{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FEBVY3T6MGOAIBHUSE4CZHBEUQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"27973b62888234c85a4c0a709be1bd24fd514c51c162f42d9fe2b809b12538bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-26T05:03:56Z","title_canon_sha256":"46ca6ef60f0e993ed8571e7eaa2d0d42857de81288c0e72c986b4b20bf37ed3a"},"schema_version":"1.0","source":{"id":"1707.08288","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08288","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08288v2","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08288","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"FEBVY3T6MGOA","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FEBVY3T6MGOAIBHU","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FEBVY3T6","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:a8525507dfa2b0b735b426245a513cc1c6a2cbe33456766a20cab3f9ef803016","target":"graph","created_at":"2026-05-18T00:18:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We choose some special unit vectors $\\boldsymbol{n}_1,\\dots,\\boldsymbol{n}_5$ in $\\mathbb{R}^3$ and denote by $\\mathscr{L}\\subset\\mathbb{R}^5$ the set of all points $(L_1,\\dots,L_5)\\in\\mathbb{R}^5$ with the following property: there exists a compact convex polytope $P\\subset\\mathbb{R}^3$ such that the vectors $\\boldsymbol{n}_1,\\dots,\\boldsymbol{n}_5$ (and no other vector) are unit outward normals to the faces of $P$ and the perimeter of the face with the outward normal $\\boldsymbol{n}_k$ is equal to $L_k$ for all $k=1,\\dots,5$. Our main result reads that $\\mathscr{L}$ is not a locally-analytic","authors_text":"Victor Alexandrov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-26T05:03:56Z","title":"Why there is no an existence theorem for a convex polytope with prescribed directions and perimeters of the faces?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08288","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c62df4c0d5a40cb9a9454f31a64a0a50e41b1c1cd9e3d9760e2227d2ed736e9a","target":"record","created_at":"2026-05-18T00:18:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"27973b62888234c85a4c0a709be1bd24fd514c51c162f42d9fe2b809b12538bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-26T05:03:56Z","title_canon_sha256":"46ca6ef60f0e993ed8571e7eaa2d0d42857de81288c0e72c986b4b20bf37ed3a"},"schema_version":"1.0","source":{"id":"1707.08288","kind":"arxiv","version":2}},"canonical_sha256":"29035c6e7e619c0404f491382c9c24a430f06a319195025dbb89db5f0befc4c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29035c6e7e619c0404f491382c9c24a430f06a319195025dbb89db5f0befc4c7","first_computed_at":"2026-05-18T00:18:31.684579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:31.684579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mDKObfgYgd27oSCHAQkbJP23DpIslhmWznvhOQ02TYRhv9hJrwyosIOY37fK/mH54oLywDSUB3bjPiO4dRQTCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:31.685131Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.08288","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c62df4c0d5a40cb9a9454f31a64a0a50e41b1c1cd9e3d9760e2227d2ed736e9a","sha256:a8525507dfa2b0b735b426245a513cc1c6a2cbe33456766a20cab3f9ef803016"],"state_sha256":"c7440131f394be017dd3f853fc327a272c4cef840dd51fdcd3d860f1428632bc"}