{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:F7PL4E72KPCZAZCO3J3YRVROOY","short_pith_number":"pith:F7PL4E72","canonical_record":{"source":{"id":"1602.05646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T01:27:39Z","cross_cats_sorted":[],"title_canon_sha256":"895e797e7e5229d5e07354a05da91eeb04c5a7c74541ace01c29a483134ab62b","abstract_canon_sha256":"ec2699d29df1284d229b1b29388ce2a20f2b91c37a1a4fa712c104f61755d14c"},"schema_version":"1.0"},"canonical_sha256":"2fdebe13fa53c590644eda7788d62e7636f9a5827587fd5414473ffc2ab9d66a","source":{"kind":"arxiv","id":"1602.05646","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05646","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05646v1","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05646","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"F7PL4E72KPCZ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F7PL4E72KPCZAZCO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F7PL4E72","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:F7PL4E72KPCZAZCO3J3YRVROOY","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T01:27:39Z","cross_cats_sorted":[],"title_canon_sha256":"895e797e7e5229d5e07354a05da91eeb04c5a7c74541ace01c29a483134ab62b","abstract_canon_sha256":"ec2699d29df1284d229b1b29388ce2a20f2b91c37a1a4fa712c104f61755d14c"},"schema_version":"1.0"},"canonical_sha256":"2fdebe13fa53c590644eda7788d62e7636f9a5827587fd5414473ffc2ab9d66a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:23.593836Z","signature_b64":"pDxXe5wFDj+ZNfHiNFZXVdkCpYWFUjCw+va5OahKXf1nLhDY8ktL89wYV0wG+cE809KjI2QR7rkS/QlyieD7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fdebe13fa53c590644eda7788d62e7636f9a5827587fd5414473ffc2ab9d66a","last_reissued_at":"2026-05-18T01:20:23.593353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:23.593353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05646","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":"2026-05-18T01:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8948Gv8O7zs7vZtDjK6BMXlI6dYi3cndXsTffVOyMuzSrJw9exIRjsZ6txoFmnvzgu+b31lk+SvI5/lIs5rBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:24:24.399223Z"},"content_sha256":"a87688ffcb19c04573d26f2b206711cac03968457049e9cbbca10b6d75e3f21c","schema_version":"1.0","event_id":"sha256:a87688ffcb19c04573d26f2b206711cac03968457049e9cbbca10b6d75e3f21c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:F7PL4E72KPCZAZCO3J3YRVROOY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recollements, sinks elimination and Leavitt path algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ju Huang, Roozbeh Hazrat","submitted_at":"2016-02-18T01:27:39Z","abstract_excerpt":"For Leavitt path algebras, we show that whereas removing sources from a graph produces a Morita equivalence, removing sinks gives rise to a recollement situation. In general, we show that for a graph $E$ and a finite hereditary subset $H$ of $E^0$ there is a recollement $$\\xymatrix{ L_K(E/\\overline H) \\rModd \\ar[r] & \\ar@<3pt>[l] \\ar@<-3pt>[l] L_K(E) \\rModd \\ar[r] & \\ar@<3pt>[l] \\ar@<-3pt>[l] L_K(E_H) \\rModd .}$$ We record several corollaries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05646","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":"2026-05-18T01:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1p40PnqhAgm+65Z+UFdOmoWsXCKJFoOggrzsKLLnFap4h2s+mCJb2+ao28AZs+ziJBi5lF+n/djO2NEg2+7zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:24:24.399573Z"},"content_sha256":"f1895a62ac5a182f8d18109c3c0c8f5ecfa17abb849189ab97c6cd128cf138a8","schema_version":"1.0","event_id":"sha256:f1895a62ac5a182f8d18109c3c0c8f5ecfa17abb849189ab97c6cd128cf138a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7PL4E72KPCZAZCO3J3YRVROOY/bundle.json","state_url":"https://pith.science/pith/F7PL4E72KPCZAZCO