{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6L4DXF4DSVBRMKRXXX32LN6BLP","short_pith_number":"pith:6L4DXF4D","canonical_record":{"source":{"id":"1412.1615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-12-04T10:52:09Z","cross_cats_sorted":["math.AG","math.RA","math.RT"],"title_canon_sha256":"6625f966a42cfbc14d2a606504a56fa43c9bf1ae50aff152da0ebd136bd085ed","abstract_canon_sha256":"12a7bf41e2eceee7f18926df0bbc0d410ac0a7a388486bee81cc09de54064d8b"},"schema_version":"1.0"},"canonical_sha256":"f2f83b97839543162a37bdf7a5b7c15bc3c071dfc02a2ec64592512859e4f4a3","source":{"kind":"arxiv","id":"1412.1615","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1615","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1615v1","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1615","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"6L4DXF4DSVBR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6L4DXF4DSVBRMKRX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6L4DXF4D","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6L4DXF4DSVBRMKRXXX32LN6BLP","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-12-04T10:52:09Z","cross_cats_sorted":["math.AG","math.RA","math.RT"],"title_canon_sha256":"6625f966a42cfbc14d2a606504a56fa43c9bf1ae50aff152da0ebd136bd085ed","abstract_canon_sha256":"12a7bf41e2eceee7f18926df0bbc0d410ac0a7a388486bee81cc09de54064d8b"},"schema_version":"1.0"},"canonical_sha256":"f2f83b97839543162a37bdf7a5b7c15bc3c071dfc02a2ec64592512859e4f4a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:06.850265Z","signature_b64":"HFN7G02ZAujHYaMjoUvjkmD13X4Bk4x7CcLO6+Oa9qFS3HjaTybQXhSHjDA/7d1+ryYeeMlsxNpe0vn3F2JrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2f83b97839543162a37bdf7a5b7c15bc3c071dfc02a2ec64592512859e4f4a3","last_reissued_at":"2026-05-18T02:32:06.849910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:06.849910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1615","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":"2026-05-18T02:32:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+fHc2mxPVUuuLXGwbxjfZuqMQ7To0G7LOEmiWdaxRzEW5LJ74gQBoH51RMbTq5jTnAds+40DDBM3usFuhFx+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:25:57.110680Z"},"content_sha256":"5cc07a4a1c7ce076cd45ab6fb137f25b79c6f463f4b3ee912d5ab1b1e2cf8912","schema_version":"1.0","event_id":"sha256:5cc07a4a1c7ce076cd45ab6fb137f25b79c6f463f4b3ee912d5ab1b1e2cf8912"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6L4DXF4DSVBRMKRXXX32LN6BLP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On purity and applications to coderived and singularity categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA","math.RT"],"primary_cat":"math.CT","authors_text":"Jan Stovicek","submitted_at":"2014-12-04T10:52:09Z","abstract_excerpt":"Given a locally coherent Grothendieck category G, we prove that the homotopy category of complexes of injective objects (also known as the coderived category of G) is compactly generated triangulated. Moreover, the full subcategory of compact objects is none other than D^b(fp G). If G admits a generating set of finitely presentable objects of finite projective dimension, then also the derived category of G is compactly generated and Krause's recollement exists. Our main tools are (a) model theoretic techniques and (b) a systematic study of the pure derived category of an additive finitely acce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1615","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":"2026-05-18T02:32:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"755RvYE2gA88LWSvI/YnGpeO8dk2X/jmnR3YXLfU9ip4KiNJmjqg/fg5L/EqZ0IqUj3WYmmG4HtP529/8dIWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:25:57.111377Z"},"content_sha256":"0b961823abc82f15743b47049f741ba6ebbd992af4b8cde9a43b2e2941591f9f","schema_version":"1.0","event_id":"sha256:0b961823abc82f15743b47049f741ba6ebbd992af4b8cde9a43b2e2941591f9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6L4DXF4DSVBRMKRXXX32LN6BLP/bundle.json","state_url":"https://pith.science/pith/6L4DXF4DSVBRMKRXXX32LN6BLