{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:2EKPPSBRVTAEWQWW4E3AGS2LAY","short_pith_number":"pith:2EKPPSBR","schema_version":"1.0","canonical_sha256":"d114f7c831acc04b42d6e136034b4b0609c94046562b84667a3c1b126b9b4fd5","source":{"kind":"arxiv","id":"2204.11761","version":2},"attestation_state":"computed","paper":{"title":"Certification of Maass cusp forms of arbitrary level and character","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kieran Child","submitted_at":"2022-04-25T16:22:58Z","abstract_excerpt":"We present a method for certifying the existence of an arbitrary Maass cusp form for any level and character. This is accomplished by producing a bound on the difference between the $\\Delta$-eigenvalue of an authentic Maass cusp form and a purported approximation of a $\\Delta$-eigenvalue, arrived at by any means. We apply this method to a proposed non-CM level 5 form with quadratic character, to present the first certified $\\Delta$-eigenvalue of such a form. This work generalises the method for certifying level 1 forms presented by Booker, Str\\\"ombergsson and Venkatesh, and is motivated by the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2204.11761","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-04-25T16:22:58Z","cross_cats_sorted":[],"title_canon_sha256":"692c156ac558b6e2af951f4b3eb7e4561c988d6be03a72315a4ae686e987900a","abstract_canon_sha256":"62f632e08363cd388058cdf6dd66f6bc3278a71b79c7a7292ca5850a28ec3656"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:17:41.241922Z","signature_b64":"dsNxmiB77djmImXv16cGKiocWSonpTp5oUFySK6jpCeYyjUtUWxnL2UR5dHJT7sk6SbTS60HQJQMrQBlWShZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d114f7c831acc04b42d6e136034b4b0609c94046562b84667a3c1b126b9b4fd5","last_reissued_at":"2026-07-05T04:17:41.241403Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:17:41.241403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Certification of Maass cusp forms of arbitrary level and character","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kieran Child","submitted_at":"2022-04-25T16:22:58Z","abstract_excerpt":"We present a method for certifying the existence of an arbitrary Maass cusp form for any level and character. This is accomplished by producing a bound on the difference between the $\\Delta$-eigenvalue of an authentic Maass cusp form and a purported approximation of a $\\Delta$-eigenvalue, arrived at by any means. We apply this method to a proposed non-CM level 5 form with quadratic character, to present the first certified $\\Delta$-eigenvalue of such a form. This work generalises the method for certifying level 1 forms presented by Booker, Str\\\"ombergsson and Venkatesh, and is motivated by the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.11761","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.11761/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2204.11761","created_at":"2026-07-05T04:17:41.241463+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.11761v2","created_at":"2026-07-05T04:17:41.241463+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.11761","created_at":"2026-07-05T04:17:41.241463+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EKPPSBRVTAE","created_at":"2026-07-05T04:17:41.241463+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EKPPSBRVTAEWQWW","created_at":"2026-07-05T04:17:41.241463+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EKPPSBR","created_at":"2026-07-05T04:17:41.241463+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.02105","citing_title":"Learning Fricke signs from Maass form Coefficients","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY","json":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY.json","graph_json":"https://pith.science/api/pith-number/2EKPPSBRVTAEWQWW4E3AGS2LAY/graph.json","events_json":"https://pith.science/api/pith-number/2EKPPSBRVTAEWQWW4E3AGS2LAY/events.json","paper":"https://pith.science/paper/2EKPPSBR"},"agent_actions":{"view_html":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY","download_json":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY.json","view_paper":"https://pith.science/paper/2EKPPSBR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.11761&json=true","fetch_graph":"https://pith.science/api/pith-number/2EKPPSBRVTAEWQWW4E3AGS2LAY/graph.json","fetch_events":"https://pith.science/api/pith-number/2EKPPSBRVTAEWQWW4E3AGS2LAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY/action/storage_attestation","attest_author":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY/action/author_attestation","sign_citation":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY/action/citation_signature","submit_replication":"https://pith.science/pith/2EKPPSBRVTAEWQWW4E3AGS2LAY/action/replication_record"}},"created_at":"2026-07-05T04:17:41.241463+00:00","updated_at":"2026-07-05T04:17:41.241463+00:00"}