{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RT4XEQSDXYWAN3G45Q4A3TFHTJ","short_pith_number":"pith:RT4XEQSD","canonical_record":{"source":{"id":"1303.3221","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-13T17:27:11Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"d6a182fd304588b13c8417748edb96b6b8a21825858bd6d2e9caeb07d790ec67","abstract_canon_sha256":"d924f5d9d3e5b45c9dcdb8a61f9fc6516558a2a55d06860b3e3de2db5ddb88b7"},"schema_version":"1.0"},"canonical_sha256":"8cf9724243be2c06ecdcec380dcca79a76de4ec04f90ed4fc804c74381e9b52d","source":{"kind":"arxiv","id":"1303.3221","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3221","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3221v3","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3221","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"pith_short_12","alias_value":"RT4XEQSDXYWA","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"pith_short_16","alias_value":"RT4XEQSDXYWAN3G4","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"pith_short_8","alias_value":"RT4XEQSD","created_at":"2026-07-05T00:57:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RT4XEQSDXYWAN3G45Q4A3TFHTJ","target":"record","payload":{"canonical_record":{"source":{"id":"1303.3221","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-13T17:27:11Z","cross_cats_sorted":["math.AG","math.GR"],"title_canon_sha256":"d6a182fd304588b13c8417748edb96b6b8a21825858bd6d2e9caeb07d790ec67","abstract_canon_sha256":"d924f5d9d3e5b45c9dcdb8a61f9fc6516558a2a55d06860b3e3de2db5ddb88b7"},"schema_version":"1.0"},"canonical_sha256":"8cf9724243be2c06ecdcec380dcca79a76de4ec04f90ed4fc804c74381e9b52d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:57:59.078298Z","signature_b64":"ikdR6zTBZSZe761D+juGcsigVcqa3T6vEOEkPFgwMxxZYHiUdGaGBZKyAf6F+lmLVr1pIPzYY43fILtFWjyaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cf9724243be2c06ecdcec380dcca79a76de4ec04f90ed4fc804c74381e9b52d","last_reissued_at":"2026-07-05T00:57:59.077771Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:57:59.077771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.3221","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":"2026-07-05T00:57:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XbUyoo9y/J9GRBq3a/SpXFZDoo4nVCIO/38gSfkaTqKJVqDX5kGkJaL/OApl+rs6/gTUOzy+FBLk2XPbLaccBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:29:00.465157Z"},"content_sha256":"26aea1afa82fb0b21bd726697e4b5fcb72d28ee6ab5be25b3e3d2e1b5d937b55","schema_version":"1.0","event_id":"sha256:26aea1afa82fb0b21bd726697e4b5fcb72d28ee6ab5be25b3e3d2e1b5d937b55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RT4XEQSDXYWAN3G45Q4A3TFHTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A twist in the M24 moonshine story","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"hep-th","authors_text":"Anne Taormina, Katrin Wendland","submitted_at":"2013-03-13T17:27:11Z","abstract_excerpt":"Prompted by the Mathieu Moonshine observation, we identify a pair of 45-dimensional vector spaces of states that account for the first order term in the massive sector of the elliptic genus of K3 in every Z2-orbifold CFT on K3. These generic states are uniquely characterized by the fact that the action of every geometric symmetry group of a Z2-orbifold CFT yields a well-defined faithful representation on them. Moreover, each such representation is obtained by restriction of the 45-dimensional irreducible representation of the Mathieu group M24 constructed by Margolin. Thus we provide a piece o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3221","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1303.3221/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:57:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"60w20/djtORXMJ7GbOGKefPMLwZxk8NOMQBoHa+mnIjXJ6QM5qHCdU7L5f30kU4oT1Rz2oxQDIFqVxBMBT6RAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:29:00.465673Z"},"content_sha256":"87aa235fd078dfb81a47bbb10ed3c2c66645f737a5bb94815b213b442c6cab7d","schema_version":"1.0","event_id":"sha256:87aa235fd078dfb81a47bbb10ed3c2c66645f737a5bb94815b213b442c6cab7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RT4XEQSDXYWAN3G45Q4A3TFHTJ/bundle.json","state_url":"https://pith.science/pith/