux with 1 in the upper-left corner. We introduce a\n  restricted version of the modular law as our main tool. ","authors_text":"Byung-Hak Hwang, Donghyun Kim, Jaeseong Oh, Jang Soo Kim, JiSun Huh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-04-12T08:17:45Z","title":"Refinement of Hikita's $e$-positivity theorem via Abreu--Nigro's $g$-functions and restricted modular law"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09123","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:bca935179c8c22b4a9f1a74b46b02176a59371243150b1052363b433e496bd0b","target":"record","created_at":"2026-07-05T10:48:04Z","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":"4f219d40feafa308b7f8ade57397470d76ffbc4e435d8c7ca72ac380cace67ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-04-12T08:17:45Z","title_canon_sha256":"519981b783e6518330800dccbe43f861fdfcca208987722bc60bcb4adee0ac03"},"schema_version":"1.0","source":{"id":"2504.09123","kind":"arxiv","version":1}},"canonical_sha256":"30a0e4e71f4566837e0e5cdfea845d9a8d8f2e68fed58511f03b4317e8ae1875","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30a0e4e71f4566837e0e5cdfea845d9a8d8f2e68fed58511f03b4317e8ae1875","first_computed_at":"2026-07-05T10:48:04.582612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:48:04.582612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JMDTU+CfJfT8QMsxCZvV2Qhs0UMvVsB6XRic/bLbA3vIUjqhe1wP4bo8Hu13xKLufiACQ7T3MPQUCV1bZ8sYBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:48:04.583035Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.09123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bca935179c8c22b4a9f1a74b46b02176a59371243150b1052363b433e496bd0b","sha256:1c2aea1f1acd2a628581c017bfcdd5ff6d150b37f92ebb3dffdde78554dee674"],"state_sha256":"cd2e847591a66df8270e47808bcc518c541cd6be09e19682dba6289f27d7c659"}