{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4IGL5MU7K5IEJTRHYBKVGE5I3U","short_pith_number":"pith:4IGL5MU7","canonical_record":{"source":{"id":"1111.4263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-18T02:57:23Z","cross_cats_sorted":[],"title_canon_sha256":"d3eb7baec27a9926323625768d2e9b62909a65113248cbb6db47107c29fabf98","abstract_canon_sha256":"4eba3c9bd22f4082ae5a8f606ef6a462ed3a54bc2fcd7c6b8e75d22a5bfaf6f4"},"schema_version":"1.0"},"canonical_sha256":"e20cbeb29f575044ce27c0555313a8dd2897c332d20458a82465fec40d1f43bc","source":{"kind":"arxiv","id":"1111.4263","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4263","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4263v2","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4263","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"pith_short_12","alias_value":"4IGL5MU7K5IE","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4IGL5MU7K5IEJTRH","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4IGL5MU7","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4IGL5MU7K5IEJTRHYBKVGE5I3U","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-18T02:57:23Z","cross_cats_sorted":[],"title_canon_sha256":"d3eb7baec27a9926323625768d2e9b62909a65113248cbb6db47107c29fabf98","abstract_canon_sha256":"4eba3c9bd22f4082ae5a8f606ef6a462ed3a54bc2fcd7c6b8e75d22a5bfaf6f4"},"schema_version":"1.0"},"canonical_sha256":"e20cbeb29f575044ce27c0555313a8dd2897c332d20458a82465fec40d1f43bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:54.756057Z","signature_b64":"iVB30Fblpr69VACE2gtUeGJKS8a4GZDvQ+dHwfrRnHvNg1gLawkUUz/GWtuZQX1aJUeyzLE7EC9gHP2BLu+3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e20cbeb29f575044ce27c0555313a8dd2897c332d20458a82465fec40d1f43bc","last_reissued_at":"2026-05-18T03:52:54.755140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:54.755140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4263","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":"2026-05-18T03:52:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQ75NMMloEwtG914uknxzKwfm7eOlK5oxCdNn2S7Y01o268+1IlxsEIVtD+H/i5OO9yYoLvyTXOdTSQ0c0ObDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:19:50.436929Z"},"content_sha256":"998bd17dd653f2ad3d0334978c731928836c18a0e79c9e25139e525f7e6da6ac","schema_version":"1.0","event_id":"sha256:998bd17dd653f2ad3d0334978c731928836c18a0e79c9e25139e525f7e6da6ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4IGL5MU7K5IEJTRHYBKVGE5I3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extension groups of tautological sheaves on Hilbert schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andreas Krug","submitted_at":"2011-11-18T02:57:23Z","abstract_excerpt":"We give formulas for the extension groups between tautological sheaves and more general between tautological objects twisted by a determinant line bundle on the Hilbert scheme of points on a smooth quasi-projective surface. We do this using L. Scala's results about the image of tautological sheaves under the Bridgeland-King-Reid equivalence. We also compute the Yoneda products in terms of these formulas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4263","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":"2026-05-18T03:52:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rn6sBZTwWlup2RbTEShKbSyWYCSwH2bugjQ6IfgCOiy7o+jghJ9Lj7ngY3B5SHvsgcXK/lJ+5DxWNCj/MfZwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:19:50.437612Z"},"content_sha256":"27e32329aed0be3fc1185ecf03e006aee51de0e0d9d11666eda9cd6b5deaa74c","schema_version":"1.0","event_id":"sha256:27e32329aed0be3fc1185ecf03e006aee51de0e0d9d11666eda9cd6b5deaa74c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4IGL5MU7K5IEJTRHYBKVGE5I3U/bundle.json","state_url":"https://pith.science/pith/4IGL5MU7K5IEJTRHYBKVGE5I3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4IGL5MU7K5IEJTRHYBKVGE5I3U/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":"2026-06-07T08:19:50Z","links":{"resolver":"https://pith.science/pith/4IGL5MU7K5IEJTRHYBKVGE5I3U","bundle":"https://pith.science/pith/4IGL5MU7K5IEJTRHYBKVGE5I3U/bundle.json","state":"https://pith.science/pith/4IGL5MU7K5IEJTRHYBKVGE5I3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4IGL5MU7K5IEJTRHYBKVGE5I3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4IGL5MU7K5IEJTRHYBKVGE5I3U","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":"4eba3c9bd22f4082ae5a8f606ef6a462ed3a54bc2fcd7c6b8e75d22a5bfaf6f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-18T02:57:23Z","title_canon_sha256":"d3eb7baec27a9926323625768d2e9b62909a65113248cbb6db47107c29fabf98"},"schema_version":"1.0","source":{"id":"1111.4263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4263","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4263v2","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4263","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"pith_short_12","alias_value":"4IGL5MU7K5IE","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4IGL5MU7K5IEJTRH","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4IGL5MU7","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:27e32329aed0be3fc1185ecf03e006aee51de0e0d9d11666eda9cd6b5deaa74c","target":"graph","created_at":"2026-05-18T03:52:54Z","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 give formulas for the extension groups between tautological sheaves and more general between tautological objects twisted by a determinant line bundle on the Hilbert scheme of points on a smooth quasi-projective surface. We do this using L. Scala's results about the image of tautological sheaves under the Bridgeland-King-Reid equivalence. We also compute the Yoneda products in terms of these formulas.","authors_text":"Andreas Krug","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-18T02:57:23Z","title":"Extension groups of tautological sheaves on Hilbert schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4263","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":"sha256:998bd17dd653f2ad3d0334978c731928836c18a0e79c9e25139e525f7e6da6ac","target":"record","created_at":"2026-05-18T03:52:54Z","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":"4eba3c9bd22f4082ae5a8f606ef6a462ed3a54bc2fcd7c6b8e75d22a5bfaf6f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-18T02:57:23Z","title_canon_sha256":"d3eb7baec27a9926323625768d2e9b62909a65113248cbb6db47107c29fabf98"},"schema_version":"1.0","source":{"id":"1111.4263","kind":"arxiv","version":2}},"canonical_sha256":"e20cbeb29f575044ce27c0555313a8dd2897c332d20458a82465fec40d1f43bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e20cbeb29f575044ce27c0555313a8dd2897c332d20458a82465fec40d1f43bc","first_computed_at":"2026-05-18T03:52:54.755140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:54.755140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iVB30Fblpr69VACE2gtUeGJKS8a4GZDvQ+dHwfrRnHvNg1gLawkUUz/GWtuZQX1aJUeyzLE7EC9gHP2BLu+3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:54.756057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:998bd17dd653f2ad3d0334978c731928836c18a0e79c9e25139e525f7e6da6ac","sha256:27e32329aed0be3fc1185ecf03e006aee51de0e0d9d11666eda9cd6b5deaa74c"],"state_sha256":"e625ee60aa72715259af2a941776b5a9d2d631e372485909cf4cd29afe82ed9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPNwtVsQcQGkmlqEtkZnngSdoKUPimyIKKq5ent2eeqolLEywEdLwL3ZT1cmdh7zxhLhPXltBOP5wV7JxcEXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T08:19:50.441207Z","bundle_sha256":"97290a5502ea9c86913c939bcd763e7246f07b6d67b861d4c40a0eb396164757"}}