RT4XEQSDXYWAN3G45Q4A3TFHTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RT4XEQSDXYWAN3G45Q4A3TFHTJ/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":"2026-08-15T21:29:00Z","links":{"resolver":"https://pith.science/pith/RT4XEQSDXYWAN3G45Q4A3TFHTJ","bundle":"https://pith.science/pith/RT4XEQSDXYWAN3G45Q4A3TFHTJ/bundle.json","state":"https://pith.science/pith/RT4XEQSDXYWAN3G45Q4A3TFHTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RT4XEQSDXYWAN3G45Q4A3TFHTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RT4XEQSDXYWAN3G45Q4A3TFHTJ","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":"d924f5d9d3e5b45c9dcdb8a61f9fc6516558a2a55d06860b3e3de2db5ddb88b7","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-13T17:27:11Z","title_canon_sha256":"d6a182fd304588b13c8417748edb96b6b8a21825858bd6d2e9caeb07d790ec67"},"schema_version":"1.0","source":{"id":"1303.3221","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3221","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3221v3","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3221","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"pith_short_12","alias_value":"RT4XEQSDXYWA","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"pith_short_16","alias_value":"RT4XEQSDXYWAN3G4","created_at":"2026-07-05T00:57:59Z"},{"alias_kind":"pith_short_8","alias_value":"RT4XEQSD","created_at":"2026-07-05T00:57:59Z"}],"graph_snapshots":[{"event_id":"sha256:87aa235fd078dfb81a47bbb10ed3c2c66645f737a5bb94815b213b442c6cab7d","target":"graph","created_at":"2026-07-05T00:57:59Z","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/1303.3221/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Prompted by the Mathieu Moonshine observation, we identify a pair of 45-dimensional vector spaces of states that account for the first order term in the massive sector of the elliptic genus of K3 in every Z2-orbifold CFT on K3. These generic states are uniquely characterized by the fact that the action of every geometric symmetry group of a Z2-orbifold CFT yields a well-defined faithful representation on them. Moreover, each such representation is obtained by restriction of the 45-dimensional irreducible representation of the Mathieu group M24 constructed by Margolin. Thus we provide a piece o","authors_text":"Anne Taormina, Katrin Wendland","cross_cats":["math.AG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-13T17:27:11Z","title":"A twist in the M24 moonshine story"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3221","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":"sha256:26aea1afa82fb0b21bd726697e4b5fcb72d28ee6ab5be25b3e3d2e1b5d937b55","target":"record","created_at":"2026-07-05T00:57:59Z","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":"d924f5d9d3e5b45c9dcdb8a61f9fc6516558a2a55d06860b3e3de2db5ddb88b7","cross_cats_sorted":["math.AG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-03-13T17:27:11Z","title_canon_sha256":"d6a182fd304588b13c8417748edb96b6b8a21825858bd6d2e9caeb07d790ec67"},"schema_version":"1.0","source":{"id":"1303.3221","kind":"arxiv","version":3}},"canonical_sha256":"8cf9724243be2c06ecdcec380dcca79a76de4ec04f90ed4fc804c74381e9b52d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cf9724243be2c06ecdcec380dcca79a76de4ec04f90ed4fc804c74381e9b52d","first_computed_at":"2026-07-05T00:57:59.077771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:57:59.077771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ikdR6zTBZSZe761D+juGcsigVcqa3T6vEOEkPFgwMxxZYHiUdGaGBZKyAf6F+lmLVr1pIPzYY43fILtFWjyaAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:57:59.078298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3221","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26aea1afa82fb0b21bd726697e4b5fcb72d28ee6ab5be25b3e3d2e1b5d937b55","sha256:87aa235fd078dfb81a47bbb10ed3c2c66645f737a5bb94815b213b442c6cab7d"],"state_sha256":"ef3f9ec4be0298a9380ba0983911832f3f138e5b31d4d9bf2d4081213b8746f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gT68bFwem/sO2X7I2Qpdyn4Sl9s2wnDW3Oqb7+aB3dIWQ+bJx3gBg/SAQSo38WjSn48ufW+5uBfyd4rRIK6tDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T21:29:00.470906Z","bundle_sha256":"95c65224fde034b3958b3abb8d6014400bba0f7684871242f8631c7b73606116"}}