{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MEQV75W4OTDEB33RN22E3SNMV7","short_pith_number":"pith:MEQV75W4","canonical_record":{"source":{"id":"1308.5233","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-08-23T20:00:44Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"0e3096501cd60ade8167226b0646ec70920499e1a2faa77b277fa6d3bed70dc1","abstract_canon_sha256":"16bdc5e3543c21a752138df56bce9aab589208324332cd07b46d0c9cef5a764a"},"schema_version":"1.0"},"canonical_sha256":"61215ff6dc74c640ef716eb44dc9acafdd66155548a760e0af25a71ad2d78d68","source":{"kind":"arxiv","id":"1308.5233","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5233","created_at":"2026-05-18T01:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5233v3","created_at":"2026-05-18T01:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5233","created_at":"2026-05-18T01:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"MEQV75W4OTDE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MEQV75W4OTDEB33R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MEQV75W4","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MEQV75W4OTDEB33RN22E3SNMV7","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5233","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-08-23T20:00:44Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"0e3096501cd60ade8167226b0646ec70920499e1a2faa77b277fa6d3bed70dc1","abstract_canon_sha256":"16bdc5e3543c21a752138df56bce9aab589208324332cd07b46d0c9cef5a764a"},"schema_version":"1.0"},"canonical_sha256":"61215ff6dc74c640ef716eb44dc9acafdd66155548a760e0af25a71ad2d78d68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:47:59.050827Z","signature_b64":"TINzB33WsHgDdR/J6nFvRIuC2uLC/pa+521qm2yVj7oUR66F6Jaiq9sgih02AMJ2/ffRMc8dyPazmc2a3av5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61215ff6dc74c640ef716eb44dc9acafdd66155548a760e0af25a71ad2d78d68","last_reissued_at":"2026-05-18T01:47:59.050305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:47:59.050305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5233","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":"2026-05-18T01:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j9gCH/TuGPeLA8f09d8cAcDZvTFM0T4yqMStBH+MjRAIawdztbQln3502ReQq9VCTMqaC9QP13QWW7UdD9qHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:12:45.732655Z"},"content_sha256":"f11acbf0dceb9e520900defd53c184d146303b8c7718c98023d32ff58731ed5d","schema_version":"1.0","event_id":"sha256:f11acbf0dceb9e520900defd53c184d146303b8c7718c98023d32ff58731ed5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MEQV75W4OTDEB33RN22E3SNMV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eta Products, BPS States and K3 Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"hep-th","authors_text":"John McKay, Yang-Hui He","submitted_at":"2013-08-23T20:00:44Z","abstract_excerpt":"Inspired by the multiplicative nature of the Ramanujan modular discriminant, Delta, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present some identities arising from q-expansions as well as relations to the sporadic Mathieu group M24"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5233","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":"2026-05-18T01:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ie6zvXCf8NxkUzc1A7oarDSeBf+tPTG82ls6J5+Yn8d+HuMvQ6hUIC5M3wZLO79m9v42xUjb1qmMdJ7ZIloYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:12:45.733022Z"},"content_sha256":"55d3ab0fa30aab573c3ed1ec4cf7e727de17ab9337c6356fb529694865e900d1","schema_version":"1.0","event_id":"sha256:55d3ab0fa30aab573c3ed1ec4cf7e727de17ab9337c6356fb529694865e900d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEQV75W4OTDEB33RN22E3SNMV7/bundle.json","state_url":"https://pith.science/pith/MEQV75W4OTDEB33RN22E3SNMV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEQV75W4OTDEB33RN22E3SNMV7/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":"2026-05-26T18:12:45Z","links":{"resolver":"https://pith.science/pith/MEQV75W4OTDEB33RN22E3SNMV7","bundle":"https://pith.science/pith/MEQV75W4OTDEB33RN22E3SNMV7/bundle.json","state":"https://pith.science/pith/MEQV75W4OTDEB33RN22E3SNMV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEQV75W4OTDEB33RN22E3SNMV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MEQV75W4OTDEB33RN22E3SNMV7","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":"16bdc5e3543c21a752138df56bce9aab589208324332cd07b46d0c9cef5a764a","cross_cats_sorted":["math.AG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-08-23T20:00:44Z","title_canon_sha256":"0e3096501cd60ade8167226b0646ec70920499e1a2faa77b277fa6d3bed70dc1"},"schema_version":"1.0","source":{"id":"1308.5233","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5233","created_at":"2026-05-18T01:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5233v3","created_at":"2026-05-18T01:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5233","created_at":"2026-05-18T01:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"MEQV75W4OTDE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MEQV75W4OTDEB33R","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MEQV75W4","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:55d3ab0fa30aab573c3ed1ec4cf7e727de17ab9337c6356fb529694865e900d1","target":"graph","created_at":"2026-05-18T01:47:59Z","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"},"paper":{"abstract_excerpt":"Inspired by the multiplicative nature of the Ramanujan modular discriminant, Delta, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present some identities arising from q-expansions as well as relations to the sporadic Mathieu group M24","authors_text":"John McKay, Yang-Hui He","cross_cats":["math.AG","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-08-23T20:00:44Z","title":"Eta Products, BPS States and K3 Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5233","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:f11acbf0dceb9e520900defd53c184d146303b8c7718c98023d32ff58731ed5d","target":"record","created_at":"2026-05-18T01:47:59Z","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":"16bdc5e3543c21a752138df56bce9aab589208324332cd07b46d0c9cef5a764a","cross_cats_sorted":["math.AG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-08-23T20:00:44Z","title_canon_sha256":"0e3096501cd60ade8167226b0646ec70920499e1a2faa77b277fa6d3bed70dc1"},"schema_version":"1.0","source":{"id":"1308.5233","kind":"arxiv","version":3}},"canonical_sha256":"61215ff6dc74c640ef716eb44dc9acafdd66155548a760e0af25a71ad2d78d68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61215ff6dc74c640ef716eb44dc9acafdd66155548a760e0af25a71ad2d78d68","first_computed_at":"2026-05-18T01:47:59.050305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:47:59.050305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TINzB33WsHgDdR/J6nFvRIuC2uLC/pa+521qm2yVj7oUR66F6Jaiq9sgih02AMJ2/ffRMc8dyPazmc2a3av5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:47:59.050827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5233","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f11acbf0dceb9e520900defd53c184d146303b8c7718c98023d32ff58731ed5d","sha256:55d3ab0fa30aab573c3ed1ec4cf7e727de17ab9337c6356fb529694865e900d1"],"state_sha256":"57bc8195f55d0cce1bd8b9770ad2a992192cd136282b5f98550e56d85cd5bb25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mV5YoRDK160MFH3fiSGidjWLovxtf/s/qCRy7TpcjXEokF66KqRofvPYR2TxuR9hpurPtQWM4GFqBSdsjhxUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:12:45.735941Z","bundle_sha256":"caa5d1ebfb19f10de03491101add37c1594fe2846a77074c9da6e91a120819e1"}}