{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:U4PRXDA7AZEZ3GDRMN46PEGEHY","short_pith_number":"pith:U4PRXDA7","canonical_record":{"source":{"id":"1106.2458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-13T14:51:34Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"bb6ebbe9a799d1b3d1f45cfb7cee8244d0e34bf5284e93d302a7d952ae8e1e75","abstract_canon_sha256":"e5dedb7b8e7e315f4bf7e9868ec8708de7076cf65f2d41b3d0e24ea91bdaebd9"},"schema_version":"1.0"},"canonical_sha256":"a71f1b8c1f06499d98716379e790c43e08794b319dfbdb9dd413b34b6723525d","source":{"kind":"arxiv","id":"1106.2458","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2458","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2458v1","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2458","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"pith_short_12","alias_value":"U4PRXDA7AZEZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4PRXDA7AZEZ3GDR","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4PRXDA7","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:U4PRXDA7AZEZ3GDRMN46PEGEHY","target":"record","payload":{"canonical_record":{"source":{"id":"1106.2458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-13T14:51:34Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"bb6ebbe9a799d1b3d1f45cfb7cee8244d0e34bf5284e93d302a7d952ae8e1e75","abstract_canon_sha256":"e5dedb7b8e7e315f4bf7e9868ec8708de7076cf65f2d41b3d0e24ea91bdaebd9"},"schema_version":"1.0"},"canonical_sha256":"a71f1b8c1f06499d98716379e790c43e08794b319dfbdb9dd413b34b6723525d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:05.779344Z","signature_b64":"s3IF3SqfNf53P9HcgF9DDJc+RMrU3TeuVecaq9TtKJBKEbvMVmHtWYMYT4WFVT5y3ecn9i9ExOWpQGedP1gtBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a71f1b8c1f06499d98716379e790c43e08794b319dfbdb9dd413b34b6723525d","last_reissued_at":"2026-05-18T04:20:05.778930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:05.778930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.2458","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bAV2QZMI8dWnAbc11aDN5/fGakKXTdu9XsQ3iVd2MQP+qzQ2/VFxiXD4niaR9JXJQpGixKdCocZxbh+EHzc1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:27:38.273645Z"},"content_sha256":"6329e1c0081c0cb6e587e924e142ea67028027f5da993d77844a581b623c75ab","schema_version":"1.0","event_id":"sha256:6329e1c0081c0cb6e587e924e142ea67028027f5da993d77844a581b623c75ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:U4PRXDA7AZEZ3GDRMN46PEGEHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Young diagrams, flips and cluster algebras of type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.CO","authors_text":"Mikhail Gorsky","submitted_at":"2011-06-13T14:51:34Z","abstract_excerpt":"We give a new simple description of the canonical bijection between the set of triangulations of n-gon and some set of Young diagrams. Using this description, we find flip transformations on this set of Young diagrams which correspond to the edges of the associahedron. This construction is generalized on the set of all Young diagrams and the corresponding infinite-dimensional associahedron is defined. We consider its relation to the properly defined infinite-type version of the cluster algebras of type A and check some properties of these algebras inherited from their finite-type counterparts."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2458","kind":"arxiv","version":1},"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":"2026-05-18T04:20:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1pK2u6bYFp7z4uBki6o/eyHoiu/ItoFU7DWqS7XG4+YBBAId9ZR+WWUrUfaLIthjtZLiz4Agt6wZerjqxXIcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:27:38.273993Z"},"content_sha256":"deab712b04e46e0aed52ebbdfb6a97452dc277c271dd0f3977515c800c639a77","schema_version":"1.0","event_id":"sha256:deab712b04e46e0aed52ebbdfb6a97452dc277c271dd0f3977515c800c639a77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4PRXDA7AZEZ3GDRMN46PEGEHY/bundle.json","state_url":"https://pith.science/pith/U4PRXDA7AZEZ3GDRMN46PEGEHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4PRXDA7AZEZ3GDRMN46PEGEHY/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":"2026-06-22T15:27:38Z","links":{"resolver":"https://pith.science/pith/U4PRXDA7AZEZ3GDRMN46PEGEHY","bundle":"https://pith.science/pith/U4PRXDA7AZEZ3GDRMN46PEGEHY/bundle.json","state":"https://pith.science/pith/U4PRXDA7AZEZ3GDRMN46PEGEHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4PRXDA7AZEZ3GDRMN46PEGEHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U4PRXDA7AZEZ3GDRMN46PEGEHY","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":"e5dedb7b8e7e315f4bf7e9868ec8708de7076cf65f2d41b3d0e24ea91bdaebd9","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-13T14:51:34Z","title_canon_sha256":"bb6ebbe9a799d1b3d1f45cfb7cee8244d0e34bf5284e93d302a7d952ae8e1e75"},"schema_version":"1.0","source":{"id":"1106.2458","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2458","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2458v1","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2458","created_at":"2026-05-18T04:20:05Z"},{"alias_kind":"pith_short_12","alias_value":"U4PRXDA7AZEZ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U4PRXDA7AZEZ3GDR","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U4PRXDA7","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:deab712b04e46e0aed52ebbdfb6a97452dc277c271dd0f3977515c800c639a77","target":"graph","created_at":"2026-05-18T04:20:05Z","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":"We give a new simple description of the canonical bijection between the set of triangulations of n-gon and some set of Young diagrams. Using this description, we find flip transformations on this set of Young diagrams which correspond to the edges of the associahedron. This construction is generalized on the set of all Young diagrams and the corresponding infinite-dimensional associahedron is defined. We consider its relation to the properly defined infinite-type version of the cluster algebras of type A and check some properties of these algebras inherited from their finite-type counterparts.","authors_text":"Mikhail Gorsky","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-13T14:51:34Z","title":"On Young diagrams, flips and cluster algebras of type A"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2458","kind":"arxiv","version":1},"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":"sha256:6329e1c0081c0cb6e587e924e142ea67028027f5da993d77844a581b623c75ab","target":"record","created_at":"2026-05-18T04:20:05Z","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":"e5dedb7b8e7e315f4bf7e9868ec8708de7076cf65f2d41b3d0e24ea91bdaebd9","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-13T14:51:34Z","title_canon_sha256":"bb6ebbe9a799d1b3d1f45cfb7cee8244d0e34bf5284e93d302a7d952ae8e1e75"},"schema_version":"1.0","source":{"id":"1106.2458","kind":"arxiv","version":1}},"canonical_sha256":"a71f1b8c1f06499d98716379e790c43e08794b319dfbdb9dd413b34b6723525d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a71f1b8c1f06499d98716379e790c43e08794b319dfbdb9dd413b34b6723525d","first_computed_at":"2026-05-18T04:20:05.778930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:05.778930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3IF3SqfNf53P9HcgF9DDJc+RMrU3TeuVecaq9TtKJBKEbvMVmHtWYMYT4WFVT5y3ecn9i9ExOWpQGedP1gtBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:05.779344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2458","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6329e1c0081c0cb6e587e924e142ea67028027f5da993d77844a581b623c75ab","sha256:deab712b04e46e0aed52ebbdfb6a97452dc277c271dd0f3977515c800c639a77"],"state_sha256":"f52c7f36140ebd1225791b320c0c8cc74254fab388066c0a398cbea4421b8689"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nzFLyKO68L81t2F2qL1+udtCSWNbHyCenVD9Ex0afSIYnvwCox0udRkxI+ZGdYO0kPfVYELtAD4391EKouftBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:27:38.276053Z","bundle_sha256":"b2faedce5273a560acf3810c6fe98147a281961f7d77530437e82b9ee22ae614"}}