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6L4DXF4DSVBRMKRXXX32LN6BLP/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":"2026-05-26T03:25:57Z","links":{"resolver":"https://pith.science/pith/6L4DXF4DSVBRMKRXXX32LN6BLP","bundle":"https://pith.science/pith/6L4DXF4DSVBRMKRXXX32LN6BLP/bundle.json","state":"https://pith.science/pith/6L4DXF4DSVBRMKRXXX32LN6BLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6L4DXF4DSVBRMKRXXX32LN6BLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6L4DXF4DSVBRMKRXXX32LN6BLP","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":"12a7bf41e2eceee7f18926df0bbc0d410ac0a7a388486bee81cc09de54064d8b","cross_cats_sorted":["math.AG","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-12-04T10:52:09Z","title_canon_sha256":"6625f966a42cfbc14d2a606504a56fa43c9bf1ae50aff152da0ebd136bd085ed"},"schema_version":"1.0","source":{"id":"1412.1615","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1615","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1615v1","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1615","created_at":"2026-05-18T02:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"6L4DXF4DSVBR","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6L4DXF4DSVBRMKRX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6L4DXF4D","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:0b961823abc82f15743b47049f741ba6ebbd992af4b8cde9a43b2e2941591f9f","target":"graph","created_at":"2026-05-18T02:32:06Z","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 locally coherent Grothendieck category G, we prove that the homotopy category of complexes of injective objects (also known as the coderived category of G) is compactly generated triangulated. Moreover, the full subcategory of compact objects is none other than D^b(fp G). If G admits a generating set of finitely presentable objects of finite projective dimension, then also the derived category of G is compactly generated and Krause's recollement exists. Our main tools are (a) model theoretic techniques and (b) a systematic study of the pure derived category of an additive finitely acce","authors_text":"Jan Stovicek","cross_cats":["math.AG","math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-12-04T10:52:09Z","title":"On purity and applications to coderived and singularity categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1615","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":"sha256:5cc07a4a1c7ce076cd45ab6fb137f25b79c6f463f4b3ee912d5ab1b1e2cf8912","target":"record","created_at":"2026-05-18T02:32:06Z","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":"12a7bf41e2eceee7f18926df0bbc0d410ac0a7a388486bee81cc09de54064d8b","cross_cats_sorted":["math.AG","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2014-12-04T10:52:09Z","title_canon_sha256":"6625f966a42cfbc14d2a606504a56fa43c9bf1ae50aff152da0ebd136bd085ed"},"schema_version":"1.0","source":{"id":"1412.1615","kind":"arxiv","version":1}},"canonical_sha256":"f2f83b97839543162a37bdf7a5b7c15bc3c071dfc02a2ec64592512859e4f4a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2f83b97839543162a37bdf7a5b7c15bc3c071dfc02a2ec64592512859e4f4a3","first_computed_at":"2026-05-18T02:32:06.849910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:06.849910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HFN7G02ZAujHYaMjoUvjkmD13X4Bk4x7CcLO6+Oa9qFS3HjaTybQXhSHjDA/7d1+ryYeeMlsxNpe0vn3F2JrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:06.850265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1615","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cc07a4a1c7ce076cd45ab6fb137f25b79c6f463f4b3ee912d5ab1b1e2cf8912","sha256:0b961823abc82f15743b47049f741ba6ebbd992af4b8cde9a43b2e2941591f9f"],"state_sha256":"ca896f1c3a3b87dc816e62bbfa9202288515d64dbf86be6085ecce3f91e18159"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FFbHzYvlwAPQ8wu9TuXwJnBuqzZ1AXaf7Hv6FnBt28rlWyFqPZaOOkgLWdcwVWJHKYYW1yCaMpseIPWz9PWFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:25:57.115051Z","bundle_sha256":"36add8447f55233701c7090b225b4362cd1f4d65be4fa1156b8ddaed7e8959d6"}}