{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YT3IUBKY2F3RFABDEGDAWB34SB","short_pith_number":"pith:YT3IUBKY","canonical_record":{"source":{"id":"1307.2463","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-09T14:07:08Z","cross_cats_sorted":[],"title_canon_sha256":"bdebd88d6841fd5738a2c5da75185f2ed68bef481e87ea1da21b537ac48f58dd","abstract_canon_sha256":"fabffd70a4839703232111350986e9e9373a0ef9c744eea688e83aa31ee06f1d"},"schema_version":"1.0"},"canonical_sha256":"c4f68a0558d17712802321860b077c90633ba730c35d1bc05a997af2369b2cf2","source":{"kind":"arxiv","id":"1307.2463","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2463","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2463v2","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2463","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"pith_short_12","alias_value":"YT3IUBKY2F3R","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YT3IUBKY2F3RFABD","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YT3IUBKY","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YT3IUBKY2F3RFABDEGDAWB34SB","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2463","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-09T14:07:08Z","cross_cats_sorted":[],"title_canon_sha256":"bdebd88d6841fd5738a2c5da75185f2ed68bef481e87ea1da21b537ac48f58dd","abstract_canon_sha256":"fabffd70a4839703232111350986e9e9373a0ef9c744eea688e83aa31ee06f1d"},"schema_version":"1.0"},"canonical_sha256":"c4f68a0558d17712802321860b077c90633ba730c35d1bc05a997af2369b2cf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:18.069383Z","signature_b64":"O1LIRK7narKSPoSk+VXTDXfkUrR/ZX/h4EkH/HLxmZZ5GxZ+K6thR8nwieQptZUvpFFe0k2xYPMoejFiWHW6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4f68a0558d17712802321860b077c90633ba730c35d1bc05a997af2369b2cf2","last_reissued_at":"2026-05-18T03:18:18.068638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:18.068638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2463","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:18:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fwcou/xIa1mgK0e/52DV00/OxjXbR+c0aoHYcBhL1Qz7l7V7G7c71uic3m2i/J9G2pn/gCk0EbhsrmdFEA2ECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:25:45.987412Z"},"content_sha256":"5cefdda303ad54c1ea041c0e0e6c2d687d9be489fac6dfde619b5ede3d2d11f6","schema_version":"1.0","event_id":"sha256:5cefdda303ad54c1ea041c0e0e6c2d687d9be489fac6dfde619b5ede3d2d11f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YT3IUBKY2F3RFABDEGDAWB34SB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some equations for the universal Kummer variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Bert van Geemen","submitted_at":"2013-07-09T14:07:08Z","abstract_excerpt":"We give a method to find quartic Heisenberg invariant equations for Kummer varieties and we give some explicit examples. From these equations for g-dimensional Kummer varieties one obtains equations for the moduli space of g+1-dimensional Kummer varieties. These again define modular forms which vanish on the period matrices of Riemann surfaces. The modular forms that we find for g=5 appear to be new and of lower weight than known before."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2463","kind":"arxiv","version":2},"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":"2026-05-18T03:18:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMgWtyI0RT8iN/yMlnPTNX9eB9aBRaEdN6q5Ak1gARhfTPKkKj7QRkeRIZH0SbPXEyT5QMC/zCs7A3cC0UvmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:25:45.988099Z"},"content_sha256":"9e80154ddba1ab6ab45f4c167a978f8f0c7ae342956458fa589599e7b0ce5327","schema_version":"1.0","event_id":"sha256:9e80154ddba1ab6ab45f4c167a978f8f0c7ae342956458fa589599e7b0ce5327"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YT3IUBKY2F3RFABDEGDAWB34SB/bundle.json","state_url":"https://pith.science/pith/YT3IUBKY2F3RFABDEGDAWB34SB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YT3IUBKY2F3RFABDEGDAWB34SB/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":"2026-06-05T20:25:45Z","links":{"resolver":"https://pith.science/pith/YT3IUBKY2F3RFABDEGDAWB34SB","bundle":"https://pith.science/pith/YT3IUBKY2F3RFABDEGDAWB34SB/bundle.json","state":"https://pith.science/pith/YT3IUBKY2F3RFABDEGDAWB34SB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YT3IUBKY2F3RFABDEGDAWB34SB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YT3IUBKY2F3RFABDEGDAWB34SB","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":"fabffd70a4839703232111350986e9e9373a0ef9c744eea688e83aa31ee06f1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-09T14:07:08Z","title_canon_sha256":"bdebd88d6841fd5738a2c5da75185f2ed68bef481e87ea1da21b537ac48f58dd"},"schema_version":"1.0","source":{"id":"1307.2463","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2463","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2463v2","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2463","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"pith_short_12","alias_value":"YT3IUBKY2F3R","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YT3IUBKY2F3RFABD","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YT3IUBKY","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:9e80154ddba1ab6ab45f4c167a978f8f0c7ae342956458fa589599e7b0ce5327","target":"graph","created_at":"2026-05-18T03:18:18Z","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 give a method to find quartic Heisenberg invariant equations for Kummer varieties and we give some explicit examples. From these equations for g-dimensional Kummer varieties one obtains equations for the moduli space of g+1-dimensional Kummer varieties. These again define modular forms which vanish on the period matrices of Riemann surfaces. The modular forms that we find for g=5 appear to be new and of lower weight than known before.","authors_text":"Bert van Geemen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-09T14:07:08Z","title":"Some equations for the universal Kummer variety"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2463","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":"sha256:5cefdda303ad54c1ea041c0e0e6c2d687d9be489fac6dfde619b5ede3d2d11f6","target":"record","created_at":"2026-05-18T03:18:18Z","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":"fabffd70a4839703232111350986e9e9373a0ef9c744eea688e83aa31ee06f1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-09T14:07:08Z","title_canon_sha256":"bdebd88d6841fd5738a2c5da75185f2ed68bef481e87ea1da21b537ac48f58dd"},"schema_version":"1.0","source":{"id":"1307.2463","kind":"arxiv","version":2}},"canonical_sha256":"c4f68a0558d17712802321860b077c90633ba730c35d1bc05a997af2369b2cf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4f68a0558d17712802321860b077c90633ba730c35d1bc05a997af2369b2cf2","first_computed_at":"2026-05-18T03:18:18.068638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:18.068638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O1LIRK7narKSPoSk+VXTDXfkUrR/ZX/h4EkH/HLxmZZ5GxZ+K6thR8nwieQptZUvpFFe0k2xYPMoejFiWHW6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:18.069383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2463","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cefdda303ad54c1ea041c0e0e6c2d687d9be489fac6dfde619b5ede3d2d11f6","sha256:9e80154ddba1ab6ab45f4c167a978f8f0c7ae342956458fa589599e7b0ce5327"],"state_sha256":"f63fa3b496a119405b6e6813edf9a0fd73bef10be339dc474812dd9cfa3e5a87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZOjXRc24ttHllzo2dkKsOCB+vb+aL0zWovcy9n+MthcEP4M5XXjcaTOfkeOE7ZdE7ix8vVxHFMV0Ws6NnpTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:25:45.992005Z","bundle_sha256":"1bb26a7c1eed000b8c15445fe31082eee00a35c23d1b1fdd3db3bb91de32c309"}}