{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SECFQKTDP6EPS754VITJQFZJXY","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":"64628d1dee95b3718f9d85ac944a0f61bf02c81d92cae4ab6633f5445615ea0e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-10-14T11:08:23Z","title_canon_sha256":"aad11c0301a8b9981f7d29871644f8b7cf7c2a34c62b5cdb10f61e162d562b77"},"schema_version":"1.0","source":{"id":"2110.07257","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.07257","created_at":"2026-07-05T07:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"2110.07257v3","created_at":"2026-07-05T07:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.07257","created_at":"2026-07-05T07:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"SECFQKTDP6EP","created_at":"2026-07-05T07:10:19Z"},{"alias_kind":"pith_short_16","alias_value":"SECFQKTDP6EPS754","created_at":"2026-07-05T07:10:19Z"},{"alias_kind":"pith_short_8","alias_value":"SECFQKTD","created_at":"2026-07-05T07:10:19Z"}],"graph_snapshots":[{"event_id":"sha256:13e37f5b5119f06a744e49cb1f7faf79a9a183786f3e052c85c9c42f32854726","target":"graph","created_at":"2026-07-05T07:10:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.07257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For each poset $P$, we construct a polytope $A(P)$ called the $P$-associahedron. Similarly to the case of graph associahedra, the faces of $A(P)$ correspond to certain nested collections of subsets of $P$. The Stasheff associahedron is a compactification of the configuration space of $n$ points on a line, and we recover $A(P)$ as an analogous compactification of the space of order-preserving maps $P\\to\\mathbb{R}$. Motivated by the study of totally nonnegative critical varieties in the Grassmannian, we introduce affine poset cyclohedra and realize these polytopes as compactifications of configu","authors_text":"Pavel Galashin","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-10-14T11:08:23Z","title":"$P$-associahedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07257","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":"sha256:95cc262453681e87d59009c34dfd24020083bf2efbf472d7367f68044d83ab2a","target":"record","created_at":"2026-07-05T07:10:19Z","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":"64628d1dee95b3718f9d85ac944a0f61bf02c81d92cae4ab6633f5445615ea0e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-10-14T11:08:23Z","title_canon_sha256":"aad11c0301a8b9981f7d29871644f8b7cf7c2a34c62b5cdb10f61e162d562b77"},"schema_version":"1.0","source":{"id":"2110.07257","kind":"arxiv","version":3}},"canonical_sha256":"9104582a637f88f97fbcaa26981729be16c063874a3b3184f4d9debff6231b63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9104582a637f88f97fbcaa26981729be16c063874a3b3184f4d9debff6231b63","first_computed_at":"2026-07-05T07:10:19.630576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:10:19.630576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PBqi3N8U30ZqkhaUcGVH4hygkgtxXtVLqLpm8wjxYehtVXEKQlzbZcr4uyXLy+4igjiZIqVPd5eOa3fHZcEfDg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:10:19.631047Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.07257","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95cc262453681e87d59009c34dfd24020083bf2efbf472d7367f68044d83ab2a","sha256:13e37f5b5119f06a744e49cb1f7faf79a9a183786f3e052c85c9c42f32854726"],"state_sha256":"d9e0b2f1e01b91f13ea2a2841d1a17611cdbaafaa803ca39631a73cffc41b17c"}