{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZWZFT2KF7NH6L6HWKU77X5RK6S","short_pith_number":"pith:ZWZFT2KF","schema_version":"1.0","canonical_sha256":"cdb259e945fb4fe5f8f6553ffbf62af48846d52f80dd7e9bf9d5a6509a0d9c0f","source":{"kind":"arxiv","id":"1312.2991","version":1},"attestation_state":"computed","paper":{"title":"Equivariant functions and vector-valued modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CA"],"primary_cat":"math.NT","authors_text":"Abdellah Sebbar, Hicham Saber","submitted_at":"2013-12-10T22:51:40Z","abstract_excerpt":"For any discrete group $\\Gamma$ and any 2-dimensional complex representation $\\rho$ of $\\Gamma$, we introduce the notion of $\\rho-$equivariant functions, and we show that they are parameterized by vector-valued modular forms. We also provide examples arising from the monodromy of differential equations."},"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":"1312.2991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-10T22:51:40Z","cross_cats_sorted":["hep-th","math.CA"],"title_canon_sha256":"83ff56c0d64b87de59915a57c889b30db642e68ad574f88eb297d49f056133cc","abstract_canon_sha256":"f4b2a13edbb1a9665fea65ced31981a6f8343bf96e5cada591fd7735979902c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:23.715721Z","signature_b64":"LlCgIQ8yV3j2VGkjUehGfmAZl7MTCNaxEwQmgSAqm3boghjPsNGX+dqx1QLIeALJ2obttGdb2+eOSUyiZEL/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdb259e945fb4fe5f8f6553ffbf62af48846d52f80dd7e9bf9d5a6509a0d9c0f","last_reissued_at":"2026-05-18T03:04:23.715329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:23.715329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivariant functions and vector-valued modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CA"],"primary_cat":"math.NT","authors_text":"Abdellah Sebbar, Hicham Saber","submitted_at":"2013-12-10T22:51:40Z","abstract_excerpt":"For any discrete group $\\Gamma$ and any 2-dimensional complex representation $\\rho$ of $\\Gamma$, we introduce the notion of $\\rho-$equivariant functions, and we show that they are parameterized by vector-valued modular forms. We also provide examples arising from the monodromy of differential equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2991","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":""},"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":"1312.2991","created_at":"2026-05-18T03:04:23.715392+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.2991v1","created_at":"2026-05-18T03:04:23.715392+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2991","created_at":"2026-05-18T03:04:23.715392+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZWZFT2KF7NH6","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZWZFT2KF7NH6L6HW","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZWZFT2KF","created_at":"2026-05-18T12:28:09.283467+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/ZWZFT2KF7NH6L6HWKU77X5RK6S","json":"https://pith.science/pith/ZWZFT2KF7NH6L6HWKU77X5RK6S.json","graph_json":"https://pith.science/api/pith-number/ZWZFT2KF7NH6L6HWKU77X5RK6S/graph.json","events_json":"https://pith.science/api/pith-number/ZWZFT2KF7NH6L6HWKU77X5RK6S/events.json","paper":"https://pith.science/paper/ZWZFT2KF"},"agent_actions":{"view_html":"https://pith.science/pith/ZWZFT2KF7NH6L6HWKU77X5RK6S","download_json":"https://pith.science/pith/ZWZFT2KF7NH6L6HWKU77X5RK6S.json","view_paper":"https://pith.science/paper/ZWZFT2KF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.2991&json=true","fetch_graph":"https://pith.science/api/pith-number/ZWZFT2KF7NH6L6HWKU77X5RK6S/graph.json","fetch_events":"https://pith.science/api/pith-number/ZWZFT2KF7NH6L6HWKU77X5RK6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZWZFT2KF7NH6L6HWKU77X5RK6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZWZFT2KF7NH6L6HWKU77X5RK6S/action/storage_attestation","attest_author":"https://pith.science/pith/ZWZFT2KF7NH6L6HWKU77X5RK6S/action/author_attestation","sign_citation":"https://pith.science/pith/ZWZFT2KF7NH6L6HWKU77X5RK6S/action/citation_signature","submit_replication":"https://pith.science/pith/ZWZFT2KF7NH6L6HWKU77X5RK6S/action/replication_record"}},"created_at":"2026-05-18T03:04:23.715392+00:00","updated_at":"2026-05-18T03:04:23.715392+00:00"}