{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Y3QH22NWITL7V276YESGMMZT2Y","short_pith_number":"pith:Y3QH22NW","canonical_record":{"source":{"id":"1205.6148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-28T15:58:51Z","cross_cats_sorted":[],"title_canon_sha256":"0a3795308f7b95035cba3cf9f7fddc2917969d0efb6d66381f00c137d5da7e64","abstract_canon_sha256":"e8518ba7ccd9ffd201a65ffe381b554affc91c021dd5536672292a99354c60e2"},"schema_version":"1.0"},"canonical_sha256":"c6e07d69b644d7faebfec124663333d63b4edd36361a9359fef0b45a65dc357b","source":{"kind":"arxiv","id":"1205.6148","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6148","created_at":"2026-05-18T03:36:04Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6148v2","created_at":"2026-05-18T03:36:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6148","created_at":"2026-05-18T03:36:04Z"},{"alias_kind":"pith_short_12","alias_value":"Y3QH22NWITL7","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3QH22NWITL7V276","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3QH22NW","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Y3QH22NWITL7V276YESGMMZT2Y","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-28T15:58:51Z","cross_cats_sorted":[],"title_canon_sha256":"0a3795308f7b95035cba3cf9f7fddc2917969d0efb6d66381f00c137d5da7e64","abstract_canon_sha256":"e8518ba7ccd9ffd201a65ffe381b554affc91c021dd5536672292a99354c60e2"},"schema_version":"1.0"},"canonical_sha256":"c6e07d69b644d7faebfec124663333d63b4edd36361a9359fef0b45a65dc357b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:04.523051Z","signature_b64":"XIGA4V5OsgQrNYKKAD3oAMufC+ygG+k/gBp1768Pietj9PaaL2bB/PIMQ2+3DI3kIrgTeBzOOgfnDiuHSOVtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6e07d69b644d7faebfec124663333d63b4edd36361a9359fef0b45a65dc357b","last_reissued_at":"2026-05-18T03:36:04.522525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:04.522525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6148","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":"2026-05-18T03:36:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G0IuV59XSDb2EOV/flye+U8MZDFnPLk4oRU5/3FsT0DKS3Gj0yh2fCuMu8byt1bZVmHWpVcL4XOyaWoCWOobDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:48:04.928194Z"},"content_sha256":"f8dcd769c0394286043b69458d2f1aa1cffa01e4229265f52fb18bda006b713d","schema_version":"1.0","event_id":"sha256:f8dcd769c0394286043b69458d2f1aa1cffa01e4229265f52fb18bda006b713d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Y3QH22NWITL7V276YESGMMZT2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"DG categories and exceptional collections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Agnieszka Bodzenta","submitted_at":"2012-05-28T15:58:51Z","abstract_excerpt":"Bondal and Kapranov describe how to assign to a full exceptional collection on a variety X a DG category C such that the bounded derived category of coherent sheaves on X is equivalent to the bounded derived category of C. In this paper we show that the category C has finite dimensional spaces of morphisms. We describe how it behaves under mutations and present an algorithm allowing to calculate it for full exceptional collections with vanishing Ext^k groups for k > 1. Finally, we use it to describe an example of a non-commutative deformation of certain rational surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6148","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":"2026-05-18T03:36:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkbRnxj8Hj0Yu1fNq+oM8YHCKjuGxxMR+Bmh2V+bMXIKdI5lHO+EDKoAhLGt8/zyqJ3dbh064hHFTeWvy2n1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:48:04.928543Z"},"content_sha256":"99bf6dea9a936833575d2f010630eb38ce5de1652f2e01cd3d01532ab800033a","schema_version":"1.0","event_id":"sha256:99bf6dea9a936833575d2f010630eb38ce5de1652f2e01cd3d01532ab800033a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3QH22NWITL7V276YESGMMZT2Y/bundle.json","state_url":"https://pith.science/pith/Y3QH22NWITL7V276YESGMMZT2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3QH22NWITL7V276YESGMMZT2Y/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":"2026-06-28T15:48:04Z","links":{"resolver":"https://pith.science/pith/Y3QH22NWITL7V276YESGMMZT2Y","bundle":"https://pith.science/pith/Y3QH22NWITL7V276YESGMMZT2Y/bundle.json","state":"https://pith.science/pith/Y3QH22NWITL7V276YESGMMZT2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3QH22NWITL7V276YESGMMZT2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y3QH22NWITL7V276YESGMMZT2Y","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":"e8518ba7ccd9ffd201a65ffe381b554affc91c021dd5536672292a99354c60e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-28T15:58:51Z","title_canon_sha256":"0a3795308f7b95035cba3cf9f7fddc2917969d0efb6d66381f00c137d5da7e64"},"schema_version":"1.0","source":{"id":"1205.6148","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6148","created_at":"2026-05-18T03:36:04Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6148v2","created_at":"2026-05-18T03:36:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6148","created_at":"2026-05-18T03:36:04Z"},{"alias_kind":"pith_short_12","alias_value":"Y3QH22NWITL7","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3QH22NWITL7V276","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3QH22NW","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:99bf6dea9a936833575d2f010630eb38ce5de1652f2e01cd3d01532ab800033a","target":"graph","created_at":"2026-05-18T03:36:04Z","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":"Bondal and Kapranov describe how to assign to a full exceptional collection on a variety X a DG category C such that the bounded derived category of coherent sheaves on X is equivalent to the bounded derived category of C. In this paper we show that the category C has finite dimensional spaces of morphisms. We describe how it behaves under mutations and present an algorithm allowing to calculate it for full exceptional collections with vanishing Ext^k groups for k > 1. Finally, we use it to describe an example of a non-commutative deformation of certain rational surfaces.","authors_text":"Agnieszka Bodzenta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-28T15:58:51Z","title":"DG categories and exceptional collections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6148","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:f8dcd769c0394286043b69458d2f1aa1cffa01e4229265f52fb18bda006b713d","target":"record","created_at":"2026-05-18T03:36:04Z","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":"e8518ba7ccd9ffd201a65ffe381b554affc91c021dd5536672292a99354c60e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-28T15:58:51Z","title_canon_sha256":"0a3795308f7b95035cba3cf9f7fddc2917969d0efb6d66381f00c137d5da7e64"},"schema_version":"1.0","source":{"id":"1205.6148","kind":"arxiv","version":2}},"canonical_sha256":"c6e07d69b644d7faebfec124663333d63b4edd36361a9359fef0b45a65dc357b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6e07d69b644d7faebfec124663333d63b4edd36361a9359fef0b45a65dc357b","first_computed_at":"2026-05-18T03:36:04.522525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:04.522525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XIGA4V5OsgQrNYKKAD3oAMufC+ygG+k/gBp1768Pietj9PaaL2bB/PIMQ2+3DI3kIrgTeBzOOgfnDiuHSOVtBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:04.523051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6148","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8dcd769c0394286043b69458d2f1aa1cffa01e4229265f52fb18bda006b713d","sha256:99bf6dea9a936833575d2f010630eb38ce5de1652f2e01cd3d01532ab800033a"],"state_sha256":"df6c3e04d4f400af589c04da84180c42db8f49485b01b1e88c36d0b004d22e32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2pewQq1SHzFJsfyc7pZiL7IwDL3/lFxc37LHhKmRgdzBJ12Ydl0ThV2wNRCSqztDE8dfEMfMghlA/nvkTiZXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T15:48:04.930443Z","bundle_sha256":"138557ac9883967ab4bd1edc1a57bebde3719b02b5bd5c39477ce8f3a4290d8c"}}