{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LILGCDCX3FGRWYQ5IUQ45QNDNJ","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":"35d2ef9c661ec7501666a7e047a1ceca7ac36108f5d80750e64b10d0eeb990bc","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-19T19:04:58Z","title_canon_sha256":"6a4904df0fbfd669821fd3012084b575273b468571d49a3d367a1e76676df054"},"schema_version":"1.0","source":{"id":"1704.05897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05897","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05897v2","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05897","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"LILGCDCX3FGR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LILGCDCX3FGRWYQ5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LILGCDCX","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:7662e4d8e368203a61d30fe09aa7823c2c8bb5366378aa8b2070429b7191395b","target":"graph","created_at":"2026-05-18T00:18:05Z","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":"Suppose $F$ is a non-archimedean local field. The classical Godement-Jacquet theory is that one can use Schwartz-Bruhat functions on $n \\times n$ matrices $M_n(F)$ to define the local standard $L$-functions on $\\mathrm{GL}_n$. The purpose of this partly expository note is to give evidence that there is an analogous and useful \"approximate\" Godement-Jacquet theory for the standard $L$-functions on the special orthogonal groups $\\mathrm{SO}(V)$: One replaces $\\mathrm{GL}_n(F)$ with $\\mathrm{GSpin}(V)(F)$ and $M_n(F)$ with $\\mathrm{Clif}(V)(F)$, the Clifford algebra of $V$. More precisely, we exp","authors_text":"Aaron Pollack","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-19T19:04:58Z","title":"Unramified Godement-Jacquet theory for the spin similitude group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05897","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:fe67a03cd179861cae71654fa78b0e20389aa28c9269bb9ade6b4ee1e98bf0df","target":"record","created_at":"2026-05-18T00:18:05Z","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":"35d2ef9c661ec7501666a7e047a1ceca7ac36108f5d80750e64b10d0eeb990bc","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-19T19:04:58Z","title_canon_sha256":"6a4904df0fbfd669821fd3012084b575273b468571d49a3d367a1e76676df054"},"schema_version":"1.0","source":{"id":"1704.05897","kind":"arxiv","version":2}},"canonical_sha256":"5a16610c57d94d1b621d4521cec1a36a66ef868a29f84298d6ed99dcfc637a93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a16610c57d94d1b621d4521cec1a36a66ef868a29f84298d6ed99dcfc637a93","first_computed_at":"2026-05-18T00:18:05.364733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:05.364733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HkGoIuKj+HO+42DJfizbpbkH1YIcnIKl+Mg3kVyzEfdZXhNxeDQOo9eaJES8KIE1END+rHSV31eDEx7ubp+rBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:05.365346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe67a03cd179861cae71654fa78b0e20389aa28c9269bb9ade6b4ee1e98bf0df","sha256:7662e4d8e368203a61d30fe09aa7823c2c8bb5366378aa8b2070429b7191395b"],"state_sha256":"6586c637a9cfc3348b864a40bcf0c3cc9a97a8a66774453bfa2f045e79f0acc6"}