3J3YRVROOY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7PL4E72KPCZAZCO3J3YRVROOY/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":"2026-07-01T12:24:24Z","links":{"resolver":"https://pith.science/pith/F7PL4E72KPCZAZCO3J3YRVROOY","bundle":"https://pith.science/pith/F7PL4E72KPCZAZCO3J3YRVROOY/bundle.json","state":"https://pith.science/pith/F7PL4E72KPCZAZCO3J3YRVROOY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7PL4E72KPCZAZCO3J3YRVROOY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:F7PL4E72KPCZAZCO3J3YRVROOY","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":"ec2699d29df1284d229b1b29388ce2a20f2b91c37a1a4fa712c104f61755d14c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T01:27:39Z","title_canon_sha256":"895e797e7e5229d5e07354a05da91eeb04c5a7c74541ace01c29a483134ab62b"},"schema_version":"1.0","source":{"id":"1602.05646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05646","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05646v1","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05646","created_at":"2026-05-18T01:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"F7PL4E72KPCZ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F7PL4E72KPCZAZCO","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F7PL4E72","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:f1895a62ac5a182f8d18109c3c0c8f5ecfa17abb849189ab97c6cd128cf138a8","target":"graph","created_at":"2026-05-18T01:20:23Z","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":"For Leavitt path algebras, we show that whereas removing sources from a graph produces a Morita equivalence, removing sinks gives rise to a recollement situation. In general, we show that for a graph $E$ and a finite hereditary subset $H$ of $E^0$ there is a recollement $$\\xymatrix{ L_K(E/\\overline H) \\rModd \\ar[r] & \\ar@<3pt>[l] \\ar@<-3pt>[l] L_K(E) \\rModd \\ar[r] & \\ar@<3pt>[l] \\ar@<-3pt>[l] L_K(E_H) \\rModd .}$$ We record several corollaries.","authors_text":"Ju Huang, Roozbeh Hazrat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T01:27:39Z","title":"Recollements, sinks elimination and Leavitt path algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05646","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:a87688ffcb19c04573d26f2b206711cac03968457049e9cbbca10b6d75e3f21c","target":"record","created_at":"2026-05-18T01:20:23Z","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":"ec2699d29df1284d229b1b29388ce2a20f2b91c37a1a4fa712c104f61755d14c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-18T01:27:39Z","title_canon_sha256":"895e797e7e5229d5e07354a05da91eeb04c5a7c74541ace01c29a483134ab62b"},"schema_version":"1.0","source":{"id":"1602.05646","kind":"arxiv","version":1}},"canonical_sha256":"2fdebe13fa53c590644eda7788d62e7636f9a5827587fd5414473ffc2ab9d66a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fdebe13fa53c590644eda7788d62e7636f9a5827587fd5414473ffc2ab9d66a","first_computed_at":"2026-05-18T01:20:23.593353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:23.593353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pDxXe5wFDj+ZNfHiNFZXVdkCpYWFUjCw+va5OahKXf1nLhDY8ktL89wYV0wG+cE809KjI2QR7rkS/QlyieD7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:23.593836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a87688ffcb19c04573d26f2b206711cac03968457049e9cbbca10b6d75e3f21c","sha256:f1895a62ac5a182f8d18109c3c0c8f5ecfa17abb849189ab97c6cd128cf138a8"],"state_sha256":"bf25b29293a4d52a37228e695b3d3f77f5ee7a9a7dd0bfb330b038a520917ce2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQXIWxyZT95jLD8PcYYRpb83E2ufDSnEGgRqrNnhfq+2SZ/ppCuGgsCyJvAvB3XV67Za53PIb+j4wZ3Yi+HQCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T12:24:24.401550Z","bundle_sha256":"8f99d64d1b08d77e16b8a46af3518db3cc2a41715eff4d3f2d0e5fd2e10a031c"}}