{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GPF6NAGDJ5LJVX4J4O353U7BMC","short_pith_number":"pith:GPF6NAGD","canonical_record":{"source":{"id":"1505.02357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-10T09:14:22Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"3f7a5cc3e2143328e6bdcbbc81f246954aac8ce54aba8633ae0d9f0dce09bbc5","abstract_canon_sha256":"10a81f2c51ee65cf1dab0a6b884ccfd70834816b8e945640afe5052f0f9e91ca"},"schema_version":"1.0"},"canonical_sha256":"33cbe680c34f569adf89e3b7ddd3e1609d708f7ba0a5dc3d3da31cf550028bb3","source":{"kind":"arxiv","id":"1505.02357","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02357","created_at":"2026-05-18T02:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02357v1","created_at":"2026-05-18T02:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02357","created_at":"2026-05-18T02:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"GPF6NAGDJ5LJ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GPF6NAGDJ5LJVX4J","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GPF6NAGD","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GPF6NAGDJ5LJVX4J4O353U7BMC","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-10T09:14:22Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"3f7a5cc3e2143328e6bdcbbc81f246954aac8ce54aba8633ae0d9f0dce09bbc5","abstract_canon_sha256":"10a81f2c51ee65cf1dab0a6b884ccfd70834816b8e945640afe5052f0f9e91ca"},"schema_version":"1.0"},"canonical_sha256":"33cbe680c34f569adf89e3b7ddd3e1609d708f7ba0a5dc3d3da31cf550028bb3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:19.015336Z","signature_b64":"DMuCEH+AwF/5ASvfD67hOCye71fQ8Pow6NoFtmugHXcjBDZS81GDri8zefKd1wqvYPHdT1hnYQ4MJKOLuKQrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33cbe680c34f569adf89e3b7ddd3e1609d708f7ba0a5dc3d3da31cf550028bb3","last_reissued_at":"2026-05-18T02:16:19.014791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:19.014791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02357","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":"2026-05-18T02:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8kUQ0DvRvKFKnhxhYYBjAvmMH87042tbBlu9+c2lS33YAjL4IlE7nuqu5iZHV11mmFDQdTmLHT+tjhtES++TAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T08:40:47.603445Z"},"content_sha256":"35a6b449e217eccbbcca47e201cdc74d41e556935991f96cbf7bb0f0782823a2","schema_version":"1.0","event_id":"sha256:35a6b449e217eccbbcca47e201cdc74d41e556935991f96cbf7bb0f0782823a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GPF6NAGDJ5LJVX4J4O353U7BMC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebras of finite representation type arising from maximal rigid objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Aslak Bakke Buan, Idun Reiten, Yann Palu","submitted_at":"2015-05-10T09:14:22Z","abstract_excerpt":"We give a complete classification of all algebras appearing as endomorphism algebras of maximal rigid objects in standard 2-Calabi-Yau categories of finite type. Such categories are equivalent to certain orbit categories of derived categories of Dynkin algebras. It turns out that with one exception, all the algebras that occur are $2$-Calabi-Yau-tilted, and therefore appear in an earlier classification by Bertani-{\\O}kland and Oppermann. We explain this phenomenon by investigating the subcategories generated by rigid objects in standard 2-Calabi-Yau categories of finite type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02357","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":"2026-05-18T02:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yuZJvVsFwbmxgCmEkRDxoNMbdoLxULLdp+kAwLzxyv7UipKo6EHpOQ9BCWOwrMime+SFHTz/fTOgUx4FzKdZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T08:40:47.603800Z"},"content_sha256":"e16b77f2eb4970a3a720645379acd2b317bdce191a497fe735fc16af47236f4a","schema_version":"1.0","event_id":"sha256:e16b77f2eb4970a3a720645379acd2b317bdce191a497fe735fc16af47236f4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GPF6NAGDJ5LJVX4J4O353U7BMC/bundle.json","state_url":"https://pith.science/pith/GPF6NAGDJ5LJVX4J4O353U7