{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HOWI5EQWG4APFFWOXOVD536UFI","short_pith_number":"pith:HOWI5EQW","schema_version":"1.0","canonical_sha256":"3bac8e92163700f296cebbaa3eefd42a2fa9fde85f5fb7c131ce2c5605ecd6fd","source":{"kind":"arxiv","id":"2509.21426","version":2},"attestation_state":"computed","paper":{"title":"Modular analogs of character formulas and minimal lifts of modular forms","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Patrick B. Allen, Preston Wake","submitted_at":"2025-09-25T11:21:36Z","abstract_excerpt":"If $f$ is a mod-$3$ eigenform of weight 2 and level $\\Gamma_0(\\ell^2)$ for a prime $\\ell$ such that $\\ell \\equiv -1 \\pmod{3}$, and $\\ell$ is a vexing prime for $f$, we show that there is no obstruction to finding a minimal lift of $f$, but that there is an obstruction to finding a nonminimal lift. The key new ingredient that we prove is a modular analog of the standard character formula for a cuspidal representation of $\\mathrm{GL}_2(\\mathbb{F}_\\ell)$, an enhancement that allows us to easily compute the group cohomology of a $3$-adic lattice in such a representation. In fact, we provide a gene"},"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":"2509.21426","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2025-09-25T11:21:36Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"775731031df06bc4df872bfdcfb249352c6082b9adaa42d0584fcf605f98c4d2","abstract_canon_sha256":"e73a7c0c0ee0ef89815e3a79f81fa37c9a2314de09932b815f1851d36b013044"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:36.404275Z","signature_b64":"mmJeSD2NcNoZyub5lZx6lbbelQKvQ8Ctp9EO0/DqOI0tT3szmesngXhJtTJPZ+TOdCyNDq6JMQazNZdmKbTMDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bac8e92163700f296cebbaa3eefd42a2fa9fde85f5fb7c131ce2c5605ecd6fd","last_reissued_at":"2026-05-29T02:05:36.403861Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:36.403861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular analogs of character formulas and minimal lifts of modular forms","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Patrick B. Allen, Preston Wake","submitted_at":"2025-09-25T11:21:36Z","abstract_excerpt":"If $f$ is a mod-$3$ eigenform of weight 2 and level $\\Gamma_0(\\ell^2)$ for a prime $\\ell$ such that $\\ell \\equiv -1 \\pmod{3}$, and $\\ell$ is a vexing prime for $f$, we show that there is no obstruction to finding a minimal lift of $f$, but that there is an obstruction to finding a nonminimal lift. The key new ingredient that we prove is a modular analog of the standard character formula for a cuspidal representation of $\\mathrm{GL}_2(\\mathbb{F}_\\ell)$, an enhancement that allows us to easily compute the group cohomology of a $3$-adic lattice in such a representation. In fact, we provide a gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.21426","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/2509.21426/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":"2509.21426","created_at":"2026-05-29T02:05:36.403918+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.21426v2","created_at":"2026-05-29T02:05:36.403918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.21426","created_at":"2026-05-29T02:05:36.403918+00:00"},{"alias_kind":"pith_short_12","alias_value":"HOWI5EQWG4AP","created_at":"2026-05-29T02:05:36.403918+00:00"},{"alias_kind":"pith_short_16","alias_value":"HOWI5EQWG4APFFWO","created_at":"2026-05-29T02:05:36.403918+00:00"},{"alias_kind":"pith_short_8","alias_value":"HOWI5EQW","created_at":"2026-05-29T02:05:36.403918+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI","json":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI.json","graph_json":"https://pith.science/api/pith-number/HOWI5EQWG4APFFWOXOVD536UFI/graph.json","events_json":"https://pith.science/api/pith-number/HOWI5EQWG4APFFWOXOVD536UFI/events.json","paper":"https://pith.science/paper/HOWI5EQW"},"agent_actions":{"view_html":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI","download_json":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI.json","view_paper":"https://pith.science/paper/HOWI5EQW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.21426&json=true","fetch_graph":"https://pith.science/api/pith-number/HOWI5EQWG4APFFWOXOVD536UFI/graph.json","fetch_events":"https://pith.science/api/pith-number/HOWI5EQWG4APFFWOXOVD536UFI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI/action/storage_attestation","attest_author":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI/action/author_attestation","sign_citation":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI/action/citation_signature","submit_replication":"https://pith.science/pith/HOWI5EQWG4APFFWOXOVD536UFI/action/replication_record"}},"created_at":"2026-05-29T02:05:36.403918+00:00","updated_at":"2026-05-29T02:05:36.403918+00:00"}