{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CSQ5LMD3R6OF5CYENTGFUPMRQS","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":"29fb1ac608fcb8ccdac7582cdf37f2feabb05df888f880f5ac72b949f460e706","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-13T18:40:15Z","title_canon_sha256":"7807b3456c7767b26ba4f1863301b32f6374bc3496903aa56f5c7edf3c07741c"},"schema_version":"1.0","source":{"id":"1109.2879","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2879","created_at":"2026-05-18T02:00:33Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2879v7","created_at":"2026-05-18T02:00:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2879","created_at":"2026-05-18T02:00:33Z"},{"alias_kind":"pith_short_12","alias_value":"CSQ5LMD3R6OF","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CSQ5LMD3R6OF5CYE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CSQ5LMD3","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:ff48705acd0d32a79fc03bfa9323caf619f4b7d42d1820201af7500357d4167a","target":"graph","created_at":"2026-05-18T02:00:33Z","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":"Using results (especially see Remark 1.14.7) of our paper \"Integral symmetric bilinear forms and some of their applications\", 1979, we clarify relation between Kahlerian K3 surfaces and Niemeier lattices. We want to emphasise that all twenty four Niemeier lattices are important for K3 surfaces, not only the one which is related to the Mathieu group.","authors_text":"Viacheslav V. Nikulin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-13T18:40:15Z","title":"Kahlerian K3 surfaces and Niemeier lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2879","kind":"arxiv","version":7},"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":"sha256:875e85fb3719a0a5fa8b9e31a498a053767e1949aaa4ffaab5be9bd19a0b04a4","target":"record","created_at":"2026-05-18T02:00:33Z","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":"29fb1ac608fcb8ccdac7582cdf37f2feabb05df888f880f5ac72b949f460e706","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-09-13T18:40:15Z","title_canon_sha256":"7807b3456c7767b26ba4f1863301b32f6374bc3496903aa56f5c7edf3c07741c"},"schema_version":"1.0","source":{"id":"1109.2879","kind":"arxiv","version":7}},"canonical_sha256":"14a1d5b07b8f9c5e8b046ccc5a3d91848932855da4d65266d8a9ed7342ea45b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14a1d5b07b8f9c5e8b046ccc5a3d91848932855da4d65266d8a9ed7342ea45b5","first_computed_at":"2026-05-18T02:00:33.473143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:33.473143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6LxunCB58kDea5PVk7AfbY6e7gUlPUn87o8NR8m1WEcRe64uuvhtN659+QJu+ib8sXT0yIYD1RYOwJwzPey3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:33.473699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2879","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:875e85fb3719a0a5fa8b9e31a498a053767e1949aaa4ffaab5be9bd19a0b04a4","sha256:ff48705acd0d32a79fc03bfa9323caf619f4b7d42d1820201af7500357d4167a"],"state_sha256":"6563e7843e2ea9de415dae4c2fef75a4548b7dae724e824ac51a7ee1e41f758d"}