{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GCQOJZY7IVTIG7QOLTP6VBC5TK","short_pith_number":"pith:GCQOJZY7","schema_version":"1.0","canonical_sha256":"30a0e4e71f4566837e0e5cdfea845d9a8d8f2e68fed58511f03b4317e8ae1875","source":{"kind":"arxiv","id":"2504.09123","version":1},"attestation_state":"computed","paper":{"title":"Refinement of Hikita's $e$-positivity theorem via Abreu--Nigro's $g$-functions and restricted modular law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Byung-Hak Hwang, Donghyun Kim, Jaeseong Oh, Jang Soo Kim, JiSun Huh","submitted_at":"2025-04-12T08:17:45Z","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. "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2504.09123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-04-12T08:17:45Z","cross_cats_sorted":[],"title_canon_sha256":"519981b783e6518330800dccbe43f861fdfcca208987722bc60bcb4adee0ac03","abstract_canon_sha256":"4f219d40feafa308b7f8ade57397470d76ffbc4e435d8c7ca72ac380cace67ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:48:04.583035Z","signature_b64":"JMDTU+CfJfT8QMsxCZvV2Qhs0UMvVsB6XRic/bLbA3vIUjqhe1wP4bo8Hu13xKLufiACQ7T3MPQUCV1bZ8sYBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30a0e4e71f4566837e0e5cdfea845d9a8d8f2e68fed58511f03b4317e8ae1875","last_reissued_at":"2026-07-05T10:48:04.582612Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:48:04.582612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Refinement of Hikita's $e$-positivity theorem via Abreu--Nigro's $g$-functions and restricted modular law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Byung-Hak Hwang, Donghyun Kim, Jaeseong Oh, Jang Soo Kim, JiSun Huh","submitted_at":"2025-04-12T08:17:45Z","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. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09123","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.09123/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2504.09123","created_at":"2026-07-05T10:48:04.582663+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.09123v1","created_at":"2026-07-05T10:48:04.582663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09123","created_at":"2026-07-05T10:48:04.582663+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCQOJZY7IVTI","created_at":"2026-07-05T10:48:04.582663+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCQOJZY7IVTIG7QO","created_at":"2026-07-05T10:48:04.582663+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCQOJZY7","created_at":"2026-07-05T10:48:04.582663+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.02841","citing_title":"Toward Lower Bounds for Chromatic Symmetric Functions in the Elementary Basis","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK","json":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK.json","graph_json":"https://pith.science/api/pith-number/GCQOJZY7IVTIG7QOLTP6VBC5TK/graph.json","events_json":"https://pith.science/api/pith-number/GCQOJZY7IVTIG7QOLTP6VBC5TK/events.json","paper":"https://pith.science/paper/GCQOJZY7"},"agent_actions":{"view_html":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK","download_json":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK.json","view_paper":"https://pith.science/paper/GCQOJZY7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.09123&json=true","fetch_graph":"https://pith.science/api/pith-number/GCQOJZY7IVTIG7QOLTP6VBC5TK/graph.json","fetch_events":"https://pith.science/api/pith-number/GCQOJZY7IVTIG7QOLTP6VBC5TK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK/action/storage_attestation","attest_author":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK/action/author_attestation","sign_citation":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK/action/citation_signature","submit_replication":"https://pith.science/pith/GCQOJZY7IVTIG7QOLTP6VBC5TK/action/replication_record"}},"created_at":"2026-07-05T10:48:04.582663+00:00","updated_at":"2026-07-05T10:48:04.582663+00:00"}