{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:H3BCCRML22QZICSALURB2IJEFE","short_pith_number":"pith:H3BCCRML","schema_version":"1.0","canonical_sha256":"3ec221458bd6a1940a405d221d2124292d24867e1334bea57cfb7086ae3be76d","source":{"kind":"arxiv","id":"1812.03212","version":1},"attestation_state":"computed","paper":{"title":"Cut polytope has vertices on a line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Nevena Maric","submitted_at":"2018-12-07T20:48:08Z","abstract_excerpt":"The cut polytope ${\\rm CUT}(n)$ is the convex hull of the cut vectors in a complete graph with vertex set $\\{1,\\ldots,n\\}$. It is well known in the area of combinatorial optimization and recently has also been studied in a direct relation with admissible correlations of symmetric Bernoulli random variables. That probabilistic interpretation is a starting point of this work in conjunction with a natural binary encoding of the CUT($n$). We show that for any $n$, with appropriate scaling, all vertices of the polytope ${\\mathbf 1}$-CUT($n$) encoded as integers are approximately on the line $y= x-1"},"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":"1812.03212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-12-07T20:48:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"45490dc4fe28c7d577a6ed9932a678cf7fba4412c24b37fbaebbda78fe46f5dc","abstract_canon_sha256":"db98cb404d17de99e9b3a8db1a3e4bfea48ae668d9ab2250e9dc313214a03603"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:46.893422Z","signature_b64":"9bpWhkNLY/jDvM8WCNWg4iCp8lNd38CgGMk2Q7NYDwnAyRk675hHmiZTS2wmygnhoFTrv4ykGobhyR9O2Ce3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ec221458bd6a1940a405d221d2124292d24867e1334bea57cfb7086ae3be76d","last_reissued_at":"2026-05-17T23:58:46.893007Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:46.893007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cut polytope has vertices on a line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Nevena Maric","submitted_at":"2018-12-07T20:48:08Z","abstract_excerpt":"The cut polytope ${\\rm CUT}(n)$ is the convex hull of the cut vectors in a complete graph with vertex set $\\{1,\\ldots,n\\}$. It is well known in the area of combinatorial optimization and recently has also been studied in a direct relation with admissible correlations of symmetric Bernoulli random variables. That probabilistic interpretation is a starting point of this work in conjunction with a natural binary encoding of the CUT($n$). We show that for any $n$, with appropriate scaling, all vertices of the polytope ${\\mathbf 1}$-CUT($n$) encoded as integers are approximately on the line $y= x-1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03212","kind":"arxiv","version":1},"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":"1812.03212","created_at":"2026-05-17T23:58:46.893083+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.03212v1","created_at":"2026-05-17T23:58:46.893083+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03212","created_at":"2026-05-17T23:58:46.893083+00:00"},{"alias_kind":"pith_short_12","alias_value":"H3BCCRML22QZ","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"H3BCCRML22QZICSA","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"H3BCCRML","created_at":"2026-05-18T12:32:28.185984+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/H3BCCRML22QZICSALURB2IJEFE","json":"https://pith.science/pith/H3BCCRML22QZICSALURB2IJEFE.json","graph_json":"https://pith.science/api/pith-number/H3BCCRML22QZICSALURB2IJEFE/graph.json","events_json":"https://pith.science/api/pith-number/H3BCCRML22QZICSALURB2IJEFE/events.json","paper":"https://pith.science/paper/H3BCCRML"},"agent_actions":{"view_html":"https://pith.science/pith/H3BCCRML22QZICSALURB2IJEFE","download_json":"https://pith.science/pith/H3BCCRML22QZICSALURB2IJEFE.json","view_paper":"https://pith.science/paper/H3BCCRML","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.03212&json=true","fetch_graph":"https://pith.science/api/pith-number/H3BCCRML22QZICSALURB2IJEFE/graph.json","fetch_events":"https://pith.science/api/pith-number/H3BCCRML22QZICSALURB2IJEFE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H3BCCRML22QZICSALURB2IJEFE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H3BCCRML22QZICSALURB2IJEFE/action/storage_attestation","attest_author":"https://pith.science/pith/H3BCCRML22QZICSALURB2IJEFE/action/author_attestation","sign_citation":"https://pith.science/pith/H3BCCRML22QZICSALURB2IJEFE/action/citation_signature","submit_replication":"https://pith.science/pith/H3BCCRML22QZICSALURB2IJEFE/action/replication_record"}},"created_at":"2026-05-17T23:58:46.893083+00:00","updated_at":"2026-05-17T23:58:46.893083+00:00"}