{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6FSG6RZTU5Q22XTKD47JNFGFXI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bd384e3c9ec0003503e04444bb902b77551f8819d08d94354e0dd0fcaa49d069","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T15:11:40Z","title_canon_sha256":"bbd5ca8328d2fea7975afbcf18262deb4f877e6948a0eb76c3d1a93d59f85db9"},"schema_version":"1.0","source":{"id":"1703.05200","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05200","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05200v1","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05200","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"6FSG6RZTU5Q2","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6FSG6RZTU5Q22XTK","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6FSG6RZT","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:8f4bd112519679eb5ad5d658ea102565153c715efb43ff64da5d35a9e97bb447","target":"graph","created_at":"2026-05-18T00:48:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Determining Fourier coefficients of modular forms of a finite index noncongruence subgroups of the modular group is still a non-trivial task. In this brief note we describe a new algorithm to reliably calculate an approximation for a modular form of a given weight. As an example we calculate the hauptmodul and Belyi map of a genus zero subgroup of the modular group defined via a canonical homomorphism by the second Janko group. Our main result is the field of definition of its Belyi map, the explicit Belyi map and the Fourier coefficients of its hauptmodul.","authors_text":"Hartmut Monien","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T15:11:40Z","title":"The sporadic group J2, Hauptmodul and Belyi map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05200","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:af82bac81723c7e4b7490ea3395944ef524f21635f897a5ea4f1a11ef6f172dc","target":"record","created_at":"2026-05-18T00:48:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bd384e3c9ec0003503e04444bb902b77551f8819d08d94354e0dd0fcaa49d069","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T15:11:40Z","title_canon_sha256":"bbd5ca8328d2fea7975afbcf18262deb4f877e6948a0eb76c3d1a93d59f85db9"},"schema_version":"1.0","source":{"id":"1703.05200","kind":"arxiv","version":1}},"canonical_sha256":"f1646f4733a761ad5e6a1f3e9694c5ba3b1af3a8a9c6a7b52513daeec5e2b3f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1646f4733a761ad5e6a1f3e9694c5ba3b1af3a8a9c6a7b52513daeec5e2b3f8","first_computed_at":"2026-05-18T00:48:38.081577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:38.081577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IEaG7/GBuorNmKqNwqNdJUsmVIF167ydRX4M/LvTK6RN0VUbgcMfs/f1w3cjeqY5E1XhhTY3+jtWW9lHNiEWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:38.082118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05200","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af82bac81723c7e4b7490ea3395944ef524f21635f897a5ea4f1a11ef6f172dc","sha256:8f4bd112519679eb5ad5d658ea102565153c715efb43ff64da5d35a9e97bb447"],"state_sha256":"0f2007758a54596ad4b78a398345173a7ad1e86e502fde8cfedb26f593f84e9e"}