{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:455EFTWW65HFVFGW3LOUEH2PG4","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":"bf9ea459f8d68aa5eb5eb24c0fbc964ad4f5340531718b3aeef9c18cc5802928","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-17T13:20:23Z","title_canon_sha256":"4a505b45e39edc25cd369e103bb54db0233d5a9d0efc3064d8e963de851a9109"},"schema_version":"1.0","source":{"id":"1401.4333","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4333","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4333v1","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4333","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"pith_short_12","alias_value":"455EFTWW65HF","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"455EFTWW65HFVFGW","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"455EFTWW","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:06c4c2ecd5cb8c4444bc27f70e59a522ec6567d816b6e51526d3aaca3a5c7db6","target":"graph","created_at":"2026-05-18T03:01:55Z","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 consider point sets in $\\mathbb{Z}_n^2$ where no three points are on a line - also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small $n$.","authors_text":"Sascha Kurz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-17T13:20:23Z","title":"Caps in $\\mathbf{\\mathbb{Z}_n^2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4333","kind":"arxiv","version":1},"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:f1a67f1b34fbb8db77a4d4a5adc1b9f94899f12742fe550a3168f640d10c479e","target":"record","created_at":"2026-05-18T03:01:55Z","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":"bf9ea459f8d68aa5eb5eb24c0fbc964ad4f5340531718b3aeef9c18cc5802928","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-17T13:20:23Z","title_canon_sha256":"4a505b45e39edc25cd369e103bb54db0233d5a9d0efc3064d8e963de851a9109"},"schema_version":"1.0","source":{"id":"1401.4333","kind":"arxiv","version":1}},"canonical_sha256":"e77a42ced6f74e5a94d6dadd421f4f37102ced3d519964e006260e25f9cb2cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e77a42ced6f74e5a94d6dadd421f4f37102ced3d519964e006260e25f9cb2cdf","first_computed_at":"2026-05-18T03:01:55.268133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:55.268133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GBFAuR6jvqwlJJKOZ/XqRUVfkUD8TZzyr1NgeeM7C0X3Omi/+c+zJ0CfvDcx04TWCKFNDvgqgzdvVMbA1RG/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:55.268634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4333","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1a67f1b34fbb8db77a4d4a5adc1b9f94899f12742fe550a3168f640d10c479e","sha256:06c4c2ecd5cb8c4444bc27f70e59a522ec6567d816b6e51526d3aaca3a5c7db6"],"state_sha256":"bcd9f37895d81e724d2baaed62c50618255a07c713e8300e6c1bdae3bcef930f"}