{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WVU5U4V5QECYOG556OEPHKTBNJ","short_pith_number":"pith:WVU5U4V5","canonical_record":{"source":{"id":"1809.06760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-18T14:20:33Z","cross_cats_sorted":[],"title_canon_sha256":"461415520763472ccdfecd5a71eff45b009ab05ef86c23357c562bceab65f1e8","abstract_canon_sha256":"5acc5b85e0cdd548f5238191a12c064606a9c2503e95298e4d93bc90e1fe9e1a"},"schema_version":"1.0"},"canonical_sha256":"b569da72bd8105871bbdf388f3aa616a426586f313e5ee76f4ec1ce743370f17","source":{"kind":"arxiv","id":"1809.06760","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06760","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06760v2","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06760","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"pith_short_12","alias_value":"WVU5U4V5QECY","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WVU5U4V5QECYOG55","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WVU5U4V5","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WVU5U4V5QECYOG556OEPHKTBNJ","target":"record","payload":{"canonical_record":{"source":{"id":"1809.06760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-18T14:20:33Z","cross_cats_sorted":[],"title_canon_sha256":"461415520763472ccdfecd5a71eff45b009ab05ef86c23357c562bceab65f1e8","abstract_canon_sha256":"5acc5b85e0cdd548f5238191a12c064606a9c2503e95298e4d93bc90e1fe9e1a"},"schema_version":"1.0"},"canonical_sha256":"b569da72bd8105871bbdf388f3aa616a426586f313e5ee76f4ec1ce743370f17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:47.002508Z","signature_b64":"RFIoRUuR8zovgVOTc7dTsYpQGKFWpOMLdBoFKypCQaSrcLMR3z+dSJjIjbJaIuKrmVoGnYJjCrEe1BVaGpZ1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b569da72bd8105871bbdf388f3aa616a426586f313e5ee76f4ec1ce743370f17","last_reissued_at":"2026-05-18T00:01:47.001781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:47.001781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.06760","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":"2026-05-18T00:01:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X51bV2BWulTjfYbAc2pmPOwFbxuGio09NBVkALoezMP42Kaa0A9hEgjZLqpW4t3LIM9kpT7XjztqXFRir9+GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:00:34.111853Z"},"content_sha256":"4cad4d9868242787fa20a98f24ffacc26a1114b31c89361838c09d8c158bdf06","schema_version":"1.0","event_id":"sha256:4cad4d9868242787fa20a98f24ffacc26a1114b31c89361838c09d8c158bdf06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WVU5U4V5QECYOG556OEPHKTBNJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the radical of the module category of an endomorphism algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Claudia Chaio, Victoria Guazzelli","submitted_at":"2018-09-18T14:20:33Z","abstract_excerpt":"Given a finite dimensional algebra $A$ over an algebraically closed field we study the relationship between the powers of the radical of a morphism in the module category of the algebra $A$ and the induced morphism in the module category of the endomorphism algebra of a tilting $A$-module. We compare the nilpotency indices of the radical of the mentioned module categories. We find an upper bound for the nilpotency index of the radical of the module category of iterated tilted algebras of Dynkin type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06760","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":""},"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":"2026-05-18T00:01:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JcgnafM1MQ96ZarFlPvKkjgYUJJtsmjLBhmfxOG/TMFqerYMG4z8XF/SQuWDuleOqDkwMEZiQsod4RqITaqzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:00:34.112193Z"},"content_sha256":"c32429e3b38cc9346b44b0b1137b25e8291607da2a2877bb0119d8b9670646e3","schema_version":"1.0","event_id":"sha256:c32429e3b38cc9346b44b0b1137b25e8291607da2a2877bb0119d8b9670646e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVU5U4V5QECYOG556OEPHKTBNJ/bundle.json","state_url":"https://pith.science/pith/WVU5U4V5QECYOG556OEPHKTBNJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVU5U4V5QECYOG556OEPHKTBNJ/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":"2026-06-26T09:00:34Z","links":{"resolver":"https://pith.science/pith/WVU5U4V5QECYOG556OEPHKTBNJ","bundle":"https://pith.science/pith/WVU5U4V5QECYOG556OEPHKTBNJ/bundle.json","state":"https://pith.science/pith/WVU5U4V5QECYOG556OEPHKTBNJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVU5U4V5QECYOG556OEPHKTBNJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WVU5U4V5QECYOG556OEPHKTBNJ","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":"5acc5b85e0cdd548f5238191a12c064606a9c2503e95298e4d93bc90e1fe9e1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-18T14:20:33Z","title_canon_sha256":"461415520763472ccdfecd5a71eff45b009ab05ef86c23357c562bceab65f1e8"},"schema_version":"1.0","source":{"id":"1809.06760","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06760","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06760v2","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06760","created_at":"2026-05-18T00:01:47Z"},{"alias_kind":"pith_short_12","alias_value":"WVU5U4V5QECY","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WVU5U4V5QECYOG55","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WVU5U4V5","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:c32429e3b38cc9346b44b0b1137b25e8291607da2a2877bb0119d8b9670646e3","target":"graph","created_at":"2026-05-18T00:01:47Z","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":"Given a finite dimensional algebra $A$ over an algebraically closed field we study the relationship between the powers of the radical of a morphism in the module category of the algebra $A$ and the induced morphism in the module category of the endomorphism algebra of a tilting $A$-module. We compare the nilpotency indices of the radical of the mentioned module categories. We find an upper bound for the nilpotency index of the radical of the module category of iterated tilted algebras of Dynkin type.","authors_text":"Claudia Chaio, Victoria Guazzelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-18T14:20:33Z","title":"On the radical of the module category of an endomorphism algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06760","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":"sha256:4cad4d9868242787fa20a98f24ffacc26a1114b31c89361838c09d8c158bdf06","target":"record","created_at":"2026-05-18T00:01:47Z","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":"5acc5b85e0cdd548f5238191a12c064606a9c2503e95298e4d93bc90e1fe9e1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-09-18T14:20:33Z","title_canon_sha256":"461415520763472ccdfecd5a71eff45b009ab05ef86c23357c562bceab65f1e8"},"schema_version":"1.0","source":{"id":"1809.06760","kind":"arxiv","version":2}},"canonical_sha256":"b569da72bd8105871bbdf388f3aa616a426586f313e5ee76f4ec1ce743370f17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b569da72bd8105871bbdf388f3aa616a426586f313e5ee76f4ec1ce743370f17","first_computed_at":"2026-05-18T00:01:47.001781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:47.001781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RFIoRUuR8zovgVOTc7dTsYpQGKFWpOMLdBoFKypCQaSrcLMR3z+dSJjIjbJaIuKrmVoGnYJjCrEe1BVaGpZ1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:47.002508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06760","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cad4d9868242787fa20a98f24ffacc26a1114b31c89361838c09d8c158bdf06","sha256:c32429e3b38cc9346b44b0b1137b25e8291607da2a2877bb0119d8b9670646e3"],"state_sha256":"d5fa0fa05e6bc96290a3a243df1c4898e6e36abac27e1291bd1ba99023dc1aad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1OQi3rgCZMHRQv7b3rHCmXfgfixDJwmw7pJBwKi/acMmZqq+8oY+y6kbnZnIQYAFHRQee2aeywXzV8NyrNjBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:00:34.114089Z","bundle_sha256":"f611e4b6f9b5cb2537a3fb9041e6cedc974d0570d05dfa04ca7da77c40fb4579"}}