{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VHPVWPUQZTS3IJ5DQCE3KSG2NV","short_pith_number":"pith:VHPVWPUQ","canonical_record":{"source":{"id":"1306.1359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-06T09:51:31Z","cross_cats_sorted":[],"title_canon_sha256":"dfe1d7e167c4052925f360393f5bc0da15b080598473b939d9106695e5a4fef5","abstract_canon_sha256":"ad3c751c92bb363d7ea52b4ebaca160410fa5ae3a6d189c3788395174e8c45a4"},"schema_version":"1.0"},"canonical_sha256":"a9df5b3e90cce5b427a38089b548da6d7041bfd5d66be4f4f87c0d24ea9051d9","source":{"kind":"arxiv","id":"1306.1359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1359","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1359v1","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1359","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"VHPVWPUQZTS3","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VHPVWPUQZTS3IJ5D","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VHPVWPUQ","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VHPVWPUQZTS3IJ5DQCE3KSG2NV","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-06T09:51:31Z","cross_cats_sorted":[],"title_canon_sha256":"dfe1d7e167c4052925f360393f5bc0da15b080598473b939d9106695e5a4fef5","abstract_canon_sha256":"ad3c751c92bb363d7ea52b4ebaca160410fa5ae3a6d189c3788395174e8c45a4"},"schema_version":"1.0"},"canonical_sha256":"a9df5b3e90cce5b427a38089b548da6d7041bfd5d66be4f4f87c0d24ea9051d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:34.483274Z","signature_b64":"HZLB4P4fXNpEH9aNuknVPUz1ZU7joBsVvmz+DiSu1z2zwgeEMvFzoMJ8+D72tVytc/Hg+p/wjlZdsesFHfYoDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9df5b3e90cce5b427a38089b548da6d7041bfd5d66be4f4f87c0d24ea9051d9","last_reissued_at":"2026-05-18T03:21:34.482411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:34.482411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1359","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":"2026-05-18T03:21:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuJkUPvolhj+qBVob5FWzeQsS3euH0K2KNhRyUMqpuL0esLco5dt2CS7KNi5ihYV0IiQJ4rU7e3GDL8h5OdiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:01:04.380420Z"},"content_sha256":"cd0c2f040dfcf952ef55d444516bd7da1eff01d38443b96bd7605f9d64fe2d72","schema_version":"1.0","event_id":"sha256:cd0c2f040dfcf952ef55d444516bd7da1eff01d38443b96bd7605f9d64fe2d72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VHPVWPUQZTS3IJ5DQCE3KSG2NV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived category of filtered objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jean-Pierre Schneiders, Pierre Schapira","submitted_at":"2013-06-06T09:51:31Z","abstract_excerpt":"For an abelian category C and a filtrant preordered set Lambda, we prove that the derived category of the quasi-abelian category of filtered objects in C indexed by Lambda is equivalent to the derived category of the abelian category of functors from Lambda to C. We apply this result to the study of the category of filtered modules over a filtered ring in a tensor category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1359","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":"2026-05-18T03:21:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RxinJPAj5/oYIavG+f8aYVRNXcmJnexLzTwsJno9mEvqHqdmj8+mWcCXIHDomLF6oRnUJ81k11oJ6y9JiT0cCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:01:04.380774Z"},"content_sha256":"dc616a61400182197a5d53eec6f5d99ab9c2bdb009a2517e677444e036ce01fd","schema_version":"1.0","event_id":"sha256:dc616a61400182197a5d53eec6f5d99ab9c2bdb009a2517e677444e036ce01fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHPVWPUQZTS3IJ5DQCE3KSG2NV/bundle.json","state_url":"https://pith.science/pith/VHPVWPUQZTS3IJ5DQCE3KSG2NV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHPVWPUQZTS3IJ5DQCE3KSG2NV/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":"2026-06-02T00:01:04Z","links":{"resolver":"https://pith.science/pith/VHPVWPUQZTS3IJ5DQCE3KSG2NV","bundle":"https://pith.science/pith/VHPVWPUQZTS3IJ5DQCE3KSG2NV/bundle.json","state":"https://pith.science/pith/VHPVWPUQZTS3IJ5DQCE3KSG2NV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHPVWPUQZTS3IJ5DQCE3KSG2NV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VHPVWPUQZTS3IJ5DQCE3KSG2NV","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":"ad3c751c92bb363d7ea52b4ebaca160410fa5ae3a6d189c3788395174e8c45a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-06T09:51:31Z","title_canon_sha256":"dfe1d7e167c4052925f360393f5bc0da15b080598473b939d9106695e5a4fef5"},"schema_version":"1.0","source":{"id":"1306.1359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1359","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1359v1","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1359","created_at":"2026-05-18T03:21:34Z"},{"alias_kind":"pith_short_12","alias_value":"VHPVWPUQZTS3","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VHPVWPUQZTS3IJ5D","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VHPVWPUQ","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:dc616a61400182197a5d53eec6f5d99ab9c2bdb009a2517e677444e036ce01fd","target":"graph","created_at":"2026-05-18T03:21:34Z","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 an abelian category C and a filtrant preordered set Lambda, we prove that the derived category of the quasi-abelian category of filtered objects in C indexed by Lambda is equivalent to the derived category of the abelian category of functors from Lambda to C. We apply this result to the study of the category of filtered modules over a filtered ring in a tensor category.","authors_text":"Jean-Pierre Schneiders, Pierre Schapira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-06T09:51:31Z","title":"Derived category of filtered objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1359","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:cd0c2f040dfcf952ef55d444516bd7da1eff01d38443b96bd7605f9d64fe2d72","target":"record","created_at":"2026-05-18T03:21:34Z","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":"ad3c751c92bb363d7ea52b4ebaca160410fa5ae3a6d189c3788395174e8c45a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-06-06T09:51:31Z","title_canon_sha256":"dfe1d7e167c4052925f360393f5bc0da15b080598473b939d9106695e5a4fef5"},"schema_version":"1.0","source":{"id":"1306.1359","kind":"arxiv","version":1}},"canonical_sha256":"a9df5b3e90cce5b427a38089b548da6d7041bfd5d66be4f4f87c0d24ea9051d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9df5b3e90cce5b427a38089b548da6d7041bfd5d66be4f4f87c0d24ea9051d9","first_computed_at":"2026-05-18T03:21:34.482411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:34.482411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZLB4P4fXNpEH9aNuknVPUz1ZU7joBsVvmz+DiSu1z2zwgeEMvFzoMJ8+D72tVytc/Hg+p/wjlZdsesFHfYoDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:34.483274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd0c2f040dfcf952ef55d444516bd7da1eff01d38443b96bd7605f9d64fe2d72","sha256:dc616a61400182197a5d53eec6f5d99ab9c2bdb009a2517e677444e036ce01fd"],"state_sha256":"0ca241656e30a0582663277b9dae9db7f67ead505abed5eca9a463f8de4225b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmGr3zhiOfiQpD9OvDIzKKeFofb4KMNIakwBnGzW0ryCtSYhV1hYjaDh72s4SeKSTTotgluftTF1LBdLPaAACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:01:04.382783Z","bundle_sha256":"2827176ccef39286b927398ea369ae48a2dc5efe33d65a6601ad8a151020e5ee"}}