{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QDAISU77IULMOQCAUMAHFRZSIJ","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":"d34e392e343d0b5234b577818f10513113c882142b7ad4ef942238a6d5e80938","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-04T11:35:39Z","title_canon_sha256":"9c9cb9534d0cc1ba10499a0767e957551b92d776c06500e38180646b504039b6"},"schema_version":"1.0","source":{"id":"2412.03234","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.03234","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2412.03234v6","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.03234","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"QDAISU77IULM","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"QDAISU77IULMOQCA","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"QDAISU77","created_at":"2026-05-28T01:04:25Z"}],"graph_snapshots":[{"event_id":"sha256:ce5bad41270327ef8aec7f3f7abda91a625a3808cb1058787a9b88c524301f78","target":"graph","created_at":"2026-05-28T01:04:25Z","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/2412.03234/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study the mixed Poincar\\'e polynomial of generic $\\mathrm{PGL}_n(\\mathbb{C})$-character stacks with coefficients in some local systems arising from the conjugacy classes of $\\mathrm{PGL}_n(\\mathbb{C})$ which have non-connected stabiliser. We give a conjectural formula that we prove to be true under the Euler specialisation. We then prove that this conjectured formula interpolates the structure coefficients of the two based rings$ \\left(\\mathcal{C}(\\mathrm{PGL}_n(\\mathbb{F}_q)),Loc(\\mathrm{PGL}_n),*\\right)$ and $\\left(\\mathcal{C}(\\mathrm{SL}_n(\\mathbb{F}_q)), CS(\\mathrm{SL}_n),","authors_text":"Emmanuel Letellier, Tommaso Scognamiglio","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-04T11:35:39Z","title":"$\\mathrm{PGL}_n(\\mathbb{C})$-character stacks and Langlands duality over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03234","kind":"arxiv","version":6},"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:ad83f7bcee189d735dc1b09fb5c54ec50068ad14370084727a54aeaf21ae9b2b","target":"record","created_at":"2026-05-28T01:04:25Z","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":"d34e392e343d0b5234b577818f10513113c882142b7ad4ef942238a6d5e80938","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-12-04T11:35:39Z","title_canon_sha256":"9c9cb9534d0cc1ba10499a0767e957551b92d776c06500e38180646b504039b6"},"schema_version":"1.0","source":{"id":"2412.03234","kind":"arxiv","version":6}},"canonical_sha256":"80c08953ff4516c74040a30072c732426e79dd4e7fb17ec200fdeb95f0fc7f08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80c08953ff4516c74040a30072c732426e79dd4e7fb17ec200fdeb95f0fc7f08","first_computed_at":"2026-05-28T01:04:25.833164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:25.833164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cp/isAJUeS14WrUf9nLuLeJIfrnsTiZ3DZMmXigwCEaEe5hyPIADMXv4K2ORkqtDYlz68WeP5G6XdOv6j4b/CA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:25.833692Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.03234","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad83f7bcee189d735dc1b09fb5c54ec50068ad14370084727a54aeaf21ae9b2b","sha256:ce5bad41270327ef8aec7f3f7abda91a625a3808cb1058787a9b88c524301f78"],"state_sha256":"09bb4976c4c7cba0cbb0524acdb086345854882d22051720f410c5d9440b9502"}