{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:JN2ZAM44CZVLQVYT5SHYNTXHSM","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":"58c284963a56031d7ed3f47376c7e382f7a688652dfe34632aa2cdf7326e6947","cross_cats_sorted":["hep-th","math.GR"],"license":"","primary_cat":"math.QA","submitted_at":"2001-06-05T11:29:23Z","title_canon_sha256":"7e60b6a3c2134dbcd9a1aeb974449909e52c0cd30e3f35c03753379562627375"},"schema_version":"1.0","source":{"id":"math/0106027","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0106027","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0106027v2","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0106027","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"JN2ZAM44CZVL","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"JN2ZAM44CZVLQVYT","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"JN2ZAM44","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:3a8fa72313ecf4bb210096a9a6bd815e02c2e834362c98a0f4153f78aea1f56f","target":"graph","created_at":"2026-05-18T01:38:29Z","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":"We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order $p=2,3,5,7$ and the other of order $pk$ for $k=1$ or $k$ prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational modular f","authors_text":"Michael P. Tuite, Rossen I. Ivanov","cross_cats":["hep-th","math.GR"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2001-06-05T11:29:23Z","title":"Rational Generalised Moonshine from Abelian Orbifoldings of the Moonshine Module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106027","kind":"arxiv","version":2},"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":"sha256:750a51005d1dad84f0cfe0dfce4e7a3025d136c3e408c34484f5477a2c70a0e6","target":"record","created_at":"2026-05-18T01:38:29Z","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":"58c284963a56031d7ed3f47376c7e382f7a688652dfe34632aa2cdf7326e6947","cross_cats_sorted":["hep-th","math.GR"],"license":"","primary_cat":"math.QA","submitted_at":"2001-06-05T11:29:23Z","title_canon_sha256":"7e60b6a3c2134dbcd9a1aeb974449909e52c0cd30e3f35c03753379562627375"},"schema_version":"1.0","source":{"id":"math/0106027","kind":"arxiv","version":2}},"canonical_sha256":"4b7590339c166ab85713ec8f86cee793099b55974f99554c3d22ed2ab52ead3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7590339c166ab85713ec8f86cee793099b55974f99554c3d22ed2ab52ead3c","first_computed_at":"2026-05-18T01:38:29.936200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.936200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6gLxpkYpjl4DxBHUGxwcvCLA0nMDPnO9lSjX7gGsHEyA8eoewPGlouucLff02HNUqfijJjzJOHSea6xTwN8QDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.936794Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0106027","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:750a51005d1dad84f0cfe0dfce4e7a3025d136c3e408c34484f5477a2c70a0e6","sha256:3a8fa72313ecf4bb210096a9a6bd815e02c2e834362c98a0f4153f78aea1f56f"],"state_sha256":"26a2d6c9e33619fe5b3e36f4770fed9f79184f40ab875cb06757e7e763798ed1"}