{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3VFTNP73JUUGSRJVTCIMGH7KMR","short_pith_number":"pith:3VFTNP73","schema_version":"1.0","canonical_sha256":"dd4b36bffb4d286945359890c31fea646e57cf53d16589f7c04da38de3ca546d","source":{"kind":"arxiv","id":"2502.04084","version":1},"attestation_state":"computed","paper":{"title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Elvira Lupoian","submitted_at":"2025-02-06T13:53:17Z","abstract_excerpt":"Modular units are functions on modular curves whose divisors are supported on the cusps. They form a free abelian group of rank at most one less than the number of cusps. In this paper we study the group of modular units on $X_{1}( p )$, with prime level $p \\ge 5$. We give an explicit basis for this group and study certain rational subgroups of it. We use the basis to numerically investigate the structure of the cuspidal group of $X_{1}( p)$ and its rational subgroup. In the later stages of this paper we use our basis to determine a specific large quotient of the cuspidal group."},"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":"2502.04084","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-06T13:53:17Z","cross_cats_sorted":[],"title_canon_sha256":"f21613c82de28c42529a331ef8b82aaa669bfc2091b4f3109ab6ac609bf98d11","abstract_canon_sha256":"1d02564f755e7a72a33753e301c3b55130740b2a038259d0db331870024bb3e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:33.900031Z","signature_b64":"MaL5EIrlhzGRPMNFnWSh/bgixCDfBlb81Wv6d+Sf2HYQ+avnshvjEZcgWxjer9auhsRxCQDbArz3XnYUBkAgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd4b36bffb4d286945359890c31fea646e57cf53d16589f7c04da38de3ca546d","last_reissued_at":"2026-07-05T10:10:33.899639Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:33.899639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular Units on $X_{1}( p)$ and Quotients of the Cuspidal Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Elvira Lupoian","submitted_at":"2025-02-06T13:53:17Z","abstract_excerpt":"Modular units are functions on modular curves whose divisors are supported on the cusps. They form a free abelian group of rank at most one less than the number of cusps. In this paper we study the group of modular units on $X_{1}( p )$, with prime level $p \\ge 5$. We give an explicit basis for this group and study certain rational subgroups of it. We use the basis to numerically investigate the structure of the cuspidal group of $X_{1}( p)$ and its rational subgroup. In the later stages of this paper we use our basis to determine a specific large quotient of the cuspidal group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04084","kind":"arxiv","version":1},"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/2502.04084/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":"2502.04084","created_at":"2026-07-05T10:10:33.899689+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.04084v1","created_at":"2026-07-05T10:10:33.899689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04084","created_at":"2026-07-05T10:10:33.899689+00:00"},{"alias_kind":"pith_short_12","alias_value":"3VFTNP73JUUG","created_at":"2026-07-05T10:10:33.899689+00:00"},{"alias_kind":"pith_short_16","alias_value":"3VFTNP73JUUGSRJV","created_at":"2026-07-05T10:10:33.899689+00:00"},{"alias_kind":"pith_short_8","alias_value":"3VFTNP73","created_at":"2026-07-05T10:10:33.899689+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/3VFTNP73JUUGSRJVTCIMGH7KMR","json":"https://pith.science/pith/3VFTNP73JUUGSRJVTCIMGH7KMR.json","graph_json":"https://pith.science/api/pith-number/3VFTNP73JUUGSRJVTCIMGH7KMR/graph.json","events_json":"https://pith.science/api/pith-number/3VFTNP73JUUGSRJVTCIMGH7KMR/events.json","paper":"https://pith.science/paper/3VFTNP73"},"agent_actions":{"view_html":"https://pith.science/pith/3VFTNP73JUUGSRJVTCIMGH7KMR","download_json":"https://pith.science/pith/3VFTNP73JUUGSRJVTCIMGH7KMR.json","view_paper":"https://pith.science/paper/3VFTNP73","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.04084&json=true","fetch_graph":"https://pith.science/api/pith-number/3VFTNP73JUUGSRJVTCIMGH7KMR/graph.json","fetch_events":"https://pith.science/api/pith-number/3VFTNP73JUUGSRJVTCIMGH7KMR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3VFTNP73JUUGSRJVTCIMGH7KMR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3VFTNP73JUUGSRJVTCIMGH7KMR/action/storage_attestation","attest_author":"https://pith.science/pith/3VFTNP73JUUGSRJVTCIMGH7KMR/action/author_attestation","sign_citation":"https://pith.science/pith/3VFTNP73JUUGSRJVTCIMGH7KMR/action/citation_signature","submit_replication":"https://pith.science/pith/3VFTNP73JUUGSRJVTCIMGH7KMR/action/replication_record"}},"created_at":"2026-07-05T10:10:33.899689+00:00","updated_at":"2026-07-05T10:10:33.899689+00:00"}