{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BYRV5SMVBJSCIJ6Z2UJZ7DBMG7","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":"abc233252125cf98b547453e12fd827919b596244ae97ad107b083a4b5d39f21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-14T11:22:49Z","title_canon_sha256":"b1744ea727aaff0db4a0e1dc54778fd708076a18e029a3139bb3c486e2d6e11e"},"schema_version":"1.0","source":{"id":"1505.03687","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03687","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03687v2","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03687","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"BYRV5SMVBJSC","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BYRV5SMVBJSCIJ6Z","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BYRV5SMV","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:1550d85ba405bda84cb823fd57badaa39084c0b6436a59e2d8688f84db63be2f","target":"graph","created_at":"2026-05-18T01:09:46Z","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":"For a lattice $L$ of $R^n$, a sphere $S(c,r)$ of center $c$ and radius $r$ is called {\\em empty} if for any $v\\in L$ we have $\\Vert v - c\\Vert \\geq r$. Then the set $S(c,r)\\cap L$ is the vertex set of a {\\em Delaunay polytope} $P=conv(S(c,r)\\cap L)$. A Delaunay polytope is called {\\em perfect} if any affine transformation $\\phi$ such that $\\phi(P)$ is a Delaunay polytope is necessarily an isometry of the space composed with an homothety.\n  Perfect Delaunay polytopes are remarkable structure that exist only if $n=1$ or $n\\geq 6$ and they have shown up recently in covering maxima studies. Here w","authors_text":"Mathieu Dutour Sikiric","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-14T11:22:49Z","title":"The seven dimensional perfect Delaunay polytopes and Delaunay simplices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03687","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":"sha256:87481c9cf3f77f095071c82c987f6580fd4d2c3e8182d926560b2e31610c9bab","target":"record","created_at":"2026-05-18T01:09:46Z","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":"abc233252125cf98b547453e12fd827919b596244ae97ad107b083a4b5d39f21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-14T11:22:49Z","title_canon_sha256":"b1744ea727aaff0db4a0e1dc54778fd708076a18e029a3139bb3c486e2d6e11e"},"schema_version":"1.0","source":{"id":"1505.03687","kind":"arxiv","version":2}},"canonical_sha256":"0e235ec9950a642427d9d5139f8c2c37fe6a8273ac8d26732d401da2f86db656","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e235ec9950a642427d9d5139f8c2c37fe6a8273ac8d26732d401da2f86db656","first_computed_at":"2026-05-18T01:09:46.929917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:46.929917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WhN67pKFYhXyrkaYBESNDiQ+6SMowWQSSFxNL/3octaOxphnOtREr8rhjC6Jwu9v36jYupjYanCppgk0WSLqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:46.930479Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03687","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87481c9cf3f77f095071c82c987f6580fd4d2c3e8182d926560b2e31610c9bab","sha256:1550d85ba405bda84cb823fd57badaa39084c0b6436a59e2d8688f84db63be2f"],"state_sha256":"fb3d4f8374a70bcacde9930a6127bd3fb2d16ae54d56ffed2e3c7207c6008cf1"}