{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:WMMOBVRX62L3EICK2DPJIBMHLB","short_pith_number":"pith:WMMOBVRX","schema_version":"1.0","canonical_sha256":"b318e0d637f697b2204ad0de94058758624768cf1bcb762cda0d7426e8c18e77","source":{"kind":"arxiv","id":"2404.02369","version":2},"attestation_state":"computed","paper":{"title":"Grid-drawings of graphs in three-dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ethan Patrick White, Jozsef Balogh","submitted_at":"2024-04-03T00:02:23Z","abstract_excerpt":"Using probabilistic methods, we obtain grid-drawings of graphs without crossings with low volume and small aspect ratio. We show that every $D$-degenerate graph on $n$ vertices can be drawn in $[m]^3$ where $m^3 = O(D^2 n\\log n)$. In particular, every graph of bounded maximum degree can be drawn in a grid with volume $O(n \\log n)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2404.02369","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-04-03T00:02:23Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"791a20f00d6fbc7d0f5f025002e2065e1b85b3a6b562c6c95b9e2fa4891e7b62","abstract_canon_sha256":"3352fc9fad676e620584a2ab3e3a2c81864a9f34e1889ce20e9b2196213d102b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:32:12.407643Z","signature_b64":"vBJJkYDuk4RsQHB1WsdgNyG6UwBTvrnU5NP1hC9EVk6t2z4nVXyZCAVlJ2NrbtNWaXm2skqucDO/s+UDA1KQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b318e0d637f697b2204ad0de94058758624768cf1bcb762cda0d7426e8c18e77","last_reissued_at":"2026-07-05T08:32:12.407147Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:32:12.407147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Grid-drawings of graphs in three-dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ethan Patrick White, Jozsef Balogh","submitted_at":"2024-04-03T00:02:23Z","abstract_excerpt":"Using probabilistic methods, we obtain grid-drawings of graphs without crossings with low volume and small aspect ratio. We show that every $D$-degenerate graph on $n$ vertices can be drawn in $[m]^3$ where $m^3 = O(D^2 n\\log n)$. In particular, every graph of bounded maximum degree can be drawn in a grid with volume $O(n \\log n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.02369","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.02369/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2404.02369","created_at":"2026-07-05T08:32:12.407202+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.02369v2","created_at":"2026-07-05T08:32:12.407202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.02369","created_at":"2026-07-05T08:32:12.407202+00:00"},{"alias_kind":"pith_short_12","alias_value":"WMMOBVRX62L3","created_at":"2026-07-05T08:32:12.407202+00:00"},{"alias_kind":"pith_short_16","alias_value":"WMMOBVRX62L3EICK","created_at":"2026-07-05T08:32:12.407202+00:00"},{"alias_kind":"pith_short_8","alias_value":"WMMOBVRX","created_at":"2026-07-05T08:32:12.407202+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB","json":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB.json","graph_json":"https://pith.science/api/pith-number/WMMOBVRX62L3EICK2DPJIBMHLB/graph.json","events_json":"https://pith.science/api/pith-number/WMMOBVRX62L3EICK2DPJIBMHLB/events.json","paper":"https://pith.science/paper/WMMOBVRX"},"agent_actions":{"view_html":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB","download_json":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB.json","view_paper":"https://pith.science/paper/WMMOBVRX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.02369&json=true","fetch_graph":"https://pith.science/api/pith-number/WMMOBVRX62L3EICK2DPJIBMHLB/graph.json","fetch_events":"https://pith.science/api/pith-number/WMMOBVRX62L3EICK2DPJIBMHLB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB/action/storage_attestation","attest_author":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB/action/author_attestation","sign_citation":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB/action/citation_signature","submit_replication":"https://pith.science/pith/WMMOBVRX62L3EICK2DPJIBMHLB/action/replication_record"}},"created_at":"2026-07-05T08:32:12.407202+00:00","updated_at":"2026-07-05T08:32:12.407202+00:00"}