{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:527UUJMHYACYVKCJTDB6GB565K","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":"68baf5ed4e9e990d5629246e1655737235a6c827ec8a3eb989dd0f2799a3557d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-19T22:47:25Z","title_canon_sha256":"94de034d32a29098392ac2d619035e66cfb8d207251bd26e214f9b1a7fc873de"},"schema_version":"1.0","source":{"id":"1705.07216","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07216","created_at":"2026-05-18T00:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07216v2","created_at":"2026-05-18T00:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07216","created_at":"2026-05-18T00:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"527UUJMHYACY","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"527UUJMHYACYVKCJ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"527UUJMH","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:f1aa70a81bed0737ae1b70a01c3decfba970cd4ee0aeec6ded663fa97320d0bf","target":"graph","created_at":"2026-05-18T00:25:23Z","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":"Some Erd\\H{o}s-Ko-Rado type extremal properties of families of vectors from $\\{-1,0,1\\}^n$ are considered.","authors_text":"Andrey Kupavskii, Peter Frankl","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-19T22:47:25Z","title":"Families of vectors without antipodal pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07216","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":"sha256:2896b340f67b3297c482b91b08a1bb65975de9abf49dfe5d16b99a376eb5b23b","target":"record","created_at":"2026-05-18T00:25:23Z","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":"68baf5ed4e9e990d5629246e1655737235a6c827ec8a3eb989dd0f2799a3557d","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-19T22:47:25Z","title_canon_sha256":"94de034d32a29098392ac2d619035e66cfb8d207251bd26e214f9b1a7fc873de"},"schema_version":"1.0","source":{"id":"1705.07216","kind":"arxiv","version":2}},"canonical_sha256":"eebf4a2587c0058aa84998c3e307beea8cc77738a62d4bc4db8f40d8148f0d2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eebf4a2587c0058aa84998c3e307beea8cc77738a62d4bc4db8f40d8148f0d2f","first_computed_at":"2026-05-18T00:25:23.753015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:23.753015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6HfdddHTngDlgD1iaobbmECqDDwv3QrFxdKxrVFmJdrARxMAqtBUDIzz6Yz+4cJVKmi/G8orbt76nSuyQP8IBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:23.753635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07216","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2896b340f67b3297c482b91b08a1bb65975de9abf49dfe5d16b99a376eb5b23b","sha256:f1aa70a81bed0737ae1b70a01c3decfba970cd4ee0aeec6ded663fa97320d0bf"],"state_sha256":"b37f669a703aa7c94eecc56645309f0b782c647dc4452354ed44bf16bb120156"}