{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GLHOOP2XSJXGXITZN4MXPWHWSM","short_pith_number":"pith:GLHOOP2X","canonical_record":{"source":{"id":"1008.3778","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-23T09:16:54Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"838dcd6b025b6b3b825297fb6e4ad215bd23a2a874dec81b6096ca802f8d8934","abstract_canon_sha256":"c645285dbbda195383ddf9c90a775f44e8138007686542774ba7dd8c16662717"},"schema_version":"1.0"},"canonical_sha256":"32cee73f57926e6ba2796f1977d8f6932e47dc9898b49e2bdc8ab32d34aa9198","source":{"kind":"arxiv","id":"1008.3778","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3778","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3778v3","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3778","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"GLHOOP2XSJXG","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GLHOOP2XSJXGXITZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GLHOOP2X","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GLHOOP2XSJXGXITZN4MXPWHWSM","target":"record","payload":{"canonical_record":{"source":{"id":"1008.3778","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-23T09:16:54Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"838dcd6b025b6b3b825297fb6e4ad215bd23a2a874dec81b6096ca802f8d8934","abstract_canon_sha256":"c645285dbbda195383ddf9c90a775f44e8138007686542774ba7dd8c16662717"},"schema_version":"1.0"},"canonical_sha256":"32cee73f57926e6ba2796f1977d8f6932e47dc9898b49e2bdc8ab32d34aa9198","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:23.319540Z","signature_b64":"Fz8swS9GKj4f+QqqXMo3Goftab5u/+kcmg01JyxjOMa17XwRIY/lRs0MXKWuVIaJx3UD8sb0pICd/XQrR+xUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32cee73f57926e6ba2796f1977d8f6932e47dc9898b49e2bdc8ab32d34aa9198","last_reissued_at":"2026-05-18T04:20:23.319051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:23.319051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.3778","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BAgoMSj4Depvw7HXEHVNxEu/2aFWCKruOt4bsVGviRHm7wTpJDV5TsbzTNHSsRK5zkhAZ5bTNH2AIvPXcUptAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:11.873939Z"},"content_sha256":"73c59715a6efee10b0221025c22abb264ff47d4cc82b42f8dd5fc0e354452382","schema_version":"1.0","event_id":"sha256:73c59715a6efee10b0221025c22abb264ff47d4cc82b42f8dd5fc0e354452382"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GLHOOP2XSJXGXITZN4MXPWHWSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mathieu Moonshine in the elliptic genus of K3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Matthias R. Gaberdiel, Roberto Volpato, Stefan Hohenegger","submitted_at":"2010-08-23T09:16:54Z","abstract_excerpt":"It has recently been conjectured that the elliptic genus of K3 can be written in terms of dimensions of Mathieu group M24 representations. Some further evidence for this idea was subsequently found by studying the twining genera that are obtained from the elliptic genus upon replacing dimensions of Mathieu group representations by their characters. In this paper we find explicit formulae for all (remaining) twining genera by making an educated guess for their general modular properties. This allows us to identify the decomposition of all expansion coefficients in terms of dimensions of M24-rep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3778","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9V896QNuOfSZ+GhNHbaIV6WAOvMgzHAicWJrALv1WdP61ZPs+la8udQtKlllwa6RdJAtovO8U3eqZ0u/p2wrDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:11.874644Z"},"content_sha256":"52d9aebf6744f2abdb507e9987b1f70826a0b6daa18c0eb14bcd87b45d3e3c40","schema_version":"1.0","event_id":"sha256:52d9aebf6744f2abdb507e9987b1f70826a0b6daa18c0eb14bcd87b45d3e3c40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLHOOP2XSJXGXITZN4MXPWHWSM/bundle.json","state_url":"https://pith.science/pith/GLHOOP2XSJXGXITZN4MXPWHWSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLHOOP2XSJXGXITZN4MXPWHWSM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T02:37:11Z","links":{"resolver":"https://pith.science/pith/GLHOOP2XSJXGXITZN4MXPWHWSM","bundle":"https://pith.science/pith/GLHOOP2XSJXGXITZN4MXPWHWSM/bundle.json","state":"https://pith.science/pith/GLHOOP2XSJXGXITZN4MXPWHWSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLHOOP2XSJXGXITZN4MXPWHWSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GLHOOP2XSJXGXITZN4MXPWHWSM","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":"c645285dbbda195383ddf9c90a775f44e8138007686542774ba7dd8c16662717","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-23T09:16:54Z","title_canon_sha256":"838dcd6b025b6b3b825297fb6e4ad215bd23a2a874dec81b6096ca802f8d8934"},"schema_version":"1.0","source":{"id":"1008.3778","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3778","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3778v3","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3778","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"GLHOOP2XSJXG","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GLHOOP2XSJXGXITZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GLHOOP2X","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:52d9aebf6744f2abdb507e9987b1f70826a0b6daa18c0eb14bcd87b45d3e3c40","target":"graph","created_at":"2026-05-18T04:20:23Z","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":"It has recently been conjectured that the elliptic genus of K3 can be written in terms of dimensions of Mathieu group M24 representations. Some further evidence for this idea was subsequently found by studying the twining genera that are obtained from the elliptic genus upon replacing dimensions of Mathieu group representations by their characters. In this paper we find explicit formulae for all (remaining) twining genera by making an educated guess for their general modular properties. This allows us to identify the decomposition of all expansion coefficients in terms of dimensions of M24-rep","authors_text":"Matthias R. Gaberdiel, Roberto Volpato, Stefan Hohenegger","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-23T09:16:54Z","title":"Mathieu Moonshine in the elliptic genus of K3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3778","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":"sha256:73c59715a6efee10b0221025c22abb264ff47d4cc82b42f8dd5fc0e354452382","target":"record","created_at":"2026-05-18T04:20:23Z","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":"c645285dbbda195383ddf9c90a775f44e8138007686542774ba7dd8c16662717","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-08-23T09:16:54Z","title_canon_sha256":"838dcd6b025b6b3b825297fb6e4ad215bd23a2a874dec81b6096ca802f8d8934"},"schema_version":"1.0","source":{"id":"1008.3778","kind":"arxiv","version":3}},"canonical_sha256":"32cee73f57926e6ba2796f1977d8f6932e47dc9898b49e2bdc8ab32d34aa9198","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32cee73f57926e6ba2796f1977d8f6932e47dc9898b49e2bdc8ab32d34aa9198","first_computed_at":"2026-05-18T04:20:23.319051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:23.319051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fz8swS9GKj4f+QqqXMo3Goftab5u/+kcmg01JyxjOMa17XwRIY/lRs0MXKWuVIaJx3UD8sb0pICd/XQrR+xUCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:23.319540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3778","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73c59715a6efee10b0221025c22abb264ff47d4cc82b42f8dd5fc0e354452382","sha256:52d9aebf6744f2abdb507e9987b1f70826a0b6daa18c0eb14bcd87b45d3e3c40"],"state_sha256":"50e743a1cecfc1b2e297a16ebfadde15b83ba2667584d4900c25e64e9db29ee8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uDvCloKWrYqtZS2BpslrjiOPFoyGO9ZkTAOJgh9TU2GnVwqEUO7xE/n3/1JJmBaj+49k3fu9avX92/JZYFO3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:37:11.877970Z","bundle_sha256":"34a40cd73f2d37950711a03c82498f56d000f4298a5406496358b8c69e04ae10"}}