BMC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GPF6NAGDJ5LJVX4J4O353U7BMC/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":"2026-07-02T08:40:47Z","links":{"resolver":"https://pith.science/pith/GPF6NAGDJ5LJVX4J4O353U7BMC","bundle":"https://pith.science/pith/GPF6NAGDJ5LJVX4J4O353U7BMC/bundle.json","state":"https://pith.science/pith/GPF6NAGDJ5LJVX4J4O353U7BMC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GPF6NAGDJ5LJVX4J4O353U7BMC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GPF6NAGDJ5LJVX4J4O353U7BMC","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":"10a81f2c51ee65cf1dab0a6b884ccfd70834816b8e945640afe5052f0f9e91ca","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-10T09:14:22Z","title_canon_sha256":"3f7a5cc3e2143328e6bdcbbc81f246954aac8ce54aba8633ae0d9f0dce09bbc5"},"schema_version":"1.0","source":{"id":"1505.02357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02357","created_at":"2026-05-18T02:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02357v1","created_at":"2026-05-18T02:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02357","created_at":"2026-05-18T02:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"GPF6NAGDJ5LJ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GPF6NAGDJ5LJVX4J","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GPF6NAGD","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:e16b77f2eb4970a3a720645379acd2b317bdce191a497fe735fc16af47236f4a","target":"graph","created_at":"2026-05-18T02:16:19Z","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 complete classification of all algebras appearing as endomorphism algebras of maximal rigid objects in standard 2-Calabi-Yau categories of finite type. Such categories are equivalent to certain orbit categories of derived categories of Dynkin algebras. It turns out that with one exception, all the algebras that occur are $2$-Calabi-Yau-tilted, and therefore appear in an earlier classification by Bertani-{\\O}kland and Oppermann. We explain this phenomenon by investigating the subcategories generated by rigid objects in standard 2-Calabi-Yau categories of finite type.","authors_text":"Aslak Bakke Buan, Idun Reiten, Yann Palu","cross_cats":["math.CT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-10T09:14:22Z","title":"Algebras of finite representation type arising from maximal rigid objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02357","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":"sha256:35a6b449e217eccbbcca47e201cdc74d41e556935991f96cbf7bb0f0782823a2","target":"record","created_at":"2026-05-18T02:16:19Z","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":"10a81f2c51ee65cf1dab0a6b884ccfd70834816b8e945640afe5052f0f9e91ca","cross_cats_sorted":["math.CT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-05-10T09:14:22Z","title_canon_sha256":"3f7a5cc3e2143328e6bdcbbc81f246954aac8ce54aba8633ae0d9f0dce09bbc5"},"schema_version":"1.0","source":{"id":"1505.02357","kind":"arxiv","version":1}},"canonical_sha256":"33cbe680c34f569adf89e3b7ddd3e1609d708f7ba0a5dc3d3da31cf550028bb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33cbe680c34f569adf89e3b7ddd3e1609d708f7ba0a5dc3d3da31cf550028bb3","first_computed_at":"2026-05-18T02:16:19.014791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:19.014791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMuCEH+AwF/5ASvfD67hOCye71fQ8Pow6NoFtmugHXcjBDZS81GDri8zefKd1wqvYPHdT1hnYQ4MJKOLuKQrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:19.015336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35a6b449e217eccbbcca47e201cdc74d41e556935991f96cbf7bb0f0782823a2","sha256:e16b77f2eb4970a3a720645379acd2b317bdce191a497fe735fc16af47236f4a"],"state_sha256":"d06ab4af7c5aa731b5a0c1a7747f9016d5249ae0dfb5662984ada6a35733a0a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"habDd72cYhsJi2D7v7JLGMq4LMNIiQkZnkurlGlZTaGsX/OoALvLZ3N8AxSH2PO/PqMqHJg13mbFH6GefWa8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T08:40:47.605675Z","bundle_sha256":"ad427bd43a2db83e716e5e3aba9248c63ca6203296401fdca0cd2ef7cbae6be1"}}