{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ITBNYSXFEC4Q3U737TVMXIEIAR","short_pith_number":"pith:ITBNYSXF","schema_version":"1.0","canonical_sha256":"44c2dc4ae520b90dd3fbfceacba088044557a0b704fac79b4a3c5c952ccbc264","source":{"kind":"arxiv","id":"2411.18419","version":2},"attestation_state":"computed","paper":{"title":"Non-repetition of second coefficients of Hecke polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Archer Clayton, Erick Ross, Helen Dai, Hui Xue, Jake Zummo, Tianyu Ni","submitted_at":"2024-11-27T15:02:45Z","abstract_excerpt":"Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(\\Gamma_0(N))$ of cuspidal modular forms of weight $2k$ and level $N$. In this paper, we study the non-repetition of the second coefficient of the characteristic polynomial of $T_m(N,2k)$. We obtain results in the horizontal aspect (where $m$ varies), the vertical aspect (where $k$ varies), and the level aspect (where $N$ varies). Finally, we use these non-repetition results to extend a result of Vilardi and Xue on distinguishing Hecke eigenforms."},"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":"2411.18419","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-11-27T15:02:45Z","cross_cats_sorted":[],"title_canon_sha256":"ea5ff140a1010d90567ab0a1044b806a3118cd27d5a5fd229e8f4a3c4e7d5738","abstract_canon_sha256":"a0ce9931b5050235c59b4a0f69aad14d6676aaf5a3a710bd5281136c4de1047c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:14:25.740483Z","signature_b64":"58g7PVhD/CYYHupwEMz0gZZylirRrxQL11GpRAxuUrIrJ1IW8h/M/BUdAVY0dWSe9/RsMO1UAVLDYakNQ7kSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44c2dc4ae520b90dd3fbfceacba088044557a0b704fac79b4a3c5c952ccbc264","last_reissued_at":"2026-07-05T11:14:25.739982Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:14:25.739982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-repetition of second coefficients of Hecke polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Archer Clayton, Erick Ross, Helen Dai, Hui Xue, Jake Zummo, Tianyu Ni","submitted_at":"2024-11-27T15:02:45Z","abstract_excerpt":"Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(\\Gamma_0(N))$ of cuspidal modular forms of weight $2k$ and level $N$. In this paper, we study the non-repetition of the second coefficient of the characteristic polynomial of $T_m(N,2k)$. We obtain results in the horizontal aspect (where $m$ varies), the vertical aspect (where $k$ varies), and the level aspect (where $N$ varies). Finally, we use these non-repetition results to extend a result of Vilardi and Xue on distinguishing Hecke eigenforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18419","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/2411.18419/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":"2411.18419","created_at":"2026-07-05T11:14:25.740041+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.18419v2","created_at":"2026-07-05T11:14:25.740041+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18419","created_at":"2026-07-05T11:14:25.740041+00:00"},{"alias_kind":"pith_short_12","alias_value":"ITBNYSXFEC4Q","created_at":"2026-07-05T11:14:25.740041+00:00"},{"alias_kind":"pith_short_16","alias_value":"ITBNYSXFEC4Q3U73","created_at":"2026-07-05T11:14:25.740041+00:00"},{"alias_kind":"pith_short_8","alias_value":"ITBNYSXF","created_at":"2026-07-05T11:14:25.740041+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/ITBNYSXFEC4Q3U737TVMXIEIAR","json":"https://pith.science/pith/ITBNYSXFEC4Q3U737TVMXIEIAR.json","graph_json":"https://pith.science/api/pith-number/ITBNYSXFEC4Q3U737TVMXIEIAR/graph.json","events_json":"https://pith.science/api/pith-number/ITBNYSXFEC4Q3U737TVMXIEIAR/events.json","paper":"https://pith.science/paper/ITBNYSXF"},"agent_actions":{"view_html":"https://pith.science/pith/ITBNYSXFEC4Q3U737TVMXIEIAR","download_json":"https://pith.science/pith/ITBNYSXFEC4Q3U737TVMXIEIAR.json","view_paper":"https://pith.science/paper/ITBNYSXF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.18419&json=true","fetch_graph":"https://pith.science/api/pith-number/ITBNYSXFEC4Q3U737TVMXIEIAR/graph.json","fetch_events":"https://pith.science/api/pith-number/ITBNYSXFEC4Q3U737TVMXIEIAR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ITBNYSXFEC4Q3U737TVMXIEIAR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ITBNYSXFEC4Q3U737TVMXIEIAR/action/storage_attestation","attest_author":"https://pith.science/pith/ITBNYSXFEC4Q3U737TVMXIEIAR/action/author_attestation","sign_citation":"https://pith.science/pith/ITBNYSXFEC4Q3U737TVMXIEIAR/action/citation_signature","submit_replication":"https://pith.science/pith/ITBNYSXFEC4Q3U737TVMXIEIAR/action/replication_record"}},"created_at":"2026-07-05T11:14:25.740041+00:00","updated_at":"2026-07-05T11:14:25.740041+00:00"}