{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:M34XVJXZOIX5OO3KKBILU6UVER","short_pith_number":"pith:M34XVJXZ","schema_version":"1.0","canonical_sha256":"66f97aa6f9722fd73b6a5050ba7a95247adecf3d00bd809332a7eb8425ea9643","source":{"kind":"arxiv","id":"1202.4701","version":2},"attestation_state":"computed","paper":{"title":"The width of 5-dimensional prismatoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Matschke, Christophe Weibel, Francisco Santos","submitted_at":"2012-02-21T17:01:35Z","abstract_excerpt":"Santos' construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width greater than d. Santos, Stephen and Thomas (2012) have shown that this cannot occur in $d \\le 4$. Motivated by this we here study the width of 5-dimensional prismatoids, obtaining the following results:\n  - There are 5-prismatoids of width six with only 25 vertices, versus the 48 vertices in Santos' original construction. This leads to non-Hirsch polytopes of dimension 20, rather than the original dimension 43.\n  - There are 5-prismatoids with $n$ vertices a"},"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":"1202.4701","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-21T17:01:35Z","cross_cats_sorted":[],"title_canon_sha256":"f0278c619265d2cde5c82757072dc940dc3bf8b4a9f1f00685ce53086faa374b","abstract_canon_sha256":"0412afbeed989fc54a958f94bc3174b3efa0ceaaa9fb9bc122fad1605caa1122"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:42.136145Z","signature_b64":"ZK4SBkwxVtVQesiIfZVhnJmUAxf9SiNz7LC3/aZR/vmtaZrG6U3F7Ulo3VEt/svVnLcECyfrxy/lwTsEQLStBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66f97aa6f9722fd73b6a5050ba7a95247adecf3d00bd809332a7eb8425ea9643","last_reissued_at":"2026-05-18T01:32:42.135718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:42.135718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The width of 5-dimensional prismatoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Matschke, Christophe Weibel, Francisco Santos","submitted_at":"2012-02-21T17:01:35Z","abstract_excerpt":"Santos' construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width greater than d. Santos, Stephen and Thomas (2012) have shown that this cannot occur in $d \\le 4$. Motivated by this we here study the width of 5-dimensional prismatoids, obtaining the following results:\n  - There are 5-prismatoids of width six with only 25 vertices, versus the 48 vertices in Santos' original construction. This leads to non-Hirsch polytopes of dimension 20, rather than the original dimension 43.\n  - There are 5-prismatoids with $n$ vertices a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4701","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":"1202.4701","created_at":"2026-05-18T01:32:42.135785+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4701v2","created_at":"2026-05-18T01:32:42.135785+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4701","created_at":"2026-05-18T01:32:42.135785+00:00"},{"alias_kind":"pith_short_12","alias_value":"M34XVJXZOIX5","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"M34XVJXZOIX5OO3K","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"M34XVJXZ","created_at":"2026-05-18T12:27:14.488303+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/M34XVJXZOIX5OO3KKBILU6UVER","json":"https://pith.science/pith/M34XVJXZOIX5OO3KKBILU6UVER.json","graph_json":"https://pith.science/api/pith-number/M34XVJXZOIX5OO3KKBILU6UVER/graph.json","events_json":"https://pith.science/api/pith-number/M34XVJXZOIX5OO3KKBILU6UVER/events.json","paper":"https://pith.science/paper/M34XVJXZ"},"agent_actions":{"view_html":"https://pith.science/pith/M34XVJXZOIX5OO3KKBILU6UVER","download_json":"https://pith.science/pith/M34XVJXZOIX5OO3KKBILU6UVER.json","view_paper":"https://pith.science/paper/M34XVJXZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4701&json=true","fetch_graph":"https://pith.science/api/pith-number/M34XVJXZOIX5OO3KKBILU6UVER/graph.json","fetch_events":"https://pith.science/api/pith-number/M34XVJXZOIX5OO3KKBILU6UVER/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M34XVJXZOIX5OO3KKBILU6UVER/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M34XVJXZOIX5OO3KKBILU6UVER/action/storage_attestation","attest_author":"https://pith.science/pith/M34XVJXZOIX5OO3KKBILU6UVER/action/author_attestation","sign_citation":"https://pith.science/pith/M34XVJXZOIX5OO3KKBILU6UVER/action/citation_signature","submit_replication":"https://pith.science/pith/M34XVJXZOIX5OO3KKBILU6UVER/action/replication_record"}},"created_at":"2026-05-18T01:32:42.135785+00:00","updated_at":"2026-05-18T01:32:42.135785+00:00"}