{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FGFYBUFUBNYJOSNLEQOZO57EMS","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":"9d6118154efd39a7669b3f7ca676f8d55cc25fc67b2ad93c68c9374c6e23bcfb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-23T02:37:29Z","title_canon_sha256":"baf3dafd441fe47771adfc225557f7a8f63eda4bd09f6d0f7483867b456865e1"},"schema_version":"1.0","source":{"id":"1212.5755","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5755","created_at":"2026-05-18T03:37:07Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5755v2","created_at":"2026-05-18T03:37:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5755","created_at":"2026-05-18T03:37:07Z"},{"alias_kind":"pith_short_12","alias_value":"FGFYBUFUBNYJ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FGFYBUFUBNYJOSNL","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FGFYBUFU","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:ba392772e2479bc0ccc69e436d0f663646516d053b27f744d7863a2404a46b28","target":"graph","created_at":"2026-05-18T03:37:07Z","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":"A certain Diophantine problem and 2D crystallography are linked through the notion of standard realizations which was introduced originally in the study of random walks. In the discussion, a complex projective quadric defined over Q is associated with a finite graph. \"Rational points\" on this quadric turns out to be related to standard realizations of 2D crystal structures.","authors_text":"Toshikazu Sunada","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-23T02:37:29Z","title":"Standard 2D Crystalline Patterns and Rational Points in Complex Quadrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5755","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:c9542fc474fc68a17b7cb6da7f16e690a52f062e6e4602a8030fbee153b9ecbe","target":"record","created_at":"2026-05-18T03:37:07Z","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":"9d6118154efd39a7669b3f7ca676f8d55cc25fc67b2ad93c68c9374c6e23bcfb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-23T02:37:29Z","title_canon_sha256":"baf3dafd441fe47771adfc225557f7a8f63eda4bd09f6d0f7483867b456865e1"},"schema_version":"1.0","source":{"id":"1212.5755","kind":"arxiv","version":2}},"canonical_sha256":"298b80d0b40b709749ab241d9777e464bf71d7b67dd1a37d546cb56000959043","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"298b80d0b40b709749ab241d9777e464bf71d7b67dd1a37d546cb56000959043","first_computed_at":"2026-05-18T03:37:07.688187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:07.688187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U+y9WykNh/jF0OScEdUwuBhdzZ/jp390kkoZVLfYOgfjhduamNqPuAGMDCjB3nmbxcvwzmYQGp0572rtjuVxAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:07.688962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5755","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9542fc474fc68a17b7cb6da7f16e690a52f062e6e4602a8030fbee153b9ecbe","sha256:ba392772e2479bc0ccc69e436d0f663646516d053b27f744d7863a2404a46b28"],"state_sha256":"fc57fb06da336264ffd73a142177c8327b42fecb384f977b5660a1fa89e58f73"}