{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KAL3A7RB25WEUL6X26ZDYEMIUS","short_pith_number":"pith:KAL3A7RB","schema_version":"1.0","canonical_sha256":"5017b07e21d76c4a2fd7d7b23c1188a4af5273b9fd26674623a7a365f451f604","source":{"kind":"arxiv","id":"2410.12231","version":2},"attestation_state":"computed","paper":{"title":"A geometric realization of the chromatic symmetric function of a unit interval graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Syu Kato","submitted_at":"2024-10-16T04:46:09Z","abstract_excerpt":"Shareshian-Wachs, Brosnan-Chow, and Guay-Pacquet [Adv. Math. ${\\bf 295}$ (2016), ${\\bf 329}$ (2018), arXiv:1601.05498] realized the chromatic (quasi-)symmetric function of a unit interval graph in terms of Hessenberg varieties. Here we exhibit another realization of these chromatic (quasi-)symmetric functions in terms of the Betti cohomology of the variety $\\mathscr X_\\Psi$ defined in [arXiv:2301.00862]. This yields a new inductive combinatorial expression of these chromatic symmetric functions. Based on this, we propose a geometric refinement of the Stanley-Stembridge conjecture, whose validi"},"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":"2410.12231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-10-16T04:46:09Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"0b7d83017a0fee4d738cb1287101a60d6b9dda2ef61a0d78daf5852629ed9b8c","abstract_canon_sha256":"745dde5eabd311e3617dda9da889174032543175576cf496ae71840083f583b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:21:50.536067Z","signature_b64":"1+02Dt6iKe/5gnSEVGnw5TWNNBDGfg+JgxpIG2+Vt4gL1Ji/tS0OCllbh1YtwFqt89m8TUwDsBGrVIh5lwAbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5017b07e21d76c4a2fd7d7b23c1188a4af5273b9fd26674623a7a365f451f604","last_reissued_at":"2026-07-05T09:21:50.535662Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:21:50.535662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A geometric realization of the chromatic symmetric function of a unit interval graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Syu Kato","submitted_at":"2024-10-16T04:46:09Z","abstract_excerpt":"Shareshian-Wachs, Brosnan-Chow, and Guay-Pacquet [Adv. Math. ${\\bf 295}$ (2016), ${\\bf 329}$ (2018), arXiv:1601.05498] realized the chromatic (quasi-)symmetric function of a unit interval graph in terms of Hessenberg varieties. Here we exhibit another realization of these chromatic (quasi-)symmetric functions in terms of the Betti cohomology of the variety $\\mathscr X_\\Psi$ defined in [arXiv:2301.00862]. This yields a new inductive combinatorial expression of these chromatic symmetric functions. Based on this, we propose a geometric refinement of the Stanley-Stembridge conjecture, whose validi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.12231","kind":"arxiv","version":2},"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/2410.12231/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":"2410.12231","created_at":"2026-07-05T09:21:50.535712+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.12231v2","created_at":"2026-07-05T09:21:50.535712+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.12231","created_at":"2026-07-05T09:21:50.535712+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAL3A7RB25WE","created_at":"2026-07-05T09:21:50.535712+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAL3A7RB25WEUL6X","created_at":"2026-07-05T09:21:50.535712+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAL3A7RB","created_at":"2026-07-05T09:21:50.535712+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":24,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS","json":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS.json","graph_json":"https://pith.science/api/pith-number/KAL3A7RB25WEUL6X26ZDYEMIUS/graph.json","events_json":"https://pith.science/api/pith-number/KAL3A7RB25WEUL6X26ZDYEMIUS/events.json","paper":"https://pith.science/paper/KAL3A7RB"},"agent_actions":{"view_html":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS","download_json":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS.json","view_paper":"https://pith.science/paper/KAL3A7RB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.12231&json=true","fetch_graph":"https://pith.science/api/pith-number/KAL3A7RB25WEUL6X26ZDYEMIUS/graph.json","fetch_events":"https://pith.science/api/pith-number/KAL3A7RB25WEUL6X26ZDYEMIUS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS/action/storage_attestation","attest_author":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS/action/author_attestation","sign_citation":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS/action/citation_signature","submit_replication":"https://pith.science/pith/KAL3A7RB25WEUL6X26ZDYEMIUS/action/replication_record"}},"created_at":"2026-07-05T09:21:50.535712+00:00","updated_at":"2026-07-05T09:21:50.535712+00:00"}