{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XET54DSW4LENFQ5K4MWBADXOAK","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":"13fbc62ca91612178a3f749f628893b50016ba208ce509684a6ff894506bf806","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-06-10T17:20:49Z","title_canon_sha256":"56c6999544fc4ebcf9000ef11bd48424e9aaa4d824f94d31e6b38bf1ad9eb30a"},"schema_version":"1.0","source":{"id":"1406.2636","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2636","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2636v1","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2636","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"XET54DSW4LEN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XET54DSW4LENFQ5K","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XET54DSW","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:f222d0565f588606260b15b75119d17d549d08feb67473f38e34abc02485b524","target":"graph","created_at":"2026-05-18T02:50:01Z","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 graph $G$ with vertex set $\\{v_1,v_2,\\ldots,v_n\\}$ is an intersection graph of segments if there are segments $s_1,\\ldots,s_n$ in the plane such that $s_i$ and $s_j$ have a common point if and only if $\\{v_i,v_j\\}$ is an edge of~$G$. In this expository paper, we consider the algorithmic problem of testing whether a given abstract graph is an intersection graph of segments.\n  It turned out that this problem is complete for an interesting recently introduced class of computational problems, denoted by $\\exists\\mathbb{R}$. This class consists of problems that can be reduced, in polynomial time,","authors_text":"Jiri Matousek","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-06-10T17:20:49Z","title":"Intersection graphs of segments and $\\exists\\mathbb{R}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2636","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:c293135bcd5b96fd3541e9b4b483ab7823e5f529df87ef4a9494ce28bae37077","target":"record","created_at":"2026-05-18T02:50:01Z","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":"13fbc62ca91612178a3f749f628893b50016ba208ce509684a6ff894506bf806","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-06-10T17:20:49Z","title_canon_sha256":"56c6999544fc4ebcf9000ef11bd48424e9aaa4d824f94d31e6b38bf1ad9eb30a"},"schema_version":"1.0","source":{"id":"1406.2636","kind":"arxiv","version":1}},"canonical_sha256":"b927de0e56e2c8d2c3aae32c100eee028ec9c62a8375ae6713910d73f0607be8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b927de0e56e2c8d2c3aae32c100eee028ec9c62a8375ae6713910d73f0607be8","first_computed_at":"2026-05-18T02:50:01.259432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:01.259432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Da/vifdYsCp42LqtXMivGFEFvg4lLP2SVyRieeShgfmV3hM9Z0CcQnsXieWqiSbPtgAxp6h9MyGXW9KLcRFkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:01.259888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2636","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c293135bcd5b96fd3541e9b4b483ab7823e5f529df87ef4a9494ce28bae37077","sha256:f222d0565f588606260b15b75119d17d549d08feb67473f38e34abc02485b524"],"state_sha256":"1a7f08f9dfaf46b9806b96fe932e7c4e1c8fa8371aba8782e865467262ea1e62"}