{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZHESIJZF63DNUQT45JQPZJXQM5","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":"9ae0e894621f9df671b9d3c870e09ac331050bfcb9dee0d93083ad99f7da8932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-08-06T15:47:26Z","title_canon_sha256":"096b16d54df3d6f4c2e6188270cb7feb1c312ec34697686add9e22e7c026943c"},"schema_version":"1.0","source":{"id":"1708.01903","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01903","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01903v2","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01903","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZHESIJZF63DN","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZHESIJZF63DNUQT4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZHESIJZF","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:a4a90d9e02d7a1d0c63bcab8f91c794d783e8b0395382b1fe86e86eb8373bde0","target":"graph","created_at":"2026-05-18T00:36:21Z","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":"In this paper, we study grid-obstacle representations of graphs where we assign grid-points to vertices and define obstacles such that an edge exists if and only if an $xy$-monotone grid path connects the two endpoints without hitting an obstacle or another vertex. It was previously argued that all planar graphs have a grid-obstacle representation in 2D, and all graphs have a grid-obstacle representation in 3D. In this paper, we show that such constructions are possible with significantly smaller grid-size than previously achieved. Then we study the variant where vertices are not blocking, and","authors_text":"Saeed Mehrabi, Therese Biedl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-08-06T15:47:26Z","title":"Grid-Obstacle Representations with Connections to Staircase Guarding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01903","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":"sha256:351acc09a1b03e729bdd8637b006d7ca1500e30f737f41e8e89b0e5d9bcf6a85","target":"record","created_at":"2026-05-18T00:36:21Z","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":"9ae0e894621f9df671b9d3c870e09ac331050bfcb9dee0d93083ad99f7da8932","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-08-06T15:47:26Z","title_canon_sha256":"096b16d54df3d6f4c2e6188270cb7feb1c312ec34697686add9e22e7c026943c"},"schema_version":"1.0","source":{"id":"1708.01903","kind":"arxiv","version":2}},"canonical_sha256":"c9c9242725f6c6da427cea60fca6f067419e7038a562bec7a0249ac12a5151a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9c9242725f6c6da427cea60fca6f067419e7038a562bec7a0249ac12a5151a4","first_computed_at":"2026-05-18T00:36:21.810290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:21.810290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TXARu3V4wBy+aohJo1IAROmaHDXTr0ibHR/OJqh1HrM1UiQyRS0uZYgGBZFpTdOoMWzksAbozznFaY79pfoEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:21.811069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01903","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:351acc09a1b03e729bdd8637b006d7ca1500e30f737f41e8e89b0e5d9bcf6a85","sha256:a4a90d9e02d7a1d0c63bcab8f91c794d783e8b0395382b1fe86e86eb8373bde0"],"state_sha256":"506446250eb9032a5cc099597aff608f8794ad996bbf46e6649c3cd5361f30f1"}