{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UPISHQSRJPXMODUDFQ5EFMR42Z","short_pith_number":"pith:UPISHQSR","schema_version":"1.0","canonical_sha256":"a3d123c2514beec70e832c3a42b23cd6493870a7770582647e6f76cac4e87680","source":{"kind":"arxiv","id":"1511.08054","version":5},"attestation_state":"computed","paper":{"title":"The excluded minors for isometric realizability in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.MG","authors_text":"Antonios Varvitsiotis, Gwena\\\"el Joret, Samuel Fiorini, Tony Huynh","submitted_at":"2015-11-25T13:39:08Z","abstract_excerpt":"Let $G$ be a graph and $p \\in [1, \\infty]$. The parameter $f_p(G)$ is the least integer $k$ such that for all $m$ and all vectors $(r_v)_{v \\in V(G)} \\subseteq \\mathbb{R}^m$, there exist vectors $(q_v)_{v \\in V(G)} \\subseteq \\mathbb{R}^k$ satisfying $$\\|r_v-r_w\\|_p=\\|q_v-q_w\\|_p, \\ \\text{ for all }\\ vw\\in E(G).$$ It is easy to check that $f_p(G)$ is always finite and that it is minor monotone. By the graph minor theorem of Robertson and Seymour, there are a finite number of excluded minors for the property $f_p(G) \\leq k$.\n  In this paper, we determine the complete set of excluded minors for $"},"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":"1511.08054","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-11-25T13:39:08Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"05199864d67eba21ca2cf12b9bbd3121686740d289024449fb0b38685dc9d929","abstract_canon_sha256":"fcdf521718649808d557240d8d310e2395c2f4b7b26e2e19022223fbd4d68ef8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:54.824863Z","signature_b64":"1Y/KuVRmTkIxtT6TglURn1KAN09v+7N4IcUlerb8E5qQJh4kytev/Jxw6ljfiSAFNJqgUkdnKzlQ0fCl6TK+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3d123c2514beec70e832c3a42b23cd6493870a7770582647e6f76cac4e87680","last_reissued_at":"2026-05-18T00:48:54.824295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:54.824295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The excluded minors for isometric realizability in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.MG","authors_text":"Antonios Varvitsiotis, Gwena\\\"el Joret, Samuel Fiorini, Tony Huynh","submitted_at":"2015-11-25T13:39:08Z","abstract_excerpt":"Let $G$ be a graph and $p \\in [1, \\infty]$. The parameter $f_p(G)$ is the least integer $k$ such that for all $m$ and all vectors $(r_v)_{v \\in V(G)} \\subseteq \\mathbb{R}^m$, there exist vectors $(q_v)_{v \\in V(G)} \\subseteq \\mathbb{R}^k$ satisfying $$\\|r_v-r_w\\|_p=\\|q_v-q_w\\|_p, \\ \\text{ for all }\\ vw\\in E(G).$$ It is easy to check that $f_p(G)$ is always finite and that it is minor monotone. By the graph minor theorem of Robertson and Seymour, there are a finite number of excluded minors for the property $f_p(G) \\leq k$.\n  In this paper, we determine the complete set of excluded minors for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08054","kind":"arxiv","version":5},"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":"1511.08054","created_at":"2026-05-18T00:48:54.824398+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.08054v5","created_at":"2026-05-18T00:48:54.824398+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08054","created_at":"2026-05-18T00:48:54.824398+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPISHQSRJPXM","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPISHQSRJPXMODUD","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPISHQSR","created_at":"2026-05-18T12:29:44.643036+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/UPISHQSRJPXMODUDFQ5EFMR42Z","json":"https://pith.science/pith/UPISHQSRJPXMODUDFQ5EFMR42Z.json","graph_json":"https://pith.science/api/pith-number/UPISHQSRJPXMODUDFQ5EFMR42Z/graph.json","events_json":"https://pith.science/api/pith-number/UPISHQSRJPXMODUDFQ5EFMR42Z/events.json","paper":"https://pith.science/paper/UPISHQSR"},"agent_actions":{"view_html":"https://pith.science/pith/UPISHQSRJPXMODUDFQ5EFMR42Z","download_json":"https://pith.science/pith/UPISHQSRJPXMODUDFQ5EFMR42Z.json","view_paper":"https://pith.science/paper/UPISHQSR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.08054&json=true","fetch_graph":"https://pith.science/api/pith-number/UPISHQSRJPXMODUDFQ5EFMR42Z/graph.json","fetch_events":"https://pith.science/api/pith-number/UPISHQSRJPXMODUDFQ5EFMR42Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPISHQSRJPXMODUDFQ5EFMR42Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPISHQSRJPXMODUDFQ5EFMR42Z/action/storage_attestation","attest_author":"https://pith.science/pith/UPISHQSRJPXMODUDFQ5EFMR42Z/action/author_attestation","sign_citation":"https://pith.science/pith/UPISHQSRJPXMODUDFQ5EFMR42Z/action/citation_signature","submit_replication":"https://pith.science/pith/UPISHQSRJPXMODUDFQ5EFMR42Z/action/replication_record"}},"created_at":"2026-05-18T00:48:54.824398+00:00","updated_at":"2026-05-18T00:48:54.824398+00:00"}