{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GJPKVJLPO5NSFYQUJG5EKO4PK6","short_pith_number":"pith:GJPKVJLP","canonical_record":{"source":{"id":"1307.4838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-18T06:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"69abfc3b3564a492f1edfd35ee4ddd85f25cb9f9c17583805c0b843112abf707","abstract_canon_sha256":"df5ad91a5aea1304a6f5618232c724cba1f5de6c5fa21a1403374dfb17ad9397"},"schema_version":"1.0"},"canonical_sha256":"325eaaa56f775b22e21449ba453b8f57b7cfabe8e4515df1b48c6ee161884f42","source":{"kind":"arxiv","id":"1307.4838","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4838","created_at":"2026-05-18T03:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4838v1","created_at":"2026-05-18T03:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4838","created_at":"2026-05-18T03:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"GJPKVJLPO5NS","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GJPKVJLPO5NSFYQU","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GJPKVJLP","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GJPKVJLPO5NSFYQUJG5EKO4PK6","target":"record","payload":{"canonical_record":{"source":{"id":"1307.4838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-18T06:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"69abfc3b3564a492f1edfd35ee4ddd85f25cb9f9c17583805c0b843112abf707","abstract_canon_sha256":"df5ad91a5aea1304a6f5618232c724cba1f5de6c5fa21a1403374dfb17ad9397"},"schema_version":"1.0"},"canonical_sha256":"325eaaa56f775b22e21449ba453b8f57b7cfabe8e4515df1b48c6ee161884f42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:07.443660Z","signature_b64":"6w5cer3C0+w96dy20LZW8xqFBvoYC5OugXkNtI8IgSG85sV1OZ26wPa5rbn4luTm2awL8xmYW1rKZ3qJg3cODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"325eaaa56f775b22e21449ba453b8f57b7cfabe8e4515df1b48c6ee161884f42","last_reissued_at":"2026-05-18T03:18:07.442765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:07.442765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.4838","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":"2026-05-18T03:18:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fdK+9b9o/kpmY8HMTn8elPqS0G6pMMX05/xe6e2CFDkFZKLUaX1pCHA2m79TSvxhG0WweDiTSMt5ZPR3/SfxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:16:49.647000Z"},"content_sha256":"c2f11545bf95a22f7d9315932d5d4f161ab5d7cefc8205c2bce6656df8b7f9e8","schema_version":"1.0","event_id":"sha256:c2f11545bf95a22f7d9315932d5d4f161ab5d7cefc8205c2bce6656df8b7f9e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GJPKVJLPO5NSFYQUJG5EKO4PK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster automorphisms and compatibility of cluster variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ibrahim Assem, Ralf Schiffler, Vasilisa Shramchenko","submitted_at":"2013-07-18T06:38:02Z","abstract_excerpt":"In this paper, we introduce a notion of unistructural cluster algebras, for which the set of cluster variables uniquely determines the clusters. We prove that cluster algebras of Dynkin type and cluster algebras of rank 2 are unistructural, then prove that if $\\mathcal{A}$ is unistructural or of Euclidean type, then $f: \\mathcal{A}\\to \\mathcal{A}$ is a cluster automorphism if and only if $f$ is an automorphism of the ambient field which restricts to a permutation of the cluster variables. In order to prove this result, we also investigate the Fomin-Zelevinsky conjecture that two cluster variab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4838","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":"2026-05-18T03:18:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xCTVhK66rthk1AQu7BA+RtnUQEY9lOt1Pt58wcLn40mgDEiWvNUVqESazgfmh062SrK3ixnDpEG1cSF6CHe6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:16:49.647349Z"},"content_sha256":"1529a8acb2f9091a6252301c7bfa257af9010d46619cd06b8a17bacdecf8f7a0","schema_version":"1.0","event_id":"sha256:1529a8acb2f9091a6252301c7bfa257af9010d46619cd06b8a17bacdecf8f7a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJPKVJLPO5NSFYQUJG5EKO4PK6/bundle.json","state