{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PRU3YMYGVO2QZXE7MIMDF3JTOT","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":"cb563fc0343d785b4239b61ad14a9b2f4d4870dd018d9b9c82f9cf1d94a02611","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-13T20:46:48Z","title_canon_sha256":"5a7de8473059271a7bc38c748b483566814a2519913be11b57d74356f9ed0287"},"schema_version":"1.0","source":{"id":"2501.16339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.16339","created_at":"2026-07-05T10:06:11Z"},{"alias_kind":"arxiv_version","alias_value":"2501.16339v1","created_at":"2026-07-05T10:06:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.16339","created_at":"2026-07-05T10:06:11Z"},{"alias_kind":"pith_short_12","alias_value":"PRU3YMYGVO2Q","created_at":"2026-07-05T10:06:11Z"},{"alias_kind":"pith_short_16","alias_value":"PRU3YMYGVO2QZXE7","created_at":"2026-07-05T10:06:11Z"},{"alias_kind":"pith_short_8","alias_value":"PRU3YMYG","created_at":"2026-07-05T10:06:11Z"}],"graph_snapshots":[{"event_id":"sha256:3fff156bf6edd4520d9e359c1926002ec0cc2174a5293f839a74182ec74ad5b6","target":"graph","created_at":"2026-07-05T10:06:11Z","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/2501.16339/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a direct proof of the local converse theorem for quasi-split non-split $\\mathrm{SO}_{2l}$ over a local non-Archimedean field of characteristic $p\\neq 2$, applying the theory of Howe vectors and partial Bessel functions.","authors_text":"Alexander Hazeltine","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-13T20:46:48Z","title":"A local converse theorem for quasi-split even special orthogonal groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.16339","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:da620a8e5a6690d18e0a4542b0cdeccf76551d2cfce5a3794999fd9b7f9f043a","target":"record","created_at":"2026-07-05T10:06:11Z","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":"cb563fc0343d785b4239b61ad14a9b2f4d4870dd018d9b9c82f9cf1d94a02611","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-01-13T20:46:48Z","title_canon_sha256":"5a7de8473059271a7bc38c748b483566814a2519913be11b57d74356f9ed0287"},"schema_version":"1.0","source":{"id":"2501.16339","kind":"arxiv","version":1}},"canonical_sha256":"7c69bc3306abb50cdc9f621832ed3374fd762f6f3d7ba37d003bbebda144d834","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c69bc3306abb50cdc9f621832ed3374fd762f6f3d7ba37d003bbebda144d834","first_computed_at":"2026-07-05T10:06:11.567963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:06:11.567963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G0/BHnFEqYXf3DKzs/zcLdw3gPuZMATGRhnluNCNVHvkkOhooi1CXGGRT/zZoF8zfQA5A6lziFmMIy8EkOCqDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:06:11.568504Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.16339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da620a8e5a6690d18e0a4542b0cdeccf76551d2cfce5a3794999fd9b7f9f043a","sha256:3fff156bf6edd4520d9e359c1926002ec0cc2174a5293f839a74182ec74ad5b6"],"state_sha256":"9866413d724e8e73e476a461507de54d12a8bcd47038c093df3e53a87912765f"}