{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XKZNPONXJLFWIEOHBY3WCJZ34L","short_pith_number":"pith:XKZNPONX","schema_version":"1.0","canonical_sha256":"bab2d7b9b74acb6411c70e3761273be2c7f456043c92587cc6a2f506386d4d69","source":{"kind":"arxiv","id":"1111.1657","version":3},"attestation_state":"computed","paper":{"title":"Polyhedral models for generalized associahedra via Coxeter elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Salvatore Stella","submitted_at":"2011-11-07T17:39:14Z","abstract_excerpt":"Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin and A. Zelevinsky associated to each finite type root system a simple convex polytope called \\emph{generalized associahedron}. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram.\n  In the first part of this paper, using the parametrization of cluster variables by their $g$-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees wi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.1657","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-07T17:39:14Z","cross_cats_sorted":[],"title_canon_sha256":"4788dbc9aa96f729b0bb195fed9bcbf0c5aaeb0e4e57bf78408b974018cd87ff","abstract_canon_sha256":"ffdfcd408ebb2aea3b8a4a6b8c634076c804d73a1a44f6066f5db4dc580fcbbf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:34.046051Z","signature_b64":"KU/Rhogz4cZ3A+e1PKxSaN+vqoQvzJZ6xyEcClpN4tHcMoXBJVy234tOceS724kuSaAq825klTRdwTqzIr88AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bab2d7b9b74acb6411c70e3761273be2c7f456043c92587cc6a2f506386d4d69","last_reissued_at":"2026-05-18T03:42:34.045660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:34.045660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polyhedral models for generalized associahedra via Coxeter elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Salvatore Stella","submitted_at":"2011-11-07T17:39:14Z","abstract_excerpt":"Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin and A. Zelevinsky associated to each finite type root system a simple convex polytope called \\emph{generalized associahedron}. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram.\n  In the first part of this paper, using the parametrization of cluster variables by their $g$-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1657","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.1657","created_at":"2026-05-18T03:42:34.045712+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.1657v3","created_at":"2026-05-18T03:42:34.045712+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1657","created_at":"2026-05-18T03:42:34.045712+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKZNPONXJLFW","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKZNPONXJLFWIEOH","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKZNPONX","created_at":"2026-05-18T12:26:47.523578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L","json":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L.json","graph_json":"https://pith.science/api/pith-number/XKZNPONXJLFWIEOHBY3WCJZ34L/graph.json","events_json":"https://pith.science/api/pith-number/XKZNPONXJLFWIEOHBY3WCJZ34L/events.json","paper":"https://pith.science/paper/XKZNPONX"},"agent_actions":{"view_html":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L","download_json":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L.json","view_paper":"https://pith.science/paper/XKZNPONX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.1657&json=true","fetch_graph":"https://pith.science/api/pith-number/XKZNPONXJLFWIEOHBY3WCJZ34L/graph.json","fetch_events":"https://pith.science/api/pith-number/XKZNPONXJLFWIEOHBY3WCJZ34L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/action/storage_attestation","attest_author":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/action/author_attestation","sign_citation":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/action/citation_signature","submit_replication":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/action/replication_record"}},"created_at":"2026-05-18T03:42:34.045712+00:00","updated_at":"2026-05-18T03:42:34.045712+00:00"}