{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XKZNPONXJLFWIEOHBY3WCJZ34L","short_pith_number":"pith:XKZNPONX","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"},"canonical_sha256":"bab2d7b9b74acb6411c70e3761273be2c7f456043c92587cc6a2f506386d4d69","source":{"kind":"arxiv","id":"1111.1657","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1657","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1657v3","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1657","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"XKZNPONXJLFW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XKZNPONXJLFWIEOH","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XKZNPONX","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XKZNPONXJLFWIEOHBY3WCJZ34L","target":"record","payload":{"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"},"canonical_sha256":"bab2d7b9b74acb6411c70e3761273be2c7f456043c92587cc6a2f506386d4d69","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"},"source_kind":"arxiv","source_id":"1111.1657","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/bzPTrDkGYIvZS5GcLYtx3a0ZhrLzZMUcrAzCBkhmVS/LIbyVDFHn30lb15H5UU+rm1AHCnzk5IvEfo7plyWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:14:58.908234Z"},"content_sha256":"1584e7788cc75ec253fecdd07ca61fbc0f0e713c573baae329e7f0762de418dd","schema_version":"1.0","event_id":"sha256:1584e7788cc75ec253fecdd07ca61fbc0f0e713c573baae329e7f0762de418dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XKZNPONXJLFWIEOHBY3WCJZ34L","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:42:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EN458uBAjSXCMmKVgshVwxp6fWNzRAlX9Zgc9BX1cCuoXkDtuWYC3e2INpxb65M/95YSiCQ2i+qdTe5q/65qBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:14:58.908597Z"},"content_sha256":"03c4117f97921f47d20fb4df3c875f17915ee3760d886b78df5616a09044be17","schema_version":"1.0","event_id":"sha256:03c4117f97921f47d20fb4df3c875f17915ee3760d886b78df5616a09044be17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/bundle.json","state_url":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T22:14:58Z","links":{"resolver":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L","bundle":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/bundle.json","state":"https://pith.science/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XKZNPONXJLFWIEOHBY3WCJZ34L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XKZNPONXJLFWIEOHBY3WCJZ34L","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":"ffdfcd408ebb2aea3b8a4a6b8c634076c804d73a1a44f6066f5db4dc580fcbbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-07T17:39:14Z","title_canon_sha256":"4788dbc9aa96f729b0bb195fed9bcbf0c5aaeb0e4e57bf78408b974018cd87ff"},"schema_version":"1.0","source":{"id":"1111.1657","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1657","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1657v3","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1657","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"XKZNPONXJLFW","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XKZNPONXJLFWIEOH","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XKZNPONX","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:03c4117f97921f47d20fb4df3c875f17915ee3760d886b78df5616a09044be17","target":"graph","created_at":"2026-05-18T03:42:34Z","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":"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","authors_text":"Salvatore Stella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-07T17:39:14Z","title":"Polyhedral models for generalized associahedra via Coxeter elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1657","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":"sha256:1584e7788cc75ec253fecdd07ca61fbc0f0e713c573baae329e7f0762de418dd","target":"record","created_at":"2026-05-18T03:42:34Z","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":"ffdfcd408ebb2aea3b8a4a6b8c634076c804d73a1a44f6066f5db4dc580fcbbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-07T17:39:14Z","title_canon_sha256":"4788dbc9aa96f729b0bb195fed9bcbf0c5aaeb0e4e57bf78408b974018cd87ff"},"schema_version":"1.0","source":{"id":"1111.1657","kind":"arxiv","version":3}},"canonical_sha256":"bab2d7b9b74acb6411c70e3761273be2c7f456043c92587cc6a2f506386d4d69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bab2d7b9b74acb6411c70e3761273be2c7f456043c92587cc6a2f506386d4d69","first_computed_at":"2026-05-18T03:42:34.045660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:34.045660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KU/Rhogz4cZ3A+e1PKxSaN+vqoQvzJZ6xyEcClpN4tHcMoXBJVy234tOceS724kuSaAq825klTRdwTqzIr88AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:34.046051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1657","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1584e7788cc75ec253fecdd07ca61fbc0f0e713c573baae329e7f0762de418dd","sha256:03c4117f97921f47d20fb4df3c875f17915ee3760d886b78df5616a09044be17"],"state_sha256":"c9097416fdb1cbfe0a890a9cdbf5830d6c61fb76771536d1a654f8a1f0fe8f72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"poBJuUpxrndgF4niG+rnPwGVjL+jQTSG6G1zRo/yR+QEYJGlB2J5oXYS6bfPxiGQBwLCDybEDjB6Ebr+9vMbDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:14:58.910534Z","bundle_sha256":"4cb208a0b03d9ae021bb541cd2bd7fd41b3bf9d08c9e1eeafb723c737c6b288c"}}