{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5Y6ONYRYO77ISB4S46XYZJLLYL","short_pith_number":"pith:5Y6ONYRY","canonical_record":{"source":{"id":"2504.06936","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-09T14:41:20Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ac65de854624e154874312d0c4ecabc588b255eb7bc36b0a277e0f85153c3d81","abstract_canon_sha256":"83eb412029aca032978ac7bbdae11f7dea2fc9e0225a84ebcb66fddd1dc631ee"},"schema_version":"1.0"},"canonical_sha256":"ee3ce6e23877fe890792e7af8ca56bc2ef873f8f6a37ae33effe4cc4b65658dc","source":{"kind":"arxiv","id":"2504.06936","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.06936","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"2504.06936v1","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.06936","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"5Y6ONYRYO77I","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"pith_short_16","alias_value":"5Y6ONYRYO77ISB4S","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"pith_short_8","alias_value":"5Y6ONYRY","created_at":"2026-07-05T10:46:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5Y6ONYRYO77ISB4S46XYZJLLYL","target":"record","payload":{"canonical_record":{"source":{"id":"2504.06936","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-09T14:41:20Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ac65de854624e154874312d0c4ecabc588b255eb7bc36b0a277e0f85153c3d81","abstract_canon_sha256":"83eb412029aca032978ac7bbdae11f7dea2fc9e0225a84ebcb66fddd1dc631ee"},"schema_version":"1.0"},"canonical_sha256":"ee3ce6e23877fe890792e7af8ca56bc2ef873f8f6a37ae33effe4cc4b65658dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:46:48.820872Z","signature_b64":"fLxGLS2aKIrxbQ8DLx1ZG6p16uGoGv3HMyZx8Hf+6ds7zAyQiQoeQD0XEe6F4RqcjYazRTtVOi1YE/g9iKlQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee3ce6e23877fe890792e7af8ca56bc2ef873f8f6a37ae33effe4cc4b65658dc","last_reissued_at":"2026-07-05T10:46:48.820413Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:46:48.820413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.06936","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vtWYCIUHfNDV/JWiR8wKaxXYe+L6y3Qg/+1aje0mVnhpDhTjpBBecsvU88oLfyXGFAZRR3pUR9C1TCt2W1hkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:44:57.421425Z"},"content_sha256":"a933ac0c86afe871424a92f020ef576cb430f6120538474f3e253f330022a241","schema_version":"1.0","event_id":"sha256:a933ac0c86afe871424a92f020ef576cb430f6120538474f3e253f330022a241"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5Y6ONYRYO77ISB4S46XYZJLLYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Macdonald expansions of $q$-chromatic symmetric functions and the Stanley-Stembridge Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Anton Mellit, Joshua Jeishing Wen, Kevin Weigl, Marino Romero, Sean T. Griffin","submitted_at":"2025-04-09T14:41:20Z","abstract_excerpt":"The Stanley-Stembridge conjecture asserts that the chromatic symmetric function of a $(3+1)$-free graph is $e$-positive. Recently, Hikita proved this conjecture by giving an explicit $e$-expansion of the Shareshian-Wachs $q$-chromatic refinement for unit interval graphs. Using the $\\mathbb{A}_{q,t}$ algebra, we give an expansion of these $q$-chromatic symmetric functions into Macdonald polynomials. Upon setting $t=1$, we obtain another proof of the Stanley-Stembridge conjecture and rederive Hikita's formula. Upon setting $t=0$, we obtain an expansion into Hall-Littlewood symmetric functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06936","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/2504.06936/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZwZj3ANw7WV1ypX0u1gOeR8diDwBE8TrClLsvGaDrae3EARtwuK0fRO7K47Xo2xjY3XQD1bQYmZm+dhyT/yAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:44:57.422299Z"},"content_sha256":"3c1bb6f952ec4e3cd0b706771d2016f4b1202ef6334ef077624fce0bd31a3069","schema_version":"1.0","event_id":"sha256:3c1bb6f952ec4e3cd0b706771d2016f4b1202ef6334ef077624fce0bd31a3069"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Y6ONYRYO77ISB4S46XYZJLLYL/bundle.json","state_url":"https://pith.science/pith/5Y6ONYRYO77ISB4S46XYZJLLYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