{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZKQBDJAXKYZJF55G3GXWPPGAN6","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":"1d8c837b18de3030dc144fdae8b0e04e01b6863aa6f2226b2d636b2039d532d7","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T01:29:55Z","title_canon_sha256":"5abb6deb2854383fdcad7d18cfc6d52ba84a846db9a11cad5095b841ec05094c"},"schema_version":"1.0","source":{"id":"1807.07210","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07210","created_at":"2026-07-05T04:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07210v3","created_at":"2026-07-05T04:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07210","created_at":"2026-07-05T04:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZKQBDJAXKYZJ","created_at":"2026-07-05T04:32:45Z"},{"alias_kind":"pith_short_16","alias_value":"ZKQBDJAXKYZJF55G","created_at":"2026-07-05T04:32:45Z"},{"alias_kind":"pith_short_8","alias_value":"ZKQBDJAX","created_at":"2026-07-05T04:32:45Z"}],"graph_snapshots":[{"event_id":"sha256:f751b7310eddd2afac8b1bfcffc134607736e7e9db7b658e26722ed82050ed31","target":"graph","created_at":"2026-07-05T04:32:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.07210/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"\\textit{Weak moonshine} for a finite group $G$ is the phenomenon where an infinite dimensional graded $G$-module $$V_G=\\bigoplus_{n\\gg-\\infty}V_G(n)$$ has the property that its trace functions, known as McKay-Thompson series, are modular functions. Recent work by DeHority, Gonzalez, Vafa, and Van Peski established that weak moonshine holds for every finite group. Since weak moonshine only relies on character tables, which are not isomorphism class invariants, non-isomorphic groups can have the same McKay-Thompson series. We address this problem by extending weak moonshine to arbitrary width $s","authors_text":"Ken Ono, Madeline Locus Dawsey","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T01:29:55Z","title":"Higher Width Moonshine"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07210","kind":"arxiv","version":3},"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":"sha256:14fe6f176be4e35a6bb5c04ad1a9c190b3f53f11d504a5cc2df778bb76af2f57","target":"record","created_at":"2026-07-05T04:32:45Z","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":"1d8c837b18de3030dc144fdae8b0e04e01b6863aa6f2226b2d636b2039d532d7","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-07-19T01:29:55Z","title_canon_sha256":"5abb6deb2854383fdcad7d18cfc6d52ba84a846db9a11cad5095b841ec05094c"},"schema_version":"1.0","source":{"id":"1807.07210","kind":"arxiv","version":3}},"canonical_sha256":"caa011a417563292f7a6d9af67bcc06f96a1602b4f13098f73fd38a56b78b97b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caa011a417563292f7a6d9af67bcc06f96a1602b4f13098f73fd38a56b78b97b","first_computed_at":"2026-07-05T04:32:45.890251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:32:45.890251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NMjaRNaf7X8bqtoNOfuMOw84mM9A/LwOKGutlwdk/dU0HCj2WSTrCVH0ldMrQ6p+mNkyisZJsIWJ12wToW1eCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:32:45.890767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07210","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14fe6f176be4e35a6bb5c04ad1a9c190b3f53f11d504a5cc2df778bb76af2f57","sha256:f751b7310eddd2afac8b1bfcffc134607736e7e9db7b658e26722ed82050ed31"],"state_sha256":"2286e05859aacc0d9354cd825ac6b533d8402b921812ce7874762588884f7fa9"}