{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BR4UTAHZ64R5ZT4F5N76ZXF6WZ","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":"29049996cb9fff2691538e26a4c9e1467249d7b1a19a7b037c4b52a2da4b786c","cross_cats_sorted":["math.AG","math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-17T10:40:08Z","title_canon_sha256":"e49b9fbd78b699163ec85000f09be35cbaee190f3cbaefd89b020fec13e2f8aa"},"schema_version":"1.0","source":{"id":"1807.06327","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06327","created_at":"2026-05-18T00:10:27Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06327v2","created_at":"2026-05-18T00:10:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06327","created_at":"2026-05-18T00:10:27Z"},{"alias_kind":"pith_short_12","alias_value":"BR4UTAHZ64R5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BR4UTAHZ64R5ZT4F","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BR4UTAHZ","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:7af558d062daee54010f9021eabde0525633668b709ca4ba0b91093aeb9e22bd","target":"graph","created_at":"2026-05-18T00:10:27Z","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":"A $d$-dimensional closed convex set $K$ in $\\mathbb{R}^d$ is said to be lattice-free if the interior of $K$ is disjoint with $\\mathbb{Z}^d$. We consider the following two families of lattice-free polytopes: the family $\\mathcal{L}^d$ of integral lattice-free polytopes in $\\mathbb{R}^d$ that are not properly contained in another integral lattice-free polytope and its subfamily $\\mathcal{M}^d$ consisting of integral lattice-free polytopes in $\\mathbb{R}^d$ which are not properly contained in another lattice-free set. It is known that $\\mathcal{M}^d = \\mathcal{L}^d$ holds for $d \\le 3$ and, for e","authors_text":"Gennadiy Averkov","cross_cats":["math.AG","math.MG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-17T10:40:08Z","title":"Difference between families of weakly and strongly maximal integral lattice-free polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06327","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":"sha256:535f14b422b7e3acdd74f9f9c6ec6c6cf0226a85048acf3f5ea4fb1092d9cc4a","target":"record","created_at":"2026-05-18T00:10:27Z","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":"29049996cb9fff2691538e26a4c9e1467249d7b1a19a7b037c4b52a2da4b786c","cross_cats_sorted":["math.AG","math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-17T10:40:08Z","title_canon_sha256":"e49b9fbd78b699163ec85000f09be35cbaee190f3cbaefd89b020fec13e2f8aa"},"schema_version":"1.0","source":{"id":"1807.06327","kind":"arxiv","version":2}},"canonical_sha256":"0c794980f9f723dccf85eb7fecdcbeb6450aba513c18473cce73e8110db2166b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c794980f9f723dccf85eb7fecdcbeb6450aba513c18473cce73e8110db2166b","first_computed_at":"2026-05-18T00:10:27.513265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:27.513265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aHrfB2lp8Uk6CIAnljQuxblH5tSbbjIN6Q71YOzSUez1sUhLFyjRRvPdMKjZSNdAKaLm50c8I2C1kZyo/nmQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:27.513815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06327","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:535f14b422b7e3acdd74f9f9c6ec6c6cf0226a85048acf3f5ea4fb1092d9cc4a","sha256:7af558d062daee54010f9021eabde0525633668b709ca4ba0b91093aeb9e22bd"],"state_sha256":"376577eaa2660cfe29e5116df4631abf44b0a97c85e4f3f454cc4f05a0eca1d7"}