{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z4AVU6OMZFD6WHWD6P7R6AWKTC","short_pith_number":"pith:Z4AVU6OM","canonical_record":{"source":{"id":"1301.3924","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-16T21:21:53Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"d6d17ec9326c38d98cec2f90b5ba031ddf85273cf1809c9359dca7cc9eb7f90e","abstract_canon_sha256":"0e9923f9871f2f832aa4ac3f11daf370cb3f3567e640ed08737f2baf79be5a5a"},"schema_version":"1.0"},"canonical_sha256":"cf015a79ccc947eb1ec3f3ff1f02ca98b6242d2558b81fd390ea34a4e3395d87","source":{"kind":"arxiv","id":"1301.3924","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3924","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3924v3","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3924","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"Z4AVU6OMZFD6","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z4AVU6OMZFD6WHWD","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z4AVU6OM","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z4AVU6OMZFD6WHWD6P7R6AWKTC","target":"record","payload":{"canonical_record":{"source":{"id":"1301.3924","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-16T21:21:53Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"d6d17ec9326c38d98cec2f90b5ba031ddf85273cf1809c9359dca7cc9eb7f90e","abstract_canon_sha256":"0e9923f9871f2f832aa4ac3f11daf370cb3f3567e640ed08737f2baf79be5a5a"},"schema_version":"1.0"},"canonical_sha256":"cf015a79ccc947eb1ec3f3ff1f02ca98b6242d2558b81fd390ea34a4e3395d87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.114946Z","signature_b64":"Kk2wORWdw9UdkkluPlJCgV8YVLJrrPzdBid5hkAauj/twgKzbGQuXnqbRuQwB8K+IwSVgRsXYXr6JcluPffWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf015a79ccc947eb1ec3f3ff1f02ca98b6242d2558b81fd390ea34a4e3395d87","last_reissued_at":"2026-05-18T00:44:30.114276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.114276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.3924","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VfbzJKbpgMKywFFJK871KQ9gnHvQctWTiiMF4sCucZuzKy4Cv47hs4FDFy2I+3JZ4Io1Z8gqcA4glZDIZTaVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:26:48.321912Z"},"content_sha256":"61ee4578c6f93f54fe80a51861000bdbb84d0cdaca1ed63f5f886c7f827b4c0b","schema_version":"1.0","event_id":"sha256:61ee4578c6f93f54fe80a51861000bdbb84d0cdaca1ed63f5f886c7f827b4c0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z4AVU6OMZFD6WHWD6P7R6AWKTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Koszul Duality II - Coherent sheaves on perfect sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Ivan Mirkovi\\'c, Simon Riche","submitted_at":"2013-01-16T21:21:53Z","abstract_excerpt":"In this paper we continue the study (initiated in a previous article) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general setting, and prove its compatibility with morphisms of vector bundles and base change."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3924","kind":"arxiv","version":3},"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":"2026-05-18T00:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KfnGcsPNrTUI848g1ZxlDpokaXHFLwAQMWVEp4DASYzmEdpJbFy9ybA5dZSN0+ZcO2snlz+VJxDxnAPGEMWuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:26:48.322260Z"},"content_sha256":"ef0be4d014cceb681ebff7d9498d215edf69a7ef43c7b595b5fdc280d8eeb664","schema_version":"1.0","event_id":"sha256:ef0be4d014cceb681ebff7d9498d215edf69a7ef43c7b595b5fdc280d8eeb664"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4AVU6OMZFD6WHWD6P7R6AWKTC/bundle.json","state_url":"https://pith.science/pith/Z4AVU6OMZFD6WHWD6P7R6AWKTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4AVU6OMZFD6WHWD6P7R6AWKTC/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":"2026-06-01T12:26:48Z","links":{"resolver":"https://pith.science/pith/Z4AVU6OMZFD6WHWD6P7R6AWKTC","bundle":"https://pith.science/pith/Z4AVU6OMZFD6WHWD6P7R6AWKTC/bundle.json","state":"https://pith.science/pith/Z4AVU6OMZFD6WHWD6P7R6AWKTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4AVU6OMZFD6WHWD6P7R6AWKTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z4AVU6OMZFD6WHWD6P7R6AWKTC","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":"0e9923f9871f2f832aa4ac3f11daf370cb3f3567e640ed08737f2baf79be5a5a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-16T21:21:53Z","title_canon_sha256":"d6d17ec9326c38d98cec2f90b5ba031ddf85273cf1809c9359dca7cc9eb7f90e"},"schema_version":"1.0","source":{"id":"1301.3924","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3924","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3924v3","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3924","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"Z4AVU6OMZFD6","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z4AVU6OMZFD6WHWD","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z4AVU6OM","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:ef0be4d014cceb681ebff7d9498d215edf69a7ef43c7b595b5fdc280d8eeb664","target":"graph","created_at":"2026-05-18T00:44:30Z","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":"In this paper we continue the study (initiated in a previous article) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general setting, and prove its compatibility with morphisms of vector bundles and base change.","authors_text":"Ivan Mirkovi\\'c, Simon Riche","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-16T21:21:53Z","title":"Linear Koszul Duality II - Coherent sheaves on perfect sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3924","kind":"arxiv","version":3},"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":"sha256:61ee4578c6f93f54fe80a51861000bdbb84d0cdaca1ed63f5f886c7f827b4c0b","target":"record","created_at":"2026-05-18T00:44:30Z","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":"0e9923f9871f2f832aa4ac3f11daf370cb3f3567e640ed08737f2baf79be5a5a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-01-16T21:21:53Z","title_canon_sha256":"d6d17ec9326c38d98cec2f90b5ba031ddf85273cf1809c9359dca7cc9eb7f90e"},"schema_version":"1.0","source":{"id":"1301.3924","kind":"arxiv","version":3}},"canonical_sha256":"cf015a79ccc947eb1ec3f3ff1f02ca98b6242d2558b81fd390ea34a4e3395d87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf015a79ccc947eb1ec3f3ff1f02ca98b6242d2558b81fd390ea34a4e3395d87","first_computed_at":"2026-05-18T00:44:30.114276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:30.114276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kk2wORWdw9UdkkluPlJCgV8YVLJrrPzdBid5hkAauj/twgKzbGQuXnqbRuQwB8K+IwSVgRsXYXr6JcluPffWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:30.114946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3924","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61ee4578c6f93f54fe80a51861000bdbb84d0cdaca1ed63f5f886c7f827b4c0b","sha256:ef0be4d014cceb681ebff7d9498d215edf69a7ef43c7b595b5fdc280d8eeb664"],"state_sha256":"cf83d359ec1e3df83bb7d0d15d44852c10a0547aa72d04ea1fdc0a857a0becd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0YqJgUH2q1CcdvZGRqhbjGFH0hxPn4lY3zb4X32ep91OCuGgGNLrDNSiw42M4w1/8ciSHpVAVZRDxmLrbGX8CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:26:48.324211Z","bundle_sha256":"042d13fb5272e994289d280c420a469aeb0b39fec67b813f138cf04ad83ca8b6"}}