{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QJHPCX7GMCQIVNDCPYXJ7YARTG","short_pith_number":"pith:QJHPCX7G","schema_version":"1.0","canonical_sha256":"824ef15fe660a08ab4627e2e9fe0119983621928937acae0cde2961968ca4a11","source":{"kind":"arxiv","id":"1503.05690","version":2},"attestation_state":"computed","paper":{"title":"Modular embeddings of Teichmueller curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GT"],"primary_cat":"math.NT","authors_text":"Don Zagier, Martin Moeller","submitted_at":"2015-03-19T10:09:49Z","abstract_excerpt":"Fuchsian groups with a modular embedding have the richest arithmetic properties among non-arithmetic Fuchsian groups. But they are very rare, all known examples being related either to triangle groups or to Teichmueller curves.\n  In Part I of this paper we study the arithmetic properties of the modular embedding and develop from scratch a theory of twisted modular forms for Fuchsian groups with a modular embedding, proving dimension formulas, coefficient growth estimates and differential equations.\n  In Part II we provide a modular proof for an Apery-like integrality statement for solutions of"},"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":"1503.05690","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-19T10:09:49Z","cross_cats_sorted":["math.AG","math.GT"],"title_canon_sha256":"2661988f4a1bfd6d633a7dc806009363a73563aa19258f3d38db0d6fd960c0d0","abstract_canon_sha256":"64439cc5d0e953956d8f202e645e584a46ec605c8e8bafc46909f4dc25d7854b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.581965Z","signature_b64":"n4wqii4ZySTfDrrc+vYCiNYggYWcekyjqNXGZ/db4lJJzcbFXNp1Bz84BH+3s9WbEq59vkC+9ufq1y9kxYesAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"824ef15fe660a08ab4627e2e9fe0119983621928937acae0cde2961968ca4a11","last_reissued_at":"2026-05-17T23:53:34.581138Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.581138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular embeddings of Teichmueller curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GT"],"primary_cat":"math.NT","authors_text":"Don Zagier, Martin Moeller","submitted_at":"2015-03-19T10:09:49Z","abstract_excerpt":"Fuchsian groups with a modular embedding have the richest arithmetic properties among non-arithmetic Fuchsian groups. But they are very rare, all known examples being related either to triangle groups or to Teichmueller curves.\n  In Part I of this paper we study the arithmetic properties of the modular embedding and develop from scratch a theory of twisted modular forms for Fuchsian groups with a modular embedding, proving dimension formulas, coefficient growth estimates and differential equations.\n  In Part II we provide a modular proof for an Apery-like integrality statement for solutions of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05690","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":""},"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":"1503.05690","created_at":"2026-05-17T23:53:34.581228+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.05690v2","created_at":"2026-05-17T23:53:34.581228+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05690","created_at":"2026-05-17T23:53:34.581228+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJHPCX7GMCQI","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJHPCX7GMCQIVNDC","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJHPCX7G","created_at":"2026-05-18T12:29:37.295048+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/QJHPCX7GMCQIVNDCPYXJ7YARTG","json":"https://pith.science/pith/QJHPCX7GMCQIVNDCPYXJ7YARTG.json","graph_json":"https://pith.science/api/pith-number/QJHPCX7GMCQIVNDCPYXJ7YARTG/graph.json","events_json":"https://pith.science/api/pith-number/QJHPCX7GMCQIVNDCPYXJ7YARTG/events.json","paper":"https://pith.science/paper/QJHPCX7G"},"agent_actions":{"view_html":"https://pith.science/pith/QJHPCX7GMCQIVNDCPYXJ7YARTG","download_json":"https://pith.science/pith/QJHPCX7GMCQIVNDCPYXJ7YARTG.json","view_paper":"https://pith.science/paper/QJHPCX7G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.05690&json=true","fetch_graph":"https://pith.science/api/pith-number/QJHPCX7GMCQIVNDCPYXJ7YARTG/graph.json","fetch_events":"https://pith.science/api/pith-number/QJHPCX7GMCQIVNDCPYXJ7YARTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJHPCX7GMCQIVNDCPYXJ7YARTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJHPCX7GMCQIVNDCPYXJ7YARTG/action/storage_attestation","attest_author":"https://pith.science/pith/QJHPCX7GMCQIVNDCPYXJ7YARTG/action/author_attestation","sign_citation":"https://pith.science/pith/QJHPCX7GMCQIVNDCPYXJ7YARTG/action/citation_signature","submit_replication":"https://pith.science/pith/QJHPCX7GMCQIVNDCPYXJ7YARTG/action/replication_record"}},"created_at":"2026-05-17T23:53:34.581228+00:00","updated_at":"2026-05-17T23:53:34.581228+00:00"}