{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TOQXZTCM7YUDOP5VWTHRWO4KNK","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":"6987807370d56efcc2e3d192fa9f57410c1dc33ccc91881f61c3efdd72ce323b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-04T05:52:37Z","title_canon_sha256":"195a72826d43e1df95cb42e6417c1a5fc955605dfc40ad1072a8ecad2949d4fe"},"schema_version":"1.0","source":{"id":"2606.05735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05735","created_at":"2026-06-05T01:15:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05735v1","created_at":"2026-06-05T01:15:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05735","created_at":"2026-06-05T01:15:01Z"},{"alias_kind":"pith_short_12","alias_value":"TOQXZTCM7YUD","created_at":"2026-06-05T01:15:01Z"},{"alias_kind":"pith_short_16","alias_value":"TOQXZTCM7YUDOP5V","created_at":"2026-06-05T01:15:01Z"},{"alias_kind":"pith_short_8","alias_value":"TOQXZTCM","created_at":"2026-06-05T01:15:01Z"}],"graph_snapshots":[{"event_id":"sha256:a0260e44207812f5932b6ac7dab01e8a6d342e302bd716cf7cb34d3d7865748d","target":"graph","created_at":"2026-06-05T01:15:01Z","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/2606.05735/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish in Theorem 1.2 the reciprocity of wavefront sets for irreducible admissible representations $\\pi$ of classical groups $G$ over any local field $F$ of characteristic zero if $\\pi$ has a generic local $L$-parameter. Over archimedean local fields, based on the progress made in our previous work (arXiv:2207.04700), we prove in Theorem 1.5 that for an irreducible Casselman--Wallach representation $\\pi$ with a generic local $L$-parameter, the Wavefront Set Conjecture (arXiv:2207.04700, Conjecture 1.2) and its refinement (Conjecture 1.1) hold for the arithmetic wavefront s","authors_text":"Dihua Jiang, Dongwen Liu, Jia-Jun Ma, Lei Zhang, Zhikang Luo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-04T05:52:37Z","title":"Arithmetic Wavefront Set and Microlocal Structure of Harish-Chandra Character"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05735","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":"sha256:366bac44c2e95e831b3c1febd7b8c8ae7eeaeffd18fdac1e1433955a668e4524","target":"record","created_at":"2026-06-05T01:15:01Z","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":"6987807370d56efcc2e3d192fa9f57410c1dc33ccc91881f61c3efdd72ce323b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-06-04T05:52:37Z","title_canon_sha256":"195a72826d43e1df95cb42e6417c1a5fc955605dfc40ad1072a8ecad2949d4fe"},"schema_version":"1.0","source":{"id":"2606.05735","kind":"arxiv","version":1}},"canonical_sha256":"9ba17ccc4cfe28373fb5b4cf1b3b8a6ab3ce05312c2af94342b13d4221160fe0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ba17ccc4cfe28373fb5b4cf1b3b8a6ab3ce05312c2af94342b13d4221160fe0","first_computed_at":"2026-06-05T01:15:01.096872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:01.096872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"au3nF1KCVBzB3rtInjF7eaPK7IDpGPK0O/P9zhO2mHOec6QFAUm9PgxArFzRuscCKD9VmfKrWk41vLV9zRTAAQ==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:01.097356Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.05735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:366bac44c2e95e831b3c1febd7b8c8ae7eeaeffd18fdac1e1433955a668e4524","sha256:a0260e44207812f5932b6ac7dab01e8a6d342e302bd716cf7cb34d3d7865748d"],"state_sha256":"2410011c5e1bcf87d1948c18a3a1415567089fcb95f8f4df023e6af35793693a"}