{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QTZBRYGMEEIH3TOYPMIFMAQW6D","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":"ac7ca69f41da8094822a92207a32cc20bf9e0d9119cc10234dfd54897678caad","cross_cats_sorted":["hep-th","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-09-10T21:04:25Z","title_canon_sha256":"6d7e2ea6b8443deba1b6036c713e4b0808706bd3427d86a794c252a07dd011b7"},"schema_version":"1.0","source":{"id":"1309.2671","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2671","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2671v2","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2671","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"QTZBRYGMEEIH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QTZBRYGMEEIH3TOY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QTZBRYGM","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:3dc8ebd800bf2c7bc54cfee0a77fbd0d5c6e13cd74bdf92ab1bb8b8e6ce46008","target":"graph","created_at":"2026-05-18T02:47:44Z","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 compare the moonshine observation of Eguchi, Ooguri and Tachikawa relating the Mathieu group M_24 and the complex elliptic genus of a K3 surface with the symmetries of geometric structures on K3 surfaces.\n  Two main results are that the complex elliptic genus of a K3 surface is a virtual module for the Mathieu group M_24 and also for a certain vertex operator superalgebra V^G where G is the holonomy group.","authors_text":"Gerald Hoehn, Thomas Creutzig","cross_cats":["hep-th","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-09-10T21:04:25Z","title":"Mathieu Moonshine and the Geometry of K3 Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2671","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":"sha256:21bb7aaa1c9050d296e7be34535e83af48db39224142b80946830af8288ce72b","target":"record","created_at":"2026-05-18T02:47:44Z","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":"ac7ca69f41da8094822a92207a32cc20bf9e0d9119cc10234dfd54897678caad","cross_cats_sorted":["hep-th","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-09-10T21:04:25Z","title_canon_sha256":"6d7e2ea6b8443deba1b6036c713e4b0808706bd3427d86a794c252a07dd011b7"},"schema_version":"1.0","source":{"id":"1309.2671","kind":"arxiv","version":2}},"canonical_sha256":"84f218e0cc21107dcdd87b10560216f0ded9d689b70a81388c0674dc928f32be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84f218e0cc21107dcdd87b10560216f0ded9d689b70a81388c0674dc928f32be","first_computed_at":"2026-05-18T02:47:44.808962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:44.808962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kl+T96RD0SNK3vunYvp1l5vUUOf22sltFQAGXdbu7U4KL6obxAg9lKwACpG+iZxy1k3ZJ2CdpQauVcY2SLhoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:44.809802Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2671","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21bb7aaa1c9050d296e7be34535e83af48db39224142b80946830af8288ce72b","sha256:3dc8ebd800bf2c7bc54cfee0a77fbd0d5c6e13cd74bdf92ab1bb8b8e6ce46008"],"state_sha256":"d714ccc2fc61b39f1d54d57a078e9211dadc9b5eae405ce7033db9850924713d"}