_url":"https://pith.science/pith/GJPKVJLPO5NSFYQUJG5EKO4PK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJPKVJLPO5NSFYQUJG5EKO4PK6/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":"2026-06-27T10:16:49Z","links":{"resolver":"https://pith.science/pith/GJPKVJLPO5NSFYQUJG5EKO4PK6","bundle":"https://pith.science/pith/GJPKVJLPO5NSFYQUJG5EKO4PK6/bundle.json","state":"https://pith.science/pith/GJPKVJLPO5NSFYQUJG5EKO4PK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJPKVJLPO5NSFYQUJG5EKO4PK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GJPKVJLPO5NSFYQUJG5EKO4PK6","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":"df5ad91a5aea1304a6f5618232c724cba1f5de6c5fa21a1403374dfb17ad9397","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-18T06:38:02Z","title_canon_sha256":"69abfc3b3564a492f1edfd35ee4ddd85f25cb9f9c17583805c0b843112abf707"},"schema_version":"1.0","source":{"id":"1307.4838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4838","created_at":"2026-05-18T03:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4838v1","created_at":"2026-05-18T03:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4838","created_at":"2026-05-18T03:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"GJPKVJLPO5NS","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GJPKVJLPO5NSFYQU","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GJPKVJLP","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:1529a8acb2f9091a6252301c7bfa257af9010d46619cd06b8a17bacdecf8f7a0","target":"graph","created_at":"2026-05-18T03:18:07Z","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":"In this paper, we introduce a notion of unistructural cluster algebras, for which the set of cluster variables uniquely determines the clusters. We prove that cluster algebras of Dynkin type and cluster algebras of rank 2 are unistructural, then prove that if $\\mathcal{A}$ is unistructural or of Euclidean type, then $f: \\mathcal{A}\\to \\mathcal{A}$ is a cluster automorphism if and only if $f$ is an automorphism of the ambient field which restricts to a permutation of the cluster variables. In order to prove this result, we also investigate the Fomin-Zelevinsky conjecture that two cluster variab","authors_text":"Ibrahim Assem, Ralf Schiffler, Vasilisa Shramchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-18T06:38:02Z","title":"Cluster automorphisms and compatibility of cluster variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4838","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:c2f11545bf95a22f7d9315932d5d4f161ab5d7cefc8205c2bce6656df8b7f9e8","target":"record","created_at":"2026-05-18T03:18:07Z","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":"df5ad91a5aea1304a6f5618232c724cba1f5de6c5fa21a1403374dfb17ad9397","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-07-18T06:38:02Z","title_canon_sha256":"69abfc3b3564a492f1edfd35ee4ddd85f25cb9f9c17583805c0b843112abf707"},"schema_version":"1.0","source":{"id":"1307.4838","kind":"arxiv","version":1}},"canonical_sha256":"325eaaa56f775b22e21449ba453b8f57b7cfabe8e4515df1b48c6ee161884f42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"325eaaa56f775b22e21449ba453b8f57b7cfabe8e4515df1b48c6ee161884f42","first_computed_at":"2026-05-18T03:18:07.442765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:07.442765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6w5cer3C0+w96dy20LZW8xqFBvoYC5OugXkNtI8IgSG85sV1OZ26wPa5rbn4luTm2awL8xmYW1rKZ3qJg3cODA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:07.443660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2f11545bf95a22f7d9315932d5d4f161ab5d7cefc8205c2bce6656df8b7f9e8","sha256:1529a8acb2f9091a6252301c7bfa257af9010d46619cd06b8a17bacdecf8f7a0"],"state_sha256":"a93d9b64f106f9a4e3ba561076263b58d8cf20b695fcc4bb4a02230f1027695f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8m99bV/aArBki2rzqwSvyGYh7MrEyVf1+ETy7Y2sQZ03DR2qHvzXTxOli9AGhWfE06q4QnKig4zNfk6rqPiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:16:49.649193Z","bundle_sha256":"b2cebf1da4e8d0ce87acdcf49c2bdff908c3df04785a3cc1569ece54fc8f6f02"}}