{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FO5EDDE5MMZTGZDIR2I3H6F3X2","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":"e275114539e6369cc34b0c024a0dcdb2fffab6dc60cd55be380c6bd9f22d9407","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-01-29T11:47:11Z","title_canon_sha256":"b5c5fc25d700699281f4fa3690361ff9f7004ad04c5680254bcffd398c97fd45"},"schema_version":"1.0","source":{"id":"1401.7476","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7476","created_at":"2026-05-18T02:38:10Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7476v3","created_at":"2026-05-18T02:38:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7476","created_at":"2026-05-18T02:38:10Z"},{"alias_kind":"pith_short_12","alias_value":"FO5EDDE5MMZT","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FO5EDDE5MMZTGZDI","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FO5EDDE5","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:7bfce5cb688694f6cdf2fcb5e712cf8d7c7d0f7e2679e16fd84caa6665c06137","target":"graph","created_at":"2026-05-18T02:38:10Z","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":"It is known that the $k$-faces of the permutohedron $\\Pi_n$ are labeled by (all possible) linearly ordered partitions of the set $[n]=\\{1,...,n\\}$ into $(n-k)$ non-empty parts. The incidence relation corresponds to the refinement: a face $F$ contains a face $F'$ whenever the label of $F'$ refines the label of $F$. In the paper we consider the cell complex ${CP}$ defined in analogous way, replacing linear ordering by cyclic ordering. Namely, $k$-cells of the complex ${CP}$ are labeled by (all possible) cyclically ordered partitions of the set $[n+1]=\\{1,...,n, n+1\\}$ into $(n+1-k)$ non-empty pa","authors_text":"Gaiane Panina","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-01-29T11:47:11Z","title":"Cyclopermutohedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7476","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:efcef5132eca8a6a4fbded7d596b985367fc143792ee4ee7cdd5387e80bb5520","target":"record","created_at":"2026-05-18T02:38:10Z","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":"e275114539e6369cc34b0c024a0dcdb2fffab6dc60cd55be380c6bd9f22d9407","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-01-29T11:47:11Z","title_canon_sha256":"b5c5fc25d700699281f4fa3690361ff9f7004ad04c5680254bcffd398c97fd45"},"schema_version":"1.0","source":{"id":"1401.7476","kind":"arxiv","version":3}},"canonical_sha256":"2bba418c9d63333364688e91b3f8bbbea8188415acfce6cef3a150b820cb0695","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bba418c9d63333364688e91b3f8bbbea8188415acfce6cef3a150b820cb0695","first_computed_at":"2026-05-18T02:38:10.331539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:10.331539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NJj4d6Tz/j1AAXE/FgubpWwkKr8XX+XChHqxVYDletcfYcUZPDOwDl490OA7D2umaqQUf8pfDO7c+MouYV5HCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:10.332034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7476","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efcef5132eca8a6a4fbded7d596b985367fc143792ee4ee7cdd5387e80bb5520","sha256:7bfce5cb688694f6cdf2fcb5e712cf8d7c7d0f7e2679e16fd84caa6665c06137"],"state_sha256":"459100f005af0c14bd7db0ff6beef7464df6473eb6f3d6b037778fedd638fc07"}