{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IKGY6AQTWJERAWULTX6F7D2TD2","short_pith_number":"pith:IKGY6AQT","canonical_record":{"source":{"id":"1308.1804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-08-08T10:15:42Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"5da85e3c20f154fae6cc275770a4dffbbc77365b50fd1fb13f56474b0c8fe03a","abstract_canon_sha256":"d32372154fd5e89ba2d02490b919876f313f33db9e0c6f6a2e015baa50b113d9"},"schema_version":"1.0"},"canonical_sha256":"428d8f0213b249105a8b9dfc5f8f531eb9815a40026da4a2e34bced81ded2aaf","source":{"kind":"arxiv","id":"1308.1804","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1804","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1804v2","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1804","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"IKGY6AQTWJER","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IKGY6AQTWJERAWUL","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IKGY6AQT","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IKGY6AQTWJERAWULTX6F7D2TD2","target":"record","payload":{"canonical_record":{"source":{"id":"1308.1804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-08-08T10:15:42Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"5da85e3c20f154fae6cc275770a4dffbbc77365b50fd1fb13f56474b0c8fe03a","abstract_canon_sha256":"d32372154fd5e89ba2d02490b919876f313f33db9e0c6f6a2e015baa50b113d9"},"schema_version":"1.0"},"canonical_sha256":"428d8f0213b249105a8b9dfc5f8f531eb9815a40026da4a2e34bced81ded2aaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:17.688811Z","signature_b64":"CxQfEiu6Xvg9fQQ1CO53UEfvd1FGOZYecgjOjlNO27GyOxFpXYtMV/UEE/doLr7DwNk5IJ5RWl//J+08L6ThBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"428d8f0213b249105a8b9dfc5f8f531eb9815a40026da4a2e34bced81ded2aaf","last_reissued_at":"2026-05-18T02:48:17.688383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:17.688383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.1804","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":"2026-05-18T02:48:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HiTkbCzU5tCrLfqPZsTwHY/nl/c075yl/j1TkDhAXdGb5n+C6lEMsuoCG92/XeVQCPkbw9AyuMLsCULw75FCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:39:45.565664Z"},"content_sha256":"5bd8cfc2483de1e22916315ff4757d3c9531b15d40981bad2040c6564dc6054b","schema_version":"1.0","event_id":"sha256:5bd8cfc2483de1e22916315ff4757d3c9531b15d40981bad2040c6564dc6054b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IKGY6AQTWJERAWULTX6F7D2TD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived equivalences induced by big cotilting modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.CT","authors_text":"Jan Stovicek","submitted_at":"2013-08-08T10:15:42Z","abstract_excerpt":"We prove that given a Grothendieck category G with a tilting object of finite projective dimension, the induced triangle equivalence sends an injective cogenerator of G to a big cotilting module. Moreover, every big cotilting module can be constructed like that in an essentially unique way. We also prove that the triangle equivalence is at the base of an equivalence of derivators, which in turn is induced by a Quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1804","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":"2026-05-18T02:48:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2AsepKA/Inxh3vKCP6ST4YIK5QKgL5A7An+xeKXFiySZw1lmgl0POSncP6HZWPHQ3qYvvAxQQ0mUnjNZgd5tCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:39:45.566002Z"},"content_sha256":"a75964ca69fed3e593ad422d186ee3d31151a2aff71cf2f91c4c6120fd46bbb4","schema_version":"1.0","event_id":"sha256:a75964ca69fed3e593ad422d186ee3d31151a2aff71cf2f91c4c6120fd46bbb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IKGY6AQTWJERAWULTX6F7D2TD2/bundle.json","state_url":"https://pith.science/pith/IKGY6AQTWJERAWULTX6F7D2TD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IKGY6AQTWJERAWULTX6F7D2TD2/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":"2026-06-03T01:39:45Z","links":{"resolver":"https://pith.science/pith/IKGY6AQTWJERAWULTX6F7D2TD2","bundle":"https://pith.science/pith/IKGY6AQTWJERAWULTX6F7D2TD2/bundle.json","state":"https://pith.science/pith/IKGY6AQTWJERAWULTX6F7D2TD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IKGY6AQTWJERAWULTX6F7D2TD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IKGY6AQTWJERAWULTX6F7D2TD2","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":"d32372154fd5e89ba2d02490b919876f313f33db9e0c6f6a2e015baa50b113d9","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-08-08T10:15:42Z","title_canon_sha256":"5da85e3c20f154fae6cc275770a4dffbbc77365b50fd1fb13f56474b0c8fe03a"},"schema_version":"1.0","source":{"id":"1308.1804","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1804","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1804v2","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1804","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"IKGY6AQTWJER","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IKGY6AQTWJERAWUL","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IKGY6AQT","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:a75964ca69fed3e593ad422d186ee3d31151a2aff71cf2f91c4c6120fd46bbb4","target":"graph","created_at":"2026-05-18T02:48:17Z","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":"We prove that given a Grothendieck category G with a tilting object of finite projective dimension, the induced triangle equivalence sends an injective cogenerator of G to a big cotilting module. Moreover, every big cotilting module can be constructed like that in an essentially unique way. We also prove that the triangle equivalence is at the base of an equivalence of derivators, which in turn is induced by a Quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes.","authors_text":"Jan Stovicek","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-08-08T10:15:42Z","title":"Derived equivalences induced by big cotilting modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1804","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":"sha256:5bd8cfc2483de1e22916315ff4757d3c9531b15d40981bad2040c6564dc6054b","target":"record","created_at":"2026-05-18T02:48:17Z","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":"d32372154fd5e89ba2d02490b919876f313f33db9e0c6f6a2e015baa50b113d9","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-08-08T10:15:42Z","title_canon_sha256":"5da85e3c20f154fae6cc275770a4dffbbc77365b50fd1fb13f56474b0c8fe03a"},"schema_version":"1.0","source":{"id":"1308.1804","kind":"arxiv","version":2}},"canonical_sha256":"428d8f0213b249105a8b9dfc5f8f531eb9815a40026da4a2e34bced81ded2aaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"428d8f0213b249105a8b9dfc5f8f531eb9815a40026da4a2e34bced81ded2aaf","first_computed_at":"2026-05-18T02:48:17.688383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:17.688383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CxQfEiu6Xvg9fQQ1CO53UEfvd1FGOZYecgjOjlNO27GyOxFpXYtMV/UEE/doLr7DwNk5IJ5RWl//J+08L6ThBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:17.688811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1804","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bd8cfc2483de1e22916315ff4757d3c9531b15d40981bad2040c6564dc6054b","sha256:a75964ca69fed3e593ad422d186ee3d31151a2aff71cf2f91c4c6120fd46bbb4"],"state_sha256":"1001002c282424ae738fec579fac7c6f995e88b40f10bb3259ea4be04efa72fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNUr4mVP3H5phDhnkIeYth8TF8UGdYT+nkDbrofVyk3AmXVuYKMFUJiy/WkI8+bKfaIDRSU96DjHoPRizX3GDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:39:45.567828Z","bundle_sha256":"d1676fca30d29bc5cc8c267a750b83c843ac4934873d16583e64f4a7c89601a7"}}