{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CXTVPEZYSFDV3T45N7BGNCUJCC","short_pith_number":"pith:CXTVPEZY","schema_version":"1.0","canonical_sha256":"15e757933891475dcf9d6fc2668a8910a4bf26e4b1ffd97d18bcff901dc9c5a4","source":{"kind":"arxiv","id":"1408.3249","version":4},"attestation_state":"computed","paper":{"title":"On certain finiteness questions in the arithmetic of modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gabor Wiese, Ian Kiming, Nadim Rustom","submitted_at":"2014-08-14T11:03:35Z","abstract_excerpt":"We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \\Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evide"},"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":"1408.3249","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-14T11:03:35Z","cross_cats_sorted":[],"title_canon_sha256":"0aceb7659ce969269cf8ac076b636df8f30445dfc59e21a07104e47fbf8de95f","abstract_canon_sha256":"9fb295b28a0e558201d1b2e8b0b1c18bddc3e22571e4bba77d987e5c7de4b4b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:28.878013Z","signature_b64":"7l7a1xQsjz7LbZRNlNYWZWXZC4hynvzPfV7hM8u8ojkp9Eaf/eW5pV19oVJsNA+dyAKE8Yv0fhcbjEQBMzwtDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15e757933891475dcf9d6fc2668a8910a4bf26e4b1ffd97d18bcff901dc9c5a4","last_reissued_at":"2026-05-18T00:44:28.877424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:28.877424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On certain finiteness questions in the arithmetic of modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gabor Wiese, Ian Kiming, Nadim Rustom","submitted_at":"2014-08-14T11:03:35Z","abstract_excerpt":"We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \\Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3249","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1408.3249","created_at":"2026-05-18T00:44:28.877512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.3249v4","created_at":"2026-05-18T00:44:28.877512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3249","created_at":"2026-05-18T00:44:28.877512+00:00"},{"alias_kind":"pith_short_12","alias_value":"CXTVPEZYSFDV","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"CXTVPEZYSFDV3T45","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"CXTVPEZY","created_at":"2026-05-18T12:28:25.294606+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/CXTVPEZYSFDV3T45N7BGNCUJCC","json":"https://pith.science/pith/CXTVPEZYSFDV3T45N7BGNCUJCC.json","graph_json":"https://pith.science/api/pith-number/CXTVPEZYSFDV3T45N7BGNCUJCC/graph.json","events_json":"https://pith.science/api/pith-number/CXTVPEZYSFDV3T45N7BGNCUJCC/events.json","paper":"https://pith.science/paper/CXTVPEZY"},"agent_actions":{"view_html":"https://pith.science/pith/CXTVPEZYSFDV3T45N7BGNCUJCC","download_json":"https://pith.science/pith/CXTVPEZYSFDV3T45N7BGNCUJCC.json","view_paper":"https://pith.science/paper/CXTVPEZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.3249&json=true","fetch_graph":"https://pith.science/api/pith-number/CXTVPEZYSFDV3T45N7BGNCUJCC/graph.json","fetch_events":"https://pith.science/api/pith-number/CXTVPEZYSFDV3T45N7BGNCUJCC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CXTVPEZYSFDV3T45N7BGNCUJCC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CXTVPEZYSFDV3T45N7BGNCUJCC/action/storage_attestation","attest_author":"https://pith.science/pith/CXTVPEZYSFDV3T45N7BGNCUJCC/action/author_attestation","sign_citation":"https://pith.science/pith/CXTVPEZYSFDV3T45N7BGNCUJCC/action/citation_signature","submit_replication":"https://pith.science/pith/CXTVPEZYSFDV3T45N7BGNCUJCC/action/replication_record"}},"created_at":"2026-05-18T00:44:28.877512+00:00","updated_at":"2026-05-18T00:44:28.877512+00:00"}