{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UK3DBQFF74DIYVVILVYOEU3N2H","short_pith_number":"pith:UK3DBQFF","canonical_record":{"source":{"id":"1903.00893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-03T12:44:06Z","cross_cats_sorted":[],"title_canon_sha256":"0d87f15f98137de679bdec90b4a0812a992bfc37f7825b6df5bb335940eb5849","abstract_canon_sha256":"25be8bb316f8bb27c737e9e9e31b3f9cb7b4b1c784716d26194cb31a76736739"},"schema_version":"1.0"},"canonical_sha256":"a2b630c0a5ff068c56a85d70e2536dd1d8e5e73beb47d5123f940174bf508fc6","source":{"kind":"arxiv","id":"1903.00893","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00893","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00893v2","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00893","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"UK3DBQFF74DI","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"pith_short_16","alias_value":"UK3DBQFF74DIYVVI","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"pith_short_8","alias_value":"UK3DBQFF","created_at":"2026-07-05T00:54:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UK3DBQFF74DIYVVILVYOEU3N2H","target":"record","payload":{"canonical_record":{"source":{"id":"1903.00893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-03T12:44:06Z","cross_cats_sorted":[],"title_canon_sha256":"0d87f15f98137de679bdec90b4a0812a992bfc37f7825b6df5bb335940eb5849","abstract_canon_sha256":"25be8bb316f8bb27c737e9e9e31b3f9cb7b4b1c784716d26194cb31a76736739"},"schema_version":"1.0"},"canonical_sha256":"a2b630c0a5ff068c56a85d70e2536dd1d8e5e73beb47d5123f940174bf508fc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:54:28.329716Z","signature_b64":"K5PP6xlMDchJUner37FRSE8bZ1jgngsgIIWNIKyo8TndT76UdHccz1SDEn9PKyfpYZwOgu/llAsR0bSnPgxeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2b630c0a5ff068c56a85d70e2536dd1d8e5e73beb47d5123f940174bf508fc6","last_reissued_at":"2026-07-05T00:54:28.329259Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:54:28.329259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.00893","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+0Cq6kpWQiOsVD8GhjknjJfTnj/Uu3M0hNw5DcajwFrReBQB0Dy49LVAqpxa66K5NK7WuUdvrKyX4WyLv/sQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:49:14.808915Z"},"content_sha256":"5df7ba4067d824a94e3b35ebeff9b1ed00a95d0e4f2de9af9a202b602f437408","schema_version":"1.0","event_id":"sha256:5df7ba4067d824a94e3b35ebeff9b1ed00a95d0e4f2de9af9a202b602f437408"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UK3DBQFF74DIYVVILVYOEU3N2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodicities in cluster algebras and cluster automorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fang Li, Siyang Liu","submitted_at":"2019-03-03T12:44:06Z","abstract_excerpt":"In this paper, we study the relations between groups related to cluster automorphism groups which are defined by Assem, Schiffler and Shamchenko in \\cite{ASS}. We establish the relationship among (strict) direct cluster automorphism groups and those groups consisting of periodicities of respectively labeled seeds and exchange matrices in the language of short exact sequences. As an application, we characterize automorphism-finite cluster algebras in the cases with bipartite seeds or finite mutation type. Finally, we study the relation between the groups $\\mathrm{Aut}\\mathcal{A}$ and $\\mathrm{A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00893","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.00893/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGOO7Xmjd3P9P5/PwopS3BvYuiv4tVMY6wL7dRgvB0m66uhL99B/0bN16YGQDbuQe1vEFBl4oYYy4V/4j0K1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:49:14.809872Z"},"content_sha256":"3cd9a6dff52531001a2ae391bf46d023c6459316fa304dee29bd317bad691de0","schema_version":"1.0","event_id":"sha256:3cd9a6dff52531001a2ae391bf46d023c6459316fa304dee29bd317bad691de0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UK3DBQFF74DIYVVILVYOEU3N2H/bundle.json","state_url":"https://pith.science/pith/UK3DBQFF74DIYVVILVYOEU3N2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