{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ABA2DXUA35WZAXZF53OE6X4KLU","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":"e601db75e1d7733fb5adbad64bff1b0b6bce0f3aac037543aeccdbba97097644","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-19T00:39:18Z","title_canon_sha256":"ef4840847e12d6f3d0832d3e4bbb7ce891290e1ebd45acdf30a56751ac787122"},"schema_version":"1.0","source":{"id":"1212.4545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4545","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4545v1","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4545","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"ABA2DXUA35WZ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ABA2DXUA35WZAXZF","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ABA2DXUA","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:0a57de20df742e9cdee349c69303e57073bd1619e7e0f0d7d64f088a617e97e4","target":"graph","created_at":"2026-05-18T03:38:12Z","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":"We describe a practical method for finding an L-function without first finding the associated underlying object. The procedure involves using the Euler product and the approximate functional equation in a new way. No use is made of the functional equation of twists of the L-function. The method is used to find a large number of Maass forms on SL(3,Z) and to give the first examples of Maass forms of higher level on GL(3), and on GL(4) and Sp(4).","authors_text":"David W. Farmer, Sally Koutsoliotas, Stefan Lemurell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-19T00:39:18Z","title":"Maass forms on GL(3) and GL(4)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4545","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":"sha256:4ac257c70bd07c7201d91390bdbb020d1e71a76c5dfad563323e0705f5469394","target":"record","created_at":"2026-05-18T03:38:12Z","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":"e601db75e1d7733fb5adbad64bff1b0b6bce0f3aac037543aeccdbba97097644","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-19T00:39:18Z","title_canon_sha256":"ef4840847e12d6f3d0832d3e4bbb7ce891290e1ebd45acdf30a56751ac787122"},"schema_version":"1.0","source":{"id":"1212.4545","kind":"arxiv","version":1}},"canonical_sha256":"0041a1de80df6d905f25eedc4f5f8a5d20def1d0a23df52b7e5552c3ff2fb2fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0041a1de80df6d905f25eedc4f5f8a5d20def1d0a23df52b7e5552c3ff2fb2fc","first_computed_at":"2026-05-18T03:38:12.080949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:12.080949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d8aowXLJ7SBHjtciu0hCjCu9MqJzXOimUSOX6Msn4VffLhbb6QGW/5pbjMvU7aDypKj3/7lbBCDFnjq/Kk5pDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:12.081658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ac257c70bd07c7201d91390bdbb020d1e71a76c5dfad563323e0705f5469394","sha256:0a57de20df742e9cdee349c69303e57073bd1619e7e0f0d7d64f088a617e97e4"],"state_sha256":"43845de46fc95cb645c9f411c8c68c72e9b450de623cbe7a874a8d80e8b9a74a"}