Y6ONYRYO77ISB4S46XYZJLLYL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T22:44:57Z","links":{"resolver":"https://pith.science/pith/5Y6ONYRYO77ISB4S46XYZJLLYL","bundle":"https://pith.science/pith/5Y6ONYRYO77ISB4S46XYZJLLYL/bundle.json","state":"https://pith.science/pith/5Y6ONYRYO77ISB4S46XYZJLLYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Y6ONYRYO77ISB4S46XYZJLLYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5Y6ONYRYO77ISB4S46XYZJLLYL","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":"83eb412029aca032978ac7bbdae11f7dea2fc9e0225a84ebcb66fddd1dc631ee","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-09T14:41:20Z","title_canon_sha256":"ac65de854624e154874312d0c4ecabc588b255eb7bc36b0a277e0f85153c3d81"},"schema_version":"1.0","source":{"id":"2504.06936","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.06936","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"2504.06936v1","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.06936","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"5Y6ONYRYO77I","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"pith_short_16","alias_value":"5Y6ONYRYO77ISB4S","created_at":"2026-07-05T10:46:48Z"},{"alias_kind":"pith_short_8","alias_value":"5Y6ONYRY","created_at":"2026-07-05T10:46:48Z"}],"graph_snapshots":[{"event_id":"sha256:3c1bb6f952ec4e3cd0b706771d2016f4b1202ef6334ef077624fce0bd31a3069","target":"graph","created_at":"2026-07-05T10:46:48Z","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/2504.06936/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Stanley-Stembridge conjecture asserts that the chromatic symmetric function of a $(3+1)$-free graph is $e$-positive. Recently, Hikita proved this conjecture by giving an explicit $e$-expansion of the Shareshian-Wachs $q$-chromatic refinement for unit interval graphs. Using the $\\mathbb{A}_{q,t}$ algebra, we give an expansion of these $q$-chromatic symmetric functions into Macdonald polynomials. Upon setting $t=1$, we obtain another proof of the Stanley-Stembridge conjecture and rederive Hikita's formula. Upon setting $t=0$, we obtain an expansion into Hall-Littlewood symmetric functions.","authors_text":"Anton Mellit, Joshua Jeishing Wen, Kevin Weigl, Marino Romero, Sean T. Griffin","cross_cats":["math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-09T14:41:20Z","title":"On Macdonald expansions of $q$-chromatic symmetric functions and the Stanley-Stembridge Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06936","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:a933ac0c86afe871424a92f020ef576cb430f6120538474f3e253f330022a241","target":"record","created_at":"2026-07-05T10:46:48Z","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":"83eb412029aca032978ac7bbdae11f7dea2fc9e0225a84ebcb66fddd1dc631ee","cross_cats_sorted":["math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-09T14:41:20Z","title_canon_sha256":"ac65de854624e154874312d0c4ecabc588b255eb7bc36b0a277e0f85153c3d81"},"schema_version":"1.0","source":{"id":"2504.06936","kind":"arxiv","version":1}},"canonical_sha256":"ee3ce6e23877fe890792e7af8ca56bc2ef873f8f6a37ae33effe4cc4b65658dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee3ce6e23877fe890792e7af8ca56bc2ef873f8f6a37ae33effe4cc4b65658dc","first_computed_at":"2026-07-05T10:46:48.820413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:46:48.820413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fLxGLS2aKIrxbQ8DLx1ZG6p16uGoGv3HMyZx8Hf+6ds7zAyQiQoeQD0XEe6F4RqcjYazRTtVOi1YE/g9iKlQCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:46:48.820872Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.06936","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a933ac0c86afe871424a92f020ef576cb430f6120538474f3e253f330022a241","sha256:3c1bb6f952ec4e3cd0b706771d2016f4b1202ef6334ef077624fce0bd31a3069"],"state_sha256":"bad0bd4063f485d1fb42794253842dcfc5fccb70c561296ec8f47a1f27082478"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VlWONUpajebCn+lgCDjdXUfvBBbZysomEZ2KxoZ07wLh5szF1NaA7X3IxySQ+tkFAzYUssO9a4dFtuMpvU3pAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T22:44:57.449078Z","bundle_sha256":"733d8c3edc97c0f821526696c6af1c956e54232395fa1cd21b61478668afd1b4"}}