UK3DBQFF74DIYVVILVYOEU3N2H/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":"2026-08-15T11:49:14Z","links":{"resolver":"https://pith.science/pith/UK3DBQFF74DIYVVILVYOEU3N2H","bundle":"https://pith.science/pith/UK3DBQFF74DIYVVILVYOEU3N2H/bundle.json","state":"https://pith.science/pith/UK3DBQFF74DIYVVILVYOEU3N2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UK3DBQFF74DIYVVILVYOEU3N2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UK3DBQFF74DIYVVILVYOEU3N2H","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":"25be8bb316f8bb27c737e9e9e31b3f9cb7b4b1c784716d26194cb31a76736739","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-03T12:44:06Z","title_canon_sha256":"0d87f15f98137de679bdec90b4a0812a992bfc37f7825b6df5bb335940eb5849"},"schema_version":"1.0","source":{"id":"1903.00893","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00893","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00893v2","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00893","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"UK3DBQFF74DI","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"pith_short_16","alias_value":"UK3DBQFF74DIYVVI","created_at":"2026-07-05T00:54:28Z"},{"alias_kind":"pith_short_8","alias_value":"UK3DBQFF","created_at":"2026-07-05T00:54:28Z"}],"graph_snapshots":[{"event_id":"sha256:3cd9a6dff52531001a2ae391bf46d023c6459316fa304dee29bd317bad691de0","target":"graph","created_at":"2026-07-05T00:54:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.00893/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the relations between groups related to cluster automorphism groups which are defined by Assem, Schiffler and Shamchenko in \\cite{ASS}. We establish the relationship among (strict) direct cluster automorphism groups and those groups consisting of periodicities of respectively labeled seeds and exchange matrices in the language of short exact sequences. As an application, we characterize automorphism-finite cluster algebras in the cases with bipartite seeds or finite mutation type. Finally, we study the relation between the groups $\\mathrm{Aut}\\mathcal{A}$ and $\\mathrm{A","authors_text":"Fang Li, Siyang Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-03T12:44:06Z","title":"Periodicities in cluster algebras and cluster automorphism groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00893","kind":"arxiv","version":2},"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":"sha256:5df7ba4067d824a94e3b35ebeff9b1ed00a95d0e4f2de9af9a202b602f437408","target":"record","created_at":"2026-07-05T00:54:28Z","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":"25be8bb316f8bb27c737e9e9e31b3f9cb7b4b1c784716d26194cb31a76736739","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-03-03T12:44:06Z","title_canon_sha256":"0d87f15f98137de679bdec90b4a0812a992bfc37f7825b6df5bb335940eb5849"},"schema_version":"1.0","source":{"id":"1903.00893","kind":"arxiv","version":2}},"canonical_sha256":"a2b630c0a5ff068c56a85d70e2536dd1d8e5e73beb47d5123f940174bf508fc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2b630c0a5ff068c56a85d70e2536dd1d8e5e73beb47d5123f940174bf508fc6","first_computed_at":"2026-07-05T00:54:28.329259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:54:28.329259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K5PP6xlMDchJUner37FRSE8bZ1jgngsgIIWNIKyo8TndT76UdHccz1SDEn9PKyfpYZwOgu/llAsR0bSnPgxeAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:54:28.329716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00893","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5df7ba4067d824a94e3b35ebeff9b1ed00a95d0e4f2de9af9a202b602f437408","sha256:3cd9a6dff52531001a2ae391bf46d023c6459316fa304dee29bd317bad691de0"],"state_sha256":"f8c5cc9463b50fce867656fa3a18764a9e573c83c2ce27468757cfbb627108e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+DAIBeUpxxH8PqD9l3jQcm58XAmxTMipJa6zFXMD0YQ3JFe5ZWa83ePS4A9pjtw2JjY2u9AoU2ftiIa1baHJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T11:49:14.817816Z","bundle_sha256":"8fb84e93244335845008fd9bf4edfee35e49f4743b3bf7d383060643bec19ab2"}}