{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5NWBFU5ZMNCICKRIVKZSCIMLYN","short_pith_number":"pith:5NWBFU5Z","schema_version":"1.0","canonical_sha256":"eb6c12d3b96344812a28aab321218bc36b648528b0bf6ea58ce3e5459abcd87e","source":{"kind":"arxiv","id":"1508.03537","version":2},"attestation_state":"computed","paper":{"title":"Scribability problems for polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Arnau Padrol, Hao Chen","submitted_at":"2015-08-14T15:05:55Z","abstract_excerpt":"In this paper we study various scribability problems for polytopes. We begin with the classical $k$-scribability problem proposed by Steiner and generalized by Schulte, which asks about the existence of $d$-polytopes that cannot be realized with all $k$-faces tangent to a sphere. We answer this problem for stacked and cyclic polytopes for all values of $d$ and $k$. We then continue with the weak scribability problem proposed by Gr\\\"unbaum and Shephard, for which we complete the work of Schulte by presenting non weakly circumscribable $3$-polytopes. Finally, we propose new $(i,j)$-scribability "},"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":"1508.03537","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-08-14T15:05:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4df85d164ae562be0eb47998280338f00a7a96cff1d012eda94f3acb58131c83","abstract_canon_sha256":"c85554bdecb0acd974ff5ff7fd34589df509a8792e39f73c4998cfd84774e9d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:56.270580Z","signature_b64":"x3J0X/3PXuW9i2eHF3AsADOXXtjvhYxe7FuJFPecm6Kdoaj3GHDOU2D8/jByp+hXR3J43MJVKMspOAj8o49QCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb6c12d3b96344812a28aab321218bc36b648528b0bf6ea58ce3e5459abcd87e","last_reissued_at":"2026-05-18T00:07:56.269876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:56.269876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scribability problems for polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Arnau Padrol, Hao Chen","submitted_at":"2015-08-14T15:05:55Z","abstract_excerpt":"In this paper we study various scribability problems for polytopes. We begin with the classical $k$-scribability problem proposed by Steiner and generalized by Schulte, which asks about the existence of $d$-polytopes that cannot be realized with all $k$-faces tangent to a sphere. We answer this problem for stacked and cyclic polytopes for all values of $d$ and $k$. We then continue with the weak scribability problem proposed by Gr\\\"unbaum and Shephard, for which we complete the work of Schulte by presenting non weakly circumscribable $3$-polytopes. Finally, we propose new $(i,j)$-scribability "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03537","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":"1508.03537","created_at":"2026-05-18T00:07:56.269998+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.03537v2","created_at":"2026-05-18T00:07:56.269998+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03537","created_at":"2026-05-18T00:07:56.269998+00:00"},{"alias_kind":"pith_short_12","alias_value":"5NWBFU5ZMNCI","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5NWBFU5ZMNCICKRI","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5NWBFU5Z","created_at":"2026-05-18T12:29:05.191682+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/5NWBFU5ZMNCICKRIVKZSCIMLYN","json":"https://pith.science/pith/5NWBFU5ZMNCICKRIVKZSCIMLYN.json","graph_json":"https://pith.science/api/pith-number/5NWBFU5ZMNCICKRIVKZSCIMLYN/graph.json","events_json":"https://pith.science/api/pith-number/5NWBFU5ZMNCICKRIVKZSCIMLYN/events.json","paper":"https://pith.science/paper/5NWBFU5Z"},"agent_actions":{"view_html":"https://pith.science/pith/5NWBFU5ZMNCICKRIVKZSCIMLYN","download_json":"https://pith.science/pith/5NWBFU5ZMNCICKRIVKZSCIMLYN.json","view_paper":"https://pith.science/paper/5NWBFU5Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.03537&json=true","fetch_graph":"https://pith.science/api/pith-number/5NWBFU5ZMNCICKRIVKZSCIMLYN/graph.json","fetch_events":"https://pith.science/api/pith-number/5NWBFU5ZMNCICKRIVKZSCIMLYN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5NWBFU5ZMNCICKRIVKZSCIMLYN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5NWBFU5ZMNCICKRIVKZSCIMLYN/action/storage_attestation","attest_author":"https://pith.science/pith/5NWBFU5ZMNCICKRIVKZSCIMLYN/action/author_attestation","sign_citation":"https://pith.science/pith/5NWBFU5ZMNCICKRIVKZSCIMLYN/action/citation_signature","submit_replication":"https://pith.science/pith/5NWBFU5ZMNCICKRIVKZSCIMLYN/action/replication_record"}},"created_at":"2026-05-18T00:07:56.269998+00:00","updated_at":"2026-05-18T00:07:56.269998+00:00"}