{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EFQWDUGVISOPAB7F2ZWH2BANKN","merge_version":"pith-open-graph-merge-v1","event_count":4,"valid_event_count":4,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"eff5dd737fb22d49f83faea1cae8d7f5f9660d4c41c3f874f2f74f902c97c52d","cross_cats_sorted":["math.AG","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-05-19T17:15:49Z","title_canon_sha256":"133aef1e94781b39d41e636ee6df72dc4a7b1160a87babf43747f47f436b45e2"},"schema_version":"1.0","source":{"id":"2605.20131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20131","created_at":"2026-05-20T02:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20131v1","created_at":"2026-05-20T02:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20131","created_at":"2026-05-20T02:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"EFQWDUGVISOP","created_at":"2026-05-20T02:06:03Z"},{"alias_kind":"pith_short_16","alias_value":"EFQWDUGVISOPAB7F","created_at":"2026-05-20T02:06:03Z"},{"alias_kind":"pith_short_8","alias_value":"EFQWDUGV","created_at":"2026-05-20T02:06:03Z"}],"graph_snapshots":[{"event_id":"sha256:65836ff34762e2403874d69e8c530942a5536d318a4be4170deaeb4520c5ce5a","target":"graph","created_at":"2026-05-20T02:06:03Z","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/2605.20131/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any connected complex reductive group $G$ and element $z$ of its Weyl group $W$, we use work of Lusztig and Abreu-Nigro to compute the graded $W$-character of the intersection cohomology of any closed Lusztig variety for $z$ over the regular semisimple locus of $G$. We relate the resulting formula to unipotent Lusztig varieties, giving a new geometric model for unicellular LLT polynomials. We then consider Laurent polynomials $\\alpha_{\\psi, G}^z$ indexed by irreducible characters $\\psi$, encoding how our formula decomposes into ungraded characters arising from the Springer theory of $G$. F","authors_text":"Minh-T\\^am Quang Trinh","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-05-19T17:15:49Z","title":"Haiman's Conjecture and Springer's Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20131","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:e70c9bf4afb89158be21f8510ccaa151acd07666b66cd13c6bfcb892207e5e0f","target":"record","created_at":"2026-05-20T02:06:03Z","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":"eff5dd737fb22d49f83faea1cae8d7f5f9660d4c41c3f874f2f74f902c97c52d","cross_cats_sorted":["math.AG","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-05-19T17:15:49Z","title_canon_sha256":"133aef1e94781b39d41e636ee6df72dc4a7b1160a87babf43747f47f436b45e2"},"schema_version":"1.0","source":{"id":"2605.20131","kind":"arxiv","version":1}},"canonical_sha256":"216161d0d5449cf007e5d66c7d040d5372400d680b1fc5c5257bebf913aa8f45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"216161d0d5449cf007e5d66c7d040d5372400d680b1fc5c5257bebf913aa8f45","first_computed_at":"2026-05-20T02:06:03.485160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T02:06:03.485160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qn3TF1oC3VPR+lYfBM4e9ZtRnbPf14qubjdSQcSG+jSo+A8ZxK/tg7t3Z9KwG3Gi2JIXCGHeSHBe6Z5Bye3wAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T02:06:03.485945Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20131","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:b199ae2ce54fb621500fe854fc4a7239fd94b697ac4acc7c22a57825643ed26c","sha256:f6e3314cccca69cad8fc27895f22a19f08d3ed5145dcb31be6a7d023da02cfa6"]}],"invalid_events":[],"applied_event_ids":["sha256:e70c9bf4afb89158be21f8510ccaa151acd07666b66cd13c6bfcb892207e5e0f","sha256:65836ff34762e2403874d69e8c530942a5536d318a4be4170deaeb4520c5ce5a"],"state_sha256":"2a1a67b2befca945be12d7a944ac6a449e75797258251cf821da55aa1d79b498"}