{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IMHZVKKYX7DYPMBBUGE4U6W267","short_pith_number":"pith:IMHZVKKY","schema_version":"1.0","canonical_sha256":"430f9aa958bfc787b021a189ca7adaf7d66f9de661b3cc0e121de0778804bb59","source":{"kind":"arxiv","id":"1207.6296","version":4},"attestation_state":"computed","paper":{"title":"The diameter of associahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lionel Pournin","submitted_at":"2012-07-26T15:21:15Z","abstract_excerpt":"It is proven here that the diameter of the d-dimensional associahedron is 2d-4 when d is greater than 9. Two maximally distant vertices of this polytope are explicitly described as triangulations of a convex polygon, and their distance is obtained using combinatorial arguments. This settles two problems posed about twenty-five years ago by Daniel Sleator, Robert Tarjan, and William Thurston."},"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":"1207.6296","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-26T15:21:15Z","cross_cats_sorted":[],"title_canon_sha256":"093a01c890bdb2d7c2d90e33c26d0d198ff0e080d0ac4245338c88b14a383507","abstract_canon_sha256":"086abd8bb2d25df96540bd5b541a5c88e6a12e898022d4bddef7971b6ac35be3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:20.714132Z","signature_b64":"nptuYXCEw/Pkfeh4IHYiGjqd6XWAWFMPenrjz4LTy7E+AxkdPtHPRPuXysoBKHFeEVYPGWjjXh8hso7WITbJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"430f9aa958bfc787b021a189ca7adaf7d66f9de661b3cc0e121de0778804bb59","last_reissued_at":"2026-05-18T02:55:20.713644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:20.713644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The diameter of associahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lionel Pournin","submitted_at":"2012-07-26T15:21:15Z","abstract_excerpt":"It is proven here that the diameter of the d-dimensional associahedron is 2d-4 when d is greater than 9. Two maximally distant vertices of this polytope are explicitly described as triangulations of a convex polygon, and their distance is obtained using combinatorial arguments. This settles two problems posed about twenty-five years ago by Daniel Sleator, Robert Tarjan, and William Thurston."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6296","kind":"arxiv","version":4},"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":"1207.6296","created_at":"2026-05-18T02:55:20.713723+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6296v4","created_at":"2026-05-18T02:55:20.713723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6296","created_at":"2026-05-18T02:55:20.713723+00:00"},{"alias_kind":"pith_short_12","alias_value":"IMHZVKKYX7DY","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IMHZVKKYX7DYPMBB","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IMHZVKKY","created_at":"2026-05-18T12:27:09.501522+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/IMHZVKKYX7DYPMBBUGE4U6W267","json":"https://pith.science/pith/IMHZVKKYX7DYPMBBUGE4U6W267.json","graph_json":"https://pith.science/api/pith-number/IMHZVKKYX7DYPMBBUGE4U6W267/graph.json","events_json":"https://pith.science/api/pith-number/IMHZVKKYX7DYPMBBUGE4U6W267/events.json","paper":"https://pith.science/paper/IMHZVKKY"},"agent_actions":{"view_html":"https://pith.science/pith/IMHZVKKYX7DYPMBBUGE4U6W267","download_json":"https://pith.science/pith/IMHZVKKYX7DYPMBBUGE4U6W267.json","view_paper":"https://pith.science/paper/IMHZVKKY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6296&json=true","fetch_graph":"https://pith.science/api/pith-number/IMHZVKKYX7DYPMBBUGE4U6W267/graph.json","fetch_events":"https://pith.science/api/pith-number/IMHZVKKYX7DYPMBBUGE4U6W267/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IMHZVKKYX7DYPMBBUGE4U6W267/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IMHZVKKYX7DYPMBBUGE4U6W267/action/storage_attestation","attest_author":"https://pith.science/pith/IMHZVKKYX7DYPMBBUGE4U6W267/action/author_attestation","sign_citation":"https://pith.science/pith/IMHZVKKYX7DYPMBBUGE4U6W267/action/citation_signature","submit_replication":"https://pith.science/pith/IMHZVKKYX7DYPMBBUGE4U6W267/action/replication_record"}},"created_at":"2026-05-18T02:55:20.713723+00:00","updated_at":"2026-05-18T02:55:20.713723+00:00"}