{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:3KWY2WWUNI4UJ6JO5FVEL4Z6XW","short_pith_number":"pith:3KWY2WWU","schema_version":"1.0","canonical_sha256":"daad8d5ad46a3944f92ee96a45f33ebd995e22392deed46af145136045b174bd","source":{"kind":"arxiv","id":"0705.2467","version":1},"attestation_state":"computed","paper":{"title":"Vector-valued modular functions for the modular group and the hypergeometric equation","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.NT","authors_text":"P. Bantay, T. Gannon","submitted_at":"2007-05-17T01:56:08Z","abstract_excerpt":"A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary half-integer weight. It is shown that the space of these modular functions is spanned, as a module over the polynomials in J, by the columns of a matrix that satisfies an abstract hypergeometric equation, providing a simple solution of the Riemann-Hilbert problem for representations of the modular group. Restrictions on the coefficients of this differential"},"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":"0705.2467","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2007-05-17T01:56:08Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"847a8cdd240ec19a0aabc1abab1c7a56a9f96933011140ab18e5a0c50395a8f9","abstract_canon_sha256":"293c2339b6b4ee1fd49beb69efdc45d9436ca2bfae366b81c12a88acfb17c543"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:01:25.774239Z","signature_b64":"Sx3ibVnVEk6bATaNuF7YXxZ74/DF1id+GclgzKJnAVws5MSkTqDRqhOEFQvbKr2T4umHeEHUc/XTLz2HeTVOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daad8d5ad46a3944f92ee96a45f33ebd995e22392deed46af145136045b174bd","last_reissued_at":"2026-07-04T15:01:25.773899Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:01:25.773899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vector-valued modular functions for the modular group and the hypergeometric equation","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.NT","authors_text":"P. Bantay, T. Gannon","submitted_at":"2007-05-17T01:56:08Z","abstract_excerpt":"A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary half-integer weight. It is shown that the space of these modular functions is spanned, as a module over the polynomials in J, by the columns of a matrix that satisfies an abstract hypergeometric equation, providing a simple solution of the Riemann-Hilbert problem for representations of the modular group. Restrictions on the coefficients of this differential"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2467","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/0705.2467/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":"0705.2467","created_at":"2026-07-04T15:01:25.773960+00:00"},{"alias_kind":"arxiv_version","alias_value":"0705.2467v1","created_at":"2026-07-04T15:01:25.773960+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.2467","created_at":"2026-07-04T15:01:25.773960+00:00"},{"alias_kind":"pith_short_12","alias_value":"3KWY2WWUNI4U","created_at":"2026-07-04T15:01:25.773960+00:00"},{"alias_kind":"pith_short_16","alias_value":"3KWY2WWUNI4UJ6JO","created_at":"2026-07-04T15:01:25.773960+00:00"},{"alias_kind":"pith_short_8","alias_value":"3KWY2WWU","created_at":"2026-07-04T15:01:25.773960+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/3KWY2WWUNI4UJ6JO5FVEL4Z6XW","json":"https://pith.science/pith/3KWY2WWUNI4UJ6JO5FVEL4Z6XW.json","graph_json":"https://pith.science/api/pith-number/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/graph.json","events_json":"https://pith.science/api/pith-number/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/events.json","paper":"https://pith.science/paper/3KWY2WWU"},"agent_actions":{"view_html":"https://pith.science/pith/3KWY2WWUNI4UJ6JO5FVEL4Z6XW","download_json":"https://pith.science/pith/3KWY2WWUNI4UJ6JO5FVEL4Z6XW.json","view_paper":"https://pith.science/paper/3KWY2WWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0705.2467&json=true","fetch_graph":"https://pith.science/api/pith-number/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/graph.json","fetch_events":"https://pith.science/api/pith-number/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/action/storage_attestation","attest_author":"https://pith.science/pith/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/action/author_attestation","sign_citation":"https://pith.science/pith/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/action/citation_signature","submit_replication":"https://pith.science/pith/3KWY2WWUNI4UJ6JO5FVEL4Z6XW/action/replication_record"}},"created_at":"2026-07-04T15:01:25.773960+00:00","updated_at":"2026-07-04T15:01:25.773960+00:00"}