{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:P2L6TRDGH4RXNTQJKKTY6ITJH3","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":"a8ebf7100ef1e336de7d2e8e6c3667052ec761a36cd107a3b4e80147759aed6c","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-06-10T11:22:59Z","title_canon_sha256":"0fb1c7391838fde1e48948d7c369169e8d4d9e35c6d082ec434e192e06df78f1"},"schema_version":"1.0","source":{"id":"2506.08696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08696","created_at":"2026-07-05T11:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08696v1","created_at":"2026-07-05T11:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08696","created_at":"2026-07-05T11:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"P2L6TRDGH4RX","created_at":"2026-07-05T11:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"P2L6TRDGH4RXNTQJ","created_at":"2026-07-05T11:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"P2L6TRDG","created_at":"2026-07-05T11:19:11Z"}],"graph_snapshots":[{"event_id":"sha256:4be57ba5b7c6929fb39ed7cf673a0025694ca1aacfcc90d33271e0e96170c071","target":"graph","created_at":"2026-07-05T11:19:11Z","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/2506.08696/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Kottwitz suggested to study all extended pure inner forms together in the local Langlands correspondence for linear reductive groups. We extend this philosophy to a large class of covers, including those defined by Brylinski and Deligne, and explain its relation with Weissman's observation that L-packets for covers are sometimes empty.","authors_text":"Luozi Shi, Yifei Zhao","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-06-10T11:22:59Z","title":"What are the extended pure inner forms of a cover?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08696","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":"sha256:141607f7644c9884e1ce35720582848e06410d184220634e62b8fd43d2ad1ac5","target":"record","created_at":"2026-07-05T11:19:11Z","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":"a8ebf7100ef1e336de7d2e8e6c3667052ec761a36cd107a3b4e80147759aed6c","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-06-10T11:22:59Z","title_canon_sha256":"0fb1c7391838fde1e48948d7c369169e8d4d9e35c6d082ec434e192e06df78f1"},"schema_version":"1.0","source":{"id":"2506.08696","kind":"arxiv","version":1}},"canonical_sha256":"7e97e9c4663f2376ce0952a78f22693efd4e1f94d025e5d7f6242bf4838b9243","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e97e9c4663f2376ce0952a78f22693efd4e1f94d025e5d7f6242bf4838b9243","first_computed_at":"2026-07-05T11:19:11.990260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:11.990260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GQTmPayZnu7ttypDSTFvv8Or2QF7Eb/r7DTO34gMEv5YK0k90pWVH1DWdYUnE7ohXvdQlm+Jq8HDkyu2wbaRCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:11.990743Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:141607f7644c9884e1ce35720582848e06410d184220634e62b8fd43d2ad1ac5","sha256:4be57ba5b7c6929fb39ed7cf673a0025694ca1aacfcc90d33271e0e96170c071"],"state_sha256":"adbd211e1aab54048ca56e72b6541aada980a056aeb2879eb597851d6ebca173"}