{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FPC5HPZ3CBZY2Z2SMHPQXOHA5Q","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":"b91a7b43366bd3b37b7e633cf3541b1a5bb3f19aeabe53e1ae7f018db9aaada8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-03T02:01:59Z","title_canon_sha256":"f93b223b21fd9df6fdbae9cfeaf93d415c44dd4abf1f06a4a731ef87f3a3e78e"},"schema_version":"1.0","source":{"id":"1212.0269","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0269","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0269v2","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0269","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"FPC5HPZ3CBZY","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FPC5HPZ3CBZY2Z2S","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FPC5HPZ3","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:174e536d143f028f3a89ead5527f57a32565a5011954fd5b98c90cec7f519232","target":"graph","created_at":"2026-05-18T03:04:06Z","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":"Let X and Y be supersingular K3 surfaces defined over an algebraically closed field. Suppose that the sum of their Artin invariants is 11. Then there exists a certain duality between their N\\'eron-Severi lattices. We investigate geometric consequences of this duality. As an application, we classify genus one fibrations on supersingular K3 surfaces with Artin invariant 10 in characteristic 2 and 3, and give a set of generators of the automorphism group of the nef cone of these supersingular K3 surfaces. The difference between the automorphism group of a supersingular K3 surface X and the automo","authors_text":"Ichiro Shimada, Shigeyuki Kondo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-03T02:01:59Z","title":"On certain duality of N\\'eron-Severi lattices of supersingular K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0269","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":"sha256:85129d5fd23a6846bb91547835f35be039795e468daa7d834444e334f2f0f71c","target":"record","created_at":"2026-05-18T03:04:06Z","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":"b91a7b43366bd3b37b7e633cf3541b1a5bb3f19aeabe53e1ae7f018db9aaada8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-03T02:01:59Z","title_canon_sha256":"f93b223b21fd9df6fdbae9cfeaf93d415c44dd4abf1f06a4a731ef87f3a3e78e"},"schema_version":"1.0","source":{"id":"1212.0269","kind":"arxiv","version":2}},"canonical_sha256":"2bc5d3bf3b10738d675261df0bb8e0ec2a6a11db4141cbd61d83ca4fd20ddc30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bc5d3bf3b10738d675261df0bb8e0ec2a6a11db4141cbd61d83ca4fd20ddc30","first_computed_at":"2026-05-18T03:04:06.757772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:06.757772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wuTO6KJXaiS4dO9JIwnujOIFnrmob7VRybuU3YcXHEJMQZTZzeunoPXH8QuWfT4HTTPHjNEqL3rBZIkDtxPACw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:06.758261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0269","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85129d5fd23a6846bb91547835f35be039795e468daa7d834444e334f2f0f71c","sha256:174e536d143f028f3a89ead5527f57a32565a5011954fd5b98c90cec7f519232"],"state_sha256":"2925397d598a4220ef08cc956bd066d5bf5a332bc16bff8dd481eaed2bbfe359"}