{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KNMRTG2QIDHGUFRSXQ5JKVENYW","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":"7f78deb4cb64ccc4d7e7b35c0fba3ef2c4640ce86f61ae5bfd816723b9d6cb3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T05:51:46Z","title_canon_sha256":"4f95a8fe7851676591f772b438a4823dd344d4c957463c2fda05a2af47a27819"},"schema_version":"1.0","source":{"id":"1708.09130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09130","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09130v1","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09130","created_at":"2026-05-18T00:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"KNMRTG2QIDHG","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KNMRTG2QIDHGUFRS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KNMRTG2Q","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:21bc21b9eb207e211189c4ac9d7be21d72eb0e495ffde47f89acabeafc2e6594","target":"graph","created_at":"2026-05-18T00:36:20Z","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":"The classical no-three-in-line problem is to find the maximum number of points that can be placed in the $n \\times n$ grid so that no three points lie on a line. Given a set $S$ of points in an Euclidean plane, the General Position Subset Selection Problem is to find a maximum subset $S'$ of $S$ such that no three points of $S'$ are collinear. Motivated by these problems, the following graph theory variation is introduced: Given a graph $G$, determine a largest set $S$ of vertices of $G$ such that no three vertices of $S$ lie on a common geodesic. Such a set is a gp-set of $G$ and its size is ","authors_text":"Paul Manuel, Sandi Klav\\v{z}ar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T05:51:46Z","title":"Graph theory general position problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09130","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":"sha256:24c66f930a63547ac5956447a9f42514db250a080b2bf10a68b69ba360d503bb","target":"record","created_at":"2026-05-18T00:36:20Z","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":"7f78deb4cb64ccc4d7e7b35c0fba3ef2c4640ce86f61ae5bfd816723b9d6cb3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T05:51:46Z","title_canon_sha256":"4f95a8fe7851676591f772b438a4823dd344d4c957463c2fda05a2af47a27819"},"schema_version":"1.0","source":{"id":"1708.09130","kind":"arxiv","version":1}},"canonical_sha256":"5359199b5040ce6a1632bc3a95548dc592ddb33eb76cbfabd89c9e9ca3deed9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5359199b5040ce6a1632bc3a95548dc592ddb33eb76cbfabd89c9e9ca3deed9f","first_computed_at":"2026-05-18T00:36:20.892596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:20.892596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UG1euqpvXxcAZR+unuLPS3vhzEqMVJyiAHf16odMczZCwvKjePqcHU2jfTIc7nKXRX29xt8BZtt8HEknqse+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:20.893166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24c66f930a63547ac5956447a9f42514db250a080b2bf10a68b69ba360d503bb","sha256:21bc21b9eb207e211189c4ac9d7be21d72eb0e495ffde47f89acabeafc2e6594"],"state_sha256":"217f815199c1d04ee15f2b7fe96a6589008bfdb2f2c6602d654e780692446ddc"}