{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OFFFEMYFZHTXGXGFCZN6CO2MWM","short_pith_number":"pith:OFFFEMYF","schema_version":"1.0","canonical_sha256":"714a523305c9e7735cc5165be13b4cb300a1ea0ef9af951cb875eca2318b86c5","source":{"kind":"arxiv","id":"1707.05249","version":1},"attestation_state":"computed","paper":{"title":"Moonshine for All Finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Neekon Vafa, Roger Van Peski, Samuel DeHority, Xavier Gonzalez","submitted_at":"2017-07-17T15:56:51Z","abstract_excerpt":"In recent literature, moonshine has been explored for some groups beyond the Monster, for example the sporadic O'Nan and Thompson groups. This collection of examples may suggest that moonshine is a rare phenomenon, but a fundamental and largely unexplored question is how general the correspondence is between modular forms and finite groups. For every finite group $G$, we give constructions of infinitely many graded infinite-dimensional $\\mathbb{C}[G]$-modules where the McKay-Thompson series for a conjugacy class $[g]$ is a weakly holomorphic modular function properly on $\\Gamma_0(\\text{ord}(g)"},"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":"1707.05249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-17T15:56:51Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"147bd1272b76e82e3ad0e568aa5b2f8e3b023608e779b7d3736209ca91d703db","abstract_canon_sha256":"e61c1cc952b8893630afa3a3bad335587caf2e68d934a3c19f1f30bb80ef3893"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:09.076360Z","signature_b64":"BDY+ps0wg+qFxPGk5UBdFBNehHaHJbyFCyEabAkGlzIlNx6IA0uVG/3SHIBcPDWD74YYNPv0cY2TFaRCGUzeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"714a523305c9e7735cc5165be13b4cb300a1ea0ef9af951cb875eca2318b86c5","last_reissued_at":"2026-05-18T00:40:09.075863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:09.075863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moonshine for All Finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Neekon Vafa, Roger Van Peski, Samuel DeHority, Xavier Gonzalez","submitted_at":"2017-07-17T15:56:51Z","abstract_excerpt":"In recent literature, moonshine has been explored for some groups beyond the Monster, for example the sporadic O'Nan and Thompson groups. This collection of examples may suggest that moonshine is a rare phenomenon, but a fundamental and largely unexplored question is how general the correspondence is between modular forms and finite groups. For every finite group $G$, we give constructions of infinitely many graded infinite-dimensional $\\mathbb{C}[G]$-modules where the McKay-Thompson series for a conjugacy class $[g]$ is a weakly holomorphic modular function properly on $\\Gamma_0(\\text{ord}(g)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05249","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":"1707.05249","created_at":"2026-05-18T00:40:09.075936+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.05249v1","created_at":"2026-05-18T00:40:09.075936+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05249","created_at":"2026-05-18T00:40:09.075936+00:00"},{"alias_kind":"pith_short_12","alias_value":"OFFFEMYFZHTX","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OFFFEMYFZHTXGXGF","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OFFFEMYF","created_at":"2026-05-18T12:31:34.259226+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/OFFFEMYFZHTXGXGFCZN6CO2MWM","json":"https://pith.science/pith/OFFFEMYFZHTXGXGFCZN6CO2MWM.json","graph_json":"https://pith.science/api/pith-number/OFFFEMYFZHTXGXGFCZN6CO2MWM/graph.json","events_json":"https://pith.science/api/pith-number/OFFFEMYFZHTXGXGFCZN6CO2MWM/events.json","paper":"https://pith.science/paper/OFFFEMYF"},"agent_actions":{"view_html":"https://pith.science/pith/OFFFEMYFZHTXGXGFCZN6CO2MWM","download_json":"https://pith.science/pith/OFFFEMYFZHTXGXGFCZN6CO2MWM.json","view_paper":"https://pith.science/paper/OFFFEMYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.05249&json=true","fetch_graph":"https://pith.science/api/pith-number/OFFFEMYFZHTXGXGFCZN6CO2MWM/graph.json","fetch_events":"https://pith.science/api/pith-number/OFFFEMYFZHTXGXGFCZN6CO2MWM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OFFFEMYFZHTXGXGFCZN6CO2MWM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OFFFEMYFZHTXGXGFCZN6CO2MWM/action/storage_attestation","attest_author":"https://pith.science/pith/OFFFEMYFZHTXGXGFCZN6CO2MWM/action/author_attestation","sign_citation":"https://pith.science/pith/OFFFEMYFZHTXGXGFCZN6CO2MWM/action/citation_signature","submit_replication":"https://pith.science/pith/OFFFEMYFZHTXGXGFCZN6CO2MWM/action/replication_record"}},"created_at":"2026-05-18T00:40:09.075936+00:00","updated_at":"2026-05-18T00:40:09.075936+00:00"}