{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AJILITLZUB5GGKUBATBG5UB6DQ","short_pith_number":"pith:AJILITLZ","canonical_record":{"source":{"id":"1506.03642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T12:06:38Z","cross_cats_sorted":[],"title_canon_sha256":"1c0779b15a5299a13886663fd730e9dce9a6f282a93f9581060c0adfe8b8328e","abstract_canon_sha256":"00be764771289266adbc3e60b7403da7edef0c900ba89b83cd78b4d076cb5439"},"schema_version":"1.0"},"canonical_sha256":"0250b44d79a07a632a8104c26ed03e1c25c73a0a65e7c5c50f17bbfa52bb1ede","source":{"kind":"arxiv","id":"1506.03642","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03642","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03642v2","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03642","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"AJILITLZUB5G","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AJILITLZUB5GGKUB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AJILITLZ","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AJILITLZUB5GGKUBATBG5UB6DQ","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T12:06:38Z","cross_cats_sorted":[],"title_canon_sha256":"1c0779b15a5299a13886663fd730e9dce9a6f282a93f9581060c0adfe8b8328e","abstract_canon_sha256":"00be764771289266adbc3e60b7403da7edef0c900ba89b83cd78b4d076cb5439"},"schema_version":"1.0"},"canonical_sha256":"0250b44d79a07a632a8104c26ed03e1c25c73a0a65e7c5c50f17bbfa52bb1ede","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:27.719981Z","signature_b64":"r8X+AFMoVdFkSv8Tll5enl/7euZtoJPJzphoaIYya7f3o19dH8+dmN2tIIwc8QLD28u7DPaeEojLT/VbL/iHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0250b44d79a07a632a8104c26ed03e1c25c73a0a65e7c5c50f17bbfa52bb1ede","last_reissued_at":"2026-05-18T00:59:27.719221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:27.719221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03642","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":"2026-05-18T00:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQFg43PoifKsBU6sjSVmDr6usrgj+vphhHSJsJyns8JBOpqH/mxN1B2TpxxkL/wRJ1N4jjAHHzjmil0VfIziAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:00:25.946598Z"},"content_sha256":"c62e5420b7deb27fdf7a9e6fca01dde8047bd9f3625ebd99640304c21bca14fa","schema_version":"1.0","event_id":"sha256:c62e5420b7deb27fdf7a9e6fca01dde8047bd9f3625ebd99640304c21bca14fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AJILITLZUB5GGKUBATBG5UB6DQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perverse sheaves and the topology of algebraic varieties (2015 PCMI)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mark Andrea A. de Cataldo","submitted_at":"2015-06-11T12:06:38Z","abstract_excerpt":"Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03642","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":"2026-05-18T00:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"to5LyeYUbmIWaCSYNN1EXECzz6NeafGY/xwmTHli9TYeupQqofzaollB8ZEiKfLU/VZFnT/e5u49ocQhFl0UCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:00:25.946965Z"},"content_sha256":"12dc2e575f104e9a5023c2b854e265dd59f22943f8e786678b3fea7a383388af","schema_version":"1.0","event_id":"sha256:12dc2e575f104e9a5023c2b854e265dd59f22943f8e786678b3fea7a383388af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJILITLZUB5GGKUBATBG5UB6DQ/bundle.json","state_url":"https://pith.science/pith/AJILITLZUB5GGKUBATBG5UB6DQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJILITLZUB5GGKUBATBG5UB6DQ/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":"2026-06-20T05:00:25Z","links":{"resolver":"https://pith.science/pith/AJILITLZUB5GGKUBATBG5UB6DQ","bundle":"https://pith.science/pith/AJILITLZUB5GGKUBATBG5UB6DQ/bundle.json","state":"https://pith.science/pith/AJILITLZUB5GGKUBATBG5UB6DQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJILITLZUB5GGKUBATBG5UB6DQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AJILITLZUB5GGKUBATBG5UB6DQ","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":"00be764771289266adbc3e60b7403da7edef0c900ba89b83cd78b4d076cb5439","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T12:06:38Z","title_canon_sha256":"1c0779b15a5299a13886663fd730e9dce9a6f282a93f9581060c0adfe8b8328e"},"schema_version":"1.0","source":{"id":"1506.03642","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03642","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03642v2","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03642","created_at":"2026-05-18T00:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"AJILITLZUB5G","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AJILITLZUB5GGKUB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AJILITLZ","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:12dc2e575f104e9a5023c2b854e265dd59f22943f8e786678b3fea7a383388af","target":"graph","created_at":"2026-05-18T00:59:27Z","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":"Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.","authors_text":"Mark Andrea A. de Cataldo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T12:06:38Z","title":"Perverse sheaves and the topology of algebraic varieties (2015 PCMI)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03642","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:c62e5420b7deb27fdf7a9e6fca01dde8047bd9f3625ebd99640304c21bca14fa","target":"record","created_at":"2026-05-18T00:59:27Z","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":"00be764771289266adbc3e60b7403da7edef0c900ba89b83cd78b4d076cb5439","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-11T12:06:38Z","title_canon_sha256":"1c0779b15a5299a13886663fd730e9dce9a6f282a93f9581060c0adfe8b8328e"},"schema_version":"1.0","source":{"id":"1506.03642","kind":"arxiv","version":2}},"canonical_sha256":"0250b44d79a07a632a8104c26ed03e1c25c73a0a65e7c5c50f17bbfa52bb1ede","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0250b44d79a07a632a8104c26ed03e1c25c73a0a65e7c5c50f17bbfa52bb1ede","first_computed_at":"2026-05-18T00:59:27.719221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:27.719221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r8X+AFMoVdFkSv8Tll5enl/7euZtoJPJzphoaIYya7f3o19dH8+dmN2tIIwc8QLD28u7DPaeEojLT/VbL/iHAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:27.719981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03642","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c62e5420b7deb27fdf7a9e6fca01dde8047bd9f3625ebd99640304c21bca14fa","sha256:12dc2e575f104e9a5023c2b854e265dd59f22943f8e786678b3fea7a383388af"],"state_sha256":"cb135ab1cc80f6866bbeb9fab9080114e08d642de66c68f7b36d40de36b49422"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zjSBJoEEzJYG4+z63ELWlp+lGTddfuYNllxq84L8jHEC3DeRo0y07Ql6vEJEmOYYYno1f2j4FxyucwydHlG5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:00:25.948838Z","bundle_sha256":"b20640fea9f2d94d4338664f3279d296f07ce20bc0eec153074a303b46da331a"}}