{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IUYOEGHNZJFPYUBMB3VQJIRZWX","short_pith_number":"pith:IUYOEGHN","canonical_record":{"source":{"id":"1403.5930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-24T12:16:11Z","cross_cats_sorted":[],"title_canon_sha256":"668979b99303c34f8ebd00534ecf1cf96c9153157afc82b69cfda4d1a91788dc","abstract_canon_sha256":"1b09af4c2e69d069dfebd43924de0caa4c513289e49364e291f369276b7ac3cc"},"schema_version":"1.0"},"canonical_sha256":"4530e218edca4afc502c0eeb04a239b5c6ef860a9dcdedde39f62123d6759b97","source":{"kind":"arxiv","id":"1403.5930","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5930","created_at":"2026-05-18T02:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5930v1","created_at":"2026-05-18T02:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5930","created_at":"2026-05-18T02:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"IUYOEGHNZJFP","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IUYOEGHNZJFPYUBM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IUYOEGHN","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IUYOEGHNZJFPYUBMB3VQJIRZWX","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5930","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-24T12:16:11Z","cross_cats_sorted":[],"title_canon_sha256":"668979b99303c34f8ebd00534ecf1cf96c9153157afc82b69cfda4d1a91788dc","abstract_canon_sha256":"1b09af4c2e69d069dfebd43924de0caa4c513289e49364e291f369276b7ac3cc"},"schema_version":"1.0"},"canonical_sha256":"4530e218edca4afc502c0eeb04a239b5c6ef860a9dcdedde39f62123d6759b97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:47.424982Z","signature_b64":"Xt4ZqY4VHVy07SsTZKdvG6zSCim+TrtGhn5TeVrjkdPKW610zcPi3YYgV5mOX+yzlH5Jyu5uiwXDXTCpXICLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4530e218edca4afc502c0eeb04a239b5c6ef860a9dcdedde39f62123d6759b97","last_reissued_at":"2026-05-18T02:55:47.424230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:47.424230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5930","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":"2026-05-18T02:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"te3wjmw7rsdWDnZJHQP3oaQqz+Em7SCO7J361sdxv3dl8XZYB2h9kvIi/HQJfgslAjyzwjfTQs0S24k3G6uQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:31:39.682718Z"},"content_sha256":"b24f8c4f3efab535976ddf0ba6a6561855ef608ab0fadc4e94c2cf892f0302f0","schema_version":"1.0","event_id":"sha256:b24f8c4f3efab535976ddf0ba6a6561855ef608ab0fadc4e94c2cf892f0302f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IUYOEGHNZJFPYUBMB3VQJIRZWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogeneity implies Tameness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Yingbo Zhang, Yunge Xu","submitted_at":"2014-03-24T12:16:11Z","abstract_excerpt":"Let $\\Lambda$ be a finite-dimensional basic algebra over an algebraically closed field $k$. The well-known Drozd's theorem asserts, that $\\Lambda$ is either tame or wild. The Crawley-Boevey's Theorem states that for a given tame algebra $\\Lambda$, and for each dimension $d$ almost all isomorphism classes of indecomposable $\\Lambda$-modules of dimension $d$ are isomorphic to their Auslander-Reiten translations and hence belong to homogeneous tubes. In this paper we prove the converse of Crawley-Boevey's Theorem and thus give an internal description of tameness in terms of AR-quivers. This gives"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5930","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":"2026-05-18T02:55:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpovJpY69bhJ0cvXCWQA4d03g1ONOXL+PqvWWFhg7tTy+npK2qB3wg9sH29LxNeGkFkVnE4KyNDM+JABumsADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:31:39.683413Z"},"content_sha256":"4e7d9cd4d7473ff74b4211f4599b1f5ae58f4b7f89cc4054ec991c750aff7886","schema_version":"1.0","event_id":"sha256:4e7d9cd4d7473ff74b4211f4599b1f5ae58f4b7f89cc4054ec991c750aff7886"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUYOEGHNZJFPYUBMB3VQJIRZWX/bundle.json","state_url":"https://pith.science/pith/IUYOEGHNZJFPYUBMB3VQJIRZWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUYOEGHNZJFPYUBMB3VQJIRZWX/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":"2026-05-25T22:31:39Z","links":{"resolver":"https://pith.science/pith/IUYOEGHNZJFPYUBMB3VQJIRZWX","bundle":"https://pith.science/pith/IUYOEGHNZJFPYUBMB3VQJIRZWX/bundle.json","state":"https://pith.science/pith/IUYOEGHNZJFPYUBMB3VQJIRZWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUYOEGHNZJFPYUBMB3VQJIRZWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IUYOEGHNZJFPYUBMB3VQJIRZWX","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":"1b09af4c2e69d069dfebd43924de0caa4c513289e49364e291f369276b7ac3cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-24T12:16:11Z","title_canon_sha256":"668979b99303c34f8ebd00534ecf1cf96c9153157afc82b69cfda4d1a91788dc"},"schema_version":"1.0","source":{"id":"1403.5930","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5930","created_at":"2026-05-18T02:55:47Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5930v1","created_at":"2026-05-18T02:55:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5930","created_at":"2026-05-18T02:55:47Z"},{"alias_kind":"pith_short_12","alias_value":"IUYOEGHNZJFP","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IUYOEGHNZJFPYUBM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IUYOEGHN","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:4e7d9cd4d7473ff74b4211f4599b1f5ae58f4b7f89cc4054ec991c750aff7886","target":"graph","created_at":"2026-05-18T02:55:47Z","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":"Let $\\Lambda$ be a finite-dimensional basic algebra over an algebraically closed field $k$. The well-known Drozd's theorem asserts, that $\\Lambda$ is either tame or wild. The Crawley-Boevey's Theorem states that for a given tame algebra $\\Lambda$, and for each dimension $d$ almost all isomorphism classes of indecomposable $\\Lambda$-modules of dimension $d$ are isomorphic to their Auslander-Reiten translations and hence belong to homogeneous tubes. In this paper we prove the converse of Crawley-Boevey's Theorem and thus give an internal description of tameness in terms of AR-quivers. This gives","authors_text":"Yingbo Zhang, Yunge Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-24T12:16:11Z","title":"Homogeneity implies Tameness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5930","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:b24f8c4f3efab535976ddf0ba6a6561855ef608ab0fadc4e94c2cf892f0302f0","target":"record","created_at":"2026-05-18T02:55:47Z","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":"1b09af4c2e69d069dfebd43924de0caa4c513289e49364e291f369276b7ac3cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-24T12:16:11Z","title_canon_sha256":"668979b99303c34f8ebd00534ecf1cf96c9153157afc82b69cfda4d1a91788dc"},"schema_version":"1.0","source":{"id":"1403.5930","kind":"arxiv","version":1}},"canonical_sha256":"4530e218edca4afc502c0eeb04a239b5c6ef860a9dcdedde39f62123d6759b97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4530e218edca4afc502c0eeb04a239b5c6ef860a9dcdedde39f62123d6759b97","first_computed_at":"2026-05-18T02:55:47.424230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:47.424230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xt4ZqY4VHVy07SsTZKdvG6zSCim+TrtGhn5TeVrjkdPKW610zcPi3YYgV5mOX+yzlH5Jyu5uiwXDXTCpXICLCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:47.424982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5930","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b24f8c4f3efab535976ddf0ba6a6561855ef608ab0fadc4e94c2cf892f0302f0","sha256:4e7d9cd4d7473ff74b4211f4599b1f5ae58f4b7f89cc4054ec991c750aff7886"],"state_sha256":"b5cf233ca33e38147520220f71ec8e14f9eb1ada8e79bb173612599aa397af29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tmbjw35TSsXAUDKwio1zo2B/B1ollVex7pToVyejxS6luGQePt3mGw4oxVsbSJhicgd/iBISLFzMSJLeQmR+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:31:39.687301Z","bundle_sha256":"add6d4841a7a6f36495ec40b9f8d0dd1cf2b22524502c25744496a907829a5c7"}}