{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BVAP5M7S3L73JKFTAQH4CHJJZ6","short_pith_number":"pith:BVAP5M7S","schema_version":"1.0","canonical_sha256":"0d40feb3f2daffb4a8b3040fc11d29cfa4e2cc23f7a6f28c1935f2e82e8177b5","source":{"kind":"arxiv","id":"1610.07468","version":2},"attestation_state":"computed","paper":{"title":"Conditions on square geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Huda Chuangpishit, Jeannette Janssen","submitted_at":"2016-10-24T16:06:31Z","abstract_excerpt":"For any metric $d$ on $\\mathbb{R}^2$, an ($\\mathbb{R}^2,d$)-geometric graph is a graph whose vertices are points in $\\mathbb{R}^2$, and two vertices are adjacent if and only if their distance is at most 1. If $d=\\|.\\|_{\\infty}$, the metric derived from the $L_{\\infty}$ norm, then $(\\mathbb{R} ^2,\\|.\\|_{\\infty})$-geometric graphs are precisely those graphs that are the intersection of two unit interval graphs. We refer to $(\\mathbb{R}^2,\\|.\\|_{\\infty})$-geometric graphs as square geometric graphs. We represent a characterization of square geometric graphs. Using this characterization we provide"},"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":"1610.07468","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-24T16:06:31Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"1976ea84aecdc8c9317e8953e51bc23a69c1c8ae184814bba7cb7fa7f5618458","abstract_canon_sha256":"d25a0f8c042fa1f544292addf712d2cc307efcf7d83867c1c7d6cc106f23c7bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:21.675958Z","signature_b64":"3pwqFYJkSCKE/p39ZbV77YFMk8HV02tGYj7drgmec3JSJQkqYOw625vn3tcoRBhf1Yya19jqwlh5D5bAj2FwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d40feb3f2daffb4a8b3040fc11d29cfa4e2cc23f7a6f28c1935f2e82e8177b5","last_reissued_at":"2026-05-18T01:01:21.675385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:21.675385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conditions on square geometric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Huda Chuangpishit, Jeannette Janssen","submitted_at":"2016-10-24T16:06:31Z","abstract_excerpt":"For any metric $d$ on $\\mathbb{R}^2$, an ($\\mathbb{R}^2,d$)-geometric graph is a graph whose vertices are points in $\\mathbb{R}^2$, and two vertices are adjacent if and only if their distance is at most 1. If $d=\\|.\\|_{\\infty}$, the metric derived from the $L_{\\infty}$ norm, then $(\\mathbb{R} ^2,\\|.\\|_{\\infty})$-geometric graphs are precisely those graphs that are the intersection of two unit interval graphs. We refer to $(\\mathbb{R}^2,\\|.\\|_{\\infty})$-geometric graphs as square geometric graphs. We represent a characterization of square geometric graphs. Using this characterization we provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07468","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":""},"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":"1610.07468","created_at":"2026-05-18T01:01:21.675480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.07468v2","created_at":"2026-05-18T01:01:21.675480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07468","created_at":"2026-05-18T01:01:21.675480+00:00"},{"alias_kind":"pith_short_12","alias_value":"BVAP5M7S3L73","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BVAP5M7S3L73JKFT","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BVAP5M7S","created_at":"2026-05-18T12:30:09.641336+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/BVAP5M7S3L73JKFTAQH4CHJJZ6","json":"https://pith.science/pith/BVAP5M7S3L73JKFTAQH4CHJJZ6.json","graph_json":"https://pith.science/api/pith-number/BVAP5M7S3L73JKFTAQH4CHJJZ6/graph.json","events_json":"https://pith.science/api/pith-number/BVAP5M7S3L73JKFTAQH4CHJJZ6/events.json","paper":"https://pith.science/paper/BVAP5M7S"},"agent_actions":{"view_html":"https://pith.science/pith/BVAP5M7S3L73JKFTAQH4CHJJZ6","download_json":"https://pith.science/pith/BVAP5M7S3L73JKFTAQH4CHJJZ6.json","view_paper":"https://pith.science/paper/BVAP5M7S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.07468&json=true","fetch_graph":"https://pith.science/api/pith-number/BVAP5M7S3L73JKFTAQH4CHJJZ6/graph.json","fetch_events":"https://pith.science/api/pith-number/BVAP5M7S3L73JKFTAQH4CHJJZ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BVAP5M7S3L73JKFTAQH4CHJJZ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BVAP5M7S3L73JKFTAQH4CHJJZ6/action/storage_attestation","attest_author":"https://pith.science/pith/BVAP5M7S3L73JKFTAQH4CHJJZ6/action/author_attestation","sign_citation":"https://pith.science/pith/BVAP5M7S3L73JKFTAQH4CHJJZ6/action/citation_signature","submit_replication":"https://pith.science/pith/BVAP5M7S3L73JKFTAQH4CHJJZ6/action/replication_record"}},"created_at":"2026-05-18T01:01:21.675480+00:00","updated_at":"2026-05-18T01:01:21.675480+00:00"}