{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CTB425DKQPPNOIFEEZ5GOXIQWP","short_pith_number":"pith:CTB425DK","schema_version":"1.0","canonical_sha256":"14c3cd746a83ded720a4267a675d10b3c0526006bd2f533176ac73b6f1f5c391","source":{"kind":"arxiv","id":"1211.2039","version":2},"attestation_state":"computed","paper":{"title":"The combinatorics of interval-vector polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Ruiz, Gabriel Dorfsman-Hopkins, Jessica De Silva, Joseph Pruitt, Matthias Beck","submitted_at":"2012-11-09T04:29:34Z","abstract_excerpt":"An \\emph{interval vector} is a $(0,1)$-vector in $\\mathbb{R}^n$ for which all the 1's appear consecutively, and an \\emph{interval-vector polytope} is the convex hull of a set of interval vectors in $\\mathbb{R}^n$. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers given by the Pascal 3-triangle."},"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":"1211.2039","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-09T04:29:34Z","cross_cats_sorted":[],"title_canon_sha256":"2f0949649f336c089b37df8776e973515fa11560ddbec82d8d7ee64bf49d099e","abstract_canon_sha256":"2e7b8faecce73e09f066233f88775e23b17a4dce94f9ab0401d132ade071ba43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.086183Z","signature_b64":"tAoCmR4ZkRBH8odJqZw3/TyDdLyfbzvIc0FaDaoEyEoArJC86JTnm/N6gFSRp0Sa4Czd+SM9IfeX+QHYZZe/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14c3cd746a83ded720a4267a675d10b3c0526006bd2f533176ac73b6f1f5c391","last_reissued_at":"2026-05-18T03:11:24.085657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.085657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The combinatorics of interval-vector polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Ruiz, Gabriel Dorfsman-Hopkins, Jessica De Silva, Joseph Pruitt, Matthias Beck","submitted_at":"2012-11-09T04:29:34Z","abstract_excerpt":"An \\emph{interval vector} is a $(0,1)$-vector in $\\mathbb{R}^n$ for which all the 1's appear consecutively, and an \\emph{interval-vector polytope} is the convex hull of a set of interval vectors in $\\mathbb{R}^n$. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers given by the Pascal 3-triangle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2039","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":"1211.2039","created_at":"2026-05-18T03:11:24.085739+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2039v2","created_at":"2026-05-18T03:11:24.085739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2039","created_at":"2026-05-18T03:11:24.085739+00:00"},{"alias_kind":"pith_short_12","alias_value":"CTB425DKQPPN","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CTB425DKQPPNOIFE","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CTB425DK","created_at":"2026-05-18T12:27:01.376967+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/CTB425DKQPPNOIFEEZ5GOXIQWP","json":"https://pith.science/pith/CTB425DKQPPNOIFEEZ5GOXIQWP.json","graph_json":"https://pith.science/api/pith-number/CTB425DKQPPNOIFEEZ5GOXIQWP/graph.json","events_json":"https://pith.science/api/pith-number/CTB425DKQPPNOIFEEZ5GOXIQWP/events.json","paper":"https://pith.science/paper/CTB425DK"},"agent_actions":{"view_html":"https://pith.science/pith/CTB425DKQPPNOIFEEZ5GOXIQWP","download_json":"https://pith.science/pith/CTB425DKQPPNOIFEEZ5GOXIQWP.json","view_paper":"https://pith.science/paper/CTB425DK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2039&json=true","fetch_graph":"https://pith.science/api/pith-number/CTB425DKQPPNOIFEEZ5GOXIQWP/graph.json","fetch_events":"https://pith.science/api/pith-number/CTB425DKQPPNOIFEEZ5GOXIQWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CTB425DKQPPNOIFEEZ5GOXIQWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CTB425DKQPPNOIFEEZ5GOXIQWP/action/storage_attestation","attest_author":"https://pith.science/pith/CTB425DKQPPNOIFEEZ5GOXIQWP/action/author_attestation","sign_citation":"https://pith.science/pith/CTB425DKQPPNOIFEEZ5GOXIQWP/action/citation_signature","submit_replication":"https://pith.science/pith/CTB425DKQPPNOIFEEZ5GOXIQWP/action/replication_record"}},"created_at":"2026-05-18T03:11:24.085739+00:00","updated_at":"2026-05-18T03:11:24.085739+00:00"}