{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NMHPZCAB4VZHAU2MBVKX5JP7G5","short_pith_number":"pith:NMHPZCAB","schema_version":"1.0","canonical_sha256":"6b0efc8801e57270534c0d557ea5ff37465f03684e91fc5b950b6caa86e919d7","source":{"kind":"arxiv","id":"1702.08739","version":4},"attestation_state":"computed","paper":{"title":"On the reconstruction of polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Yost, Eran Nevo, Guillermo Pineda-Villavicencio, Joseph Doolittle, Julien Ugon","submitted_at":"2017-02-28T11:02:44Z","abstract_excerpt":"Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined by its graph, namely its $1$-skeleton. Call a vertex of a $d$-polytope \\emph{nonsimple} if the number of edges incident to it is more than $d$.\n  We show that (1) the face lattice of any $d$-polytope with at most two nonsimple vertices is determined by its $1$-skeleton; (2) the face lattice of any $d$-polytope with at most $d-2$ nonsimple vertices is determined by its $2$-skeleton; and (3) for any $d>3$ there are two $d$-polytopes with $d-1$ nonsimple vertices, isomorphic $(d-3)$-skeleta and noniso"},"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":"1702.08739","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-28T11:02:44Z","cross_cats_sorted":[],"title_canon_sha256":"6af9de7f3f45da5bb66c9776e7dfb752f916cc38caec7f5a31d8567ac3adedec","abstract_canon_sha256":"404f33cec88dacf8581b0fbd2cbf28f38bf1094c56dd4141621e0358d792b597"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:56.659903Z","signature_b64":"BJ3/zrXfuPLsBCCRDO2FoxqpnJHX7O2Vn1xF+H0OdBH64ZCan+2H7dygBm7cU/DghYMMTwkhCEtmCVdO4HsJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b0efc8801e57270534c0d557ea5ff37465f03684e91fc5b950b6caa86e919d7","last_reissued_at":"2026-05-18T00:20:56.659494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:56.659494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the reconstruction of polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Yost, Eran Nevo, Guillermo Pineda-Villavicencio, Joseph Doolittle, Julien Ugon","submitted_at":"2017-02-28T11:02:44Z","abstract_excerpt":"Blind and Mani, and later Kalai, showed that the face lattice of a simple polytope is determined by its graph, namely its $1$-skeleton. Call a vertex of a $d$-polytope \\emph{nonsimple} if the number of edges incident to it is more than $d$.\n  We show that (1) the face lattice of any $d$-polytope with at most two nonsimple vertices is determined by its $1$-skeleton; (2) the face lattice of any $d$-polytope with at most $d-2$ nonsimple vertices is determined by its $2$-skeleton; and (3) for any $d>3$ there are two $d$-polytopes with $d-1$ nonsimple vertices, isomorphic $(d-3)$-skeleta and noniso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08739","kind":"arxiv","version":4},"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":"1702.08739","created_at":"2026-05-18T00:20:56.659563+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.08739v4","created_at":"2026-05-18T00:20:56.659563+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08739","created_at":"2026-05-18T00:20:56.659563+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMHPZCAB4VZH","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMHPZCAB4VZHAU2M","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMHPZCAB","created_at":"2026-05-18T12:31:34.259226+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/NMHPZCAB4VZHAU2MBVKX5JP7G5","json":"https://pith.science/pith/NMHPZCAB4VZHAU2MBVKX5JP7G5.json","graph_json":"https://pith.science/api/pith-number/NMHPZCAB4VZHAU2MBVKX5JP7G5/graph.json","events_json":"https://pith.science/api/pith-number/NMHPZCAB4VZHAU2MBVKX5JP7G5/events.json","paper":"https://pith.science/paper/NMHPZCAB"},"agent_actions":{"view_html":"https://pith.science/pith/NMHPZCAB4VZHAU2MBVKX5JP7G5","download_json":"https://pith.science/pith/NMHPZCAB4VZHAU2MBVKX5JP7G5.json","view_paper":"https://pith.science/paper/NMHPZCAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.08739&json=true","fetch_graph":"https://pith.science/api/pith-number/NMHPZCAB4VZHAU2MBVKX5JP7G5/graph.json","fetch_events":"https://pith.science/api/pith-number/NMHPZCAB4VZHAU2MBVKX5JP7G5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMHPZCAB4VZHAU2MBVKX5JP7G5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMHPZCAB4VZHAU2MBVKX5JP7G5/action/storage_attestation","attest_author":"https://pith.science/pith/NMHPZCAB4VZHAU2MBVKX5JP7G5/action/author_attestation","sign_citation":"https://pith.science/pith/NMHPZCAB4VZHAU2MBVKX5JP7G5/action/citation_signature","submit_replication":"https://pith.science/pith/NMHPZCAB4VZHAU2MBVKX5JP7G5/action/replication_record"}},"created_at":"2026-05-18T00:20:56.659563+00:00","updated_at":"2026-05-18T00:20:56.659563+00:00"}