{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NULCHBIFLSGIYW4ZH5DQ355FYK","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":"3ec152d513eb529842d05abc746cfed957bd2113b9890cb5612d51eb11963123","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-25T13:36:20Z","title_canon_sha256":"20d6ef87bb0a3fd5ebded799f2916422442bd17ce895ab8d03e6a3cb641afcbd"},"schema_version":"1.0","source":{"id":"1411.6862","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6862","created_at":"2026-05-18T02:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6862v2","created_at":"2026-05-18T02:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6862","created_at":"2026-05-18T02:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"NULCHBIFLSGI","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NULCHBIFLSGIYW4Z","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NULCHBIF","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:d096c55eaf469a147dbfbb5637e129f15c3ec1806920bc9432924739f10f5e2f","target":"graph","created_at":"2026-05-18T02:32:45Z","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"},"paper":{"abstract_excerpt":"Let $q$ be a power of a prime, $l$ a prime not dividing $q$, $d$ a positive integer coprime to both $l$ and the multiplicative order of $q\\mod l$ and $n$ a positive integer. A. Watanabe proved that there is a perfect isometry between the principal $l-$blocks of $GL_n(q)$ and $GL_n(q^d)$ where the correspondence of characters is give by Shintani descent. In the same paper Watanabe also prove that if $l$ and $q$ are odd and $l$ does not divide $GL_n(q^2)|/|U_n(q)|$ then there is a perfect isometry between the principal $l-$blocks of $U_n(q)$ and $GL_n(q^2)$ with the correspondence of characters ","authors_text":"Michael Livesey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-25T13:36:20Z","title":"A note on perfect isometries between finite general linear and unitary groups at unitary primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6862","kind":"arxiv","version":2},"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":"sha256:54b98d75f1ae24df58cb88ef75b9f36fbcb94d46cfa8f4cec1de4b29e4f9c245","target":"record","created_at":"2026-05-18T02:32:45Z","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":"3ec152d513eb529842d05abc746cfed957bd2113b9890cb5612d51eb11963123","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-11-25T13:36:20Z","title_canon_sha256":"20d6ef87bb0a3fd5ebded799f2916422442bd17ce895ab8d03e6a3cb641afcbd"},"schema_version":"1.0","source":{"id":"1411.6862","kind":"arxiv","version":2}},"canonical_sha256":"6d162385055c8c8c5b993f470df7a5c2a6b6e4650af7a9d03d6d4ed6ce57e7a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d162385055c8c8c5b993f470df7a5c2a6b6e4650af7a9d03d6d4ed6ce57e7a1","first_computed_at":"2026-05-18T02:32:45.557012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:45.557012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ev2itN22ucyjrUH8zD4EjYrLqM9sRxXhY/p0QT7HtwNDIo/uqgRaLTrVh3VuuYmSyB5gbyr6PDrjq1xCglvTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:45.557585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6862","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54b98d75f1ae24df58cb88ef75b9f36fbcb94d46cfa8f4cec1de4b29e4f9c245","sha256:d096c55eaf469a147dbfbb5637e129f15c3ec1806920bc9432924739f10f5e2f"],"state_sha256":"f3c16e91c770c70cf485d18a21f1e0a6b0353b0576b40b41ea0c35d7101ff2c4"}