{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4VCRL5UR6HVELL24X3KNG4X4L2","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":"ac3e11760f766ac1440714aa0ead2bc30d2f5f5b143b3df6f10467dbe5e397ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-07T19:08:39Z","title_canon_sha256":"d10fdc3843950251c9e6ed1226dda6e0a730b6284992c697022c4900a1c56dd7"},"schema_version":"1.0","source":{"id":"1504.01706","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01706","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01706v3","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01706","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"pith_short_12","alias_value":"4VCRL5UR6HVE","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4VCRL5UR6HVELL24","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4VCRL5UR","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:86e85bb49d3a8c0387bb2ce7f1b11894c75cbb7103c884ca51b1351b565bad4c","target":"graph","created_at":"2026-05-18T01:08:26Z","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":"Given two families $X$ and $Y$ of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate new class of polytopes is to take the intersection $\\mathcal{P}=\\mathcal{P}_1\\cap\\mathcal{P}_2$, where $\\mathcal{P}_1\\in X$, $\\mathcal{P}_2\\in Y$. Two basic questions then arise: 1) when $\\mathcal{P}$ is integral and 2) whether $\\mathcal{P}$ inherits the \"old type\" from $\\mathcal{P}_1, \\mathcal{P}_2$ or has a \"new type\", that is, whether $\\mathcal{P}$ is unimodularly equivalent to some polytope in $X\\cup Y$ or not. In this paper, we focus on the families of order pol","authors_text":"Akiyoshi Tsuchiya, Lili Mu, Nan Li, Takayuki Hibi, Teresa Xueshan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-07T19:08:39Z","title":"Order-Chain Polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01706","kind":"arxiv","version":3},"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":"sha256:741c4e2b2376569b0c5475c2fe3408317bad80269c7cca581a3740906e20b0aa","target":"record","created_at":"2026-05-18T01:08:26Z","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":"ac3e11760f766ac1440714aa0ead2bc30d2f5f5b143b3df6f10467dbe5e397ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-07T19:08:39Z","title_canon_sha256":"d10fdc3843950251c9e6ed1226dda6e0a730b6284992c697022c4900a1c56dd7"},"schema_version":"1.0","source":{"id":"1504.01706","kind":"arxiv","version":3}},"canonical_sha256":"e54515f691f1ea45af5cbed4d372fc5eb74a6e732a6d69b8e971d71b2f60b618","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e54515f691f1ea45af5cbed4d372fc5eb74a6e732a6d69b8e971d71b2f60b618","first_computed_at":"2026-05-18T01:08:26.655182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:26.655182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oEkieI1x16yYGW39QUeAL515waxUlDicqlgOmSbkQuRJf6Lx1jLGcvqNNVYuosEewzgsbi/5QN7GfGJNzXIPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:26.655908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01706","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:741c4e2b2376569b0c5475c2fe3408317bad80269c7cca581a3740906e20b0aa","sha256:86e85bb49d3a8c0387bb2ce7f1b11894c75cbb7103c884ca51b1351b565bad4c"],"state_sha256":"5a05fb24adad86c999cf83ff5f21ec607d03c0634d94a9dbae3c6bfa77a5105b"}