{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:642WSPX22LR6VCHKMEYQN54UAE","short_pith_number":"pith:642WSPX2","canonical_record":{"source":{"id":"0911.1773","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-09T21:13:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"815d0d7d09f11274214d5fb5a5aacecfc81258020dcc34ee32f4110ca7bec629","abstract_canon_sha256":"68c15c5246d96d221ac20a0695e3b0c116ba7717ed1e283da6de1921e4016c93"},"schema_version":"1.0"},"canonical_sha256":"f735693efad2e3ea88ea613106f79401293f0e71f1c0a05489b02758f5d99a9c","source":{"kind":"arxiv","id":"0911.1773","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1773","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1773v3","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1773","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"pith_short_12","alias_value":"642WSPX22LR6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"642WSPX22LR6VCHK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"642WSPX2","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:642WSPX22LR6VCHKMEYQN54UAE","target":"record","payload":{"canonical_record":{"source":{"id":"0911.1773","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-09T21:13:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"815d0d7d09f11274214d5fb5a5aacecfc81258020dcc34ee32f4110ca7bec629","abstract_canon_sha256":"68c15c5246d96d221ac20a0695e3b0c116ba7717ed1e283da6de1921e4016c93"},"schema_version":"1.0"},"canonical_sha256":"f735693efad2e3ea88ea613106f79401293f0e71f1c0a05489b02758f5d99a9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:30.367462Z","signature_b64":"Zo9lTil4u5IXp3V65KaeLBC7uyXAt+bMW+pUuEJ0+DcmieotzDCqf1TmT7YaS1snXLXeq07t6YHO8VwZLcU9BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f735693efad2e3ea88ea613106f79401293f0e71f1c0a05489b02758f5d99a9c","last_reissued_at":"2026-05-18T02:29:30.367024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:30.367024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.1773","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":"2026-05-18T02:29:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oNkO6BYXP8t1DxEuAwarIszJRpNcXBp7cqX0yoYIFdFMllB5kZzhPUvFKHfLrpJG00cWwZljdQvAAePdya9ZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T19:45:23.026450Z"},"content_sha256":"e07678d12a53606b8744b04744bed5583cefc5d7088e899e6dd08add3998afa3","schema_version":"1.0","event_id":"sha256:e07678d12a53606b8744b04744bed5583cefc5d7088e899e6dd08add3998afa3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:642WSPX22LR6VCHKMEYQN54UAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perverse coherent sheaves on blow-up. III. Blow-up formula from wall-crossing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Hiraku Nakajima, Kota Yoshioka","submitted_at":"2009-11-09T21:13:08Z","abstract_excerpt":"In earlier papers arXiv:0802.3120, arXiv:0806.0463 of this series we constructed a sequence of intermediate moduli spaces $\\bM^m(c)$ connecting a moduli space $M(c)$ of stable torsion free sheaves on a nonsingular complex projective surface and $\\bM(c)$ on its one point blow-up. They are moduli spaces of perverse coherent sheaves on the blow-up.\n  In this paper we study how Donaldson-type invariants (integrals of cohomology classes given by universal sheaves) change from $\\bM^m(c)$ to $\\bM^{m+1}(c)$, and then from $M(c)$ to $\\bM(c)$.\n  As an application we prove that Nekrasov-type partition fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1773","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":"2026-05-18T02:29:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rd7wiAjTqQoRY5RZIv54Xh12yGo4n6cWnIwepSs/MvZeSZk0Zd5UsFrMqDeCd2UJ/Rci1TUhiA9iMTKlm/hADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T19:45:23.027041Z"},"content_sha256":"75d447dc16d201fe1ba5c237ec6a98f533c930b8d3b91038a43f715ee8d2fe5b","schema_version":"1.0","event_id":"sha256:75d447dc16d201fe1ba5c237ec6a98f533c930b8d3b91038a43f715ee8d2fe5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/642WSPX22LR6VCHKMEYQN54UAE/bundle.json","state_url":"https://pith.science/pith/642WSPX22LR6VCHKMEYQN54UAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/642WSPX22LR6VCHKMEYQN54UAE/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":"2026-05-18T19:45:23Z","links":{"resolver":"https://pith.science/pith/642WSPX22LR6VCHKMEYQN54UAE","bundle":"https://pith.science/pith/642WSPX22LR6VCHKMEYQN54UAE/bundle.json","state":"https://pith.science/pith/642WSPX22LR6VCHKMEYQN54UAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/642WSPX22LR6VCHKMEYQN54UAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:642WSPX22LR6VCHKMEYQN54UAE","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":"68c15c5246d96d221ac20a0695e3b0c116ba7717ed1e283da6de1921e4016c93","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-09T21:13:08Z","title_canon_sha256":"815d0d7d09f11274214d5fb5a5aacecfc81258020dcc34ee32f4110ca7bec629"},"schema_version":"1.0","source":{"id":"0911.1773","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1773","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1773v3","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1773","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"pith_short_12","alias_value":"642WSPX22LR6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"642WSPX22LR6VCHK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"642WSPX2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:75d447dc16d201fe1ba5c237ec6a98f533c930b8d3b91038a43f715ee8d2fe5b","target":"graph","created_at":"2026-05-18T02:29:30Z","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 earlier papers arXiv:0802.3120, arXiv:0806.0463 of this series we constructed a sequence of intermediate moduli spaces $\\bM^m(c)$ connecting a moduli space $M(c)$ of stable torsion free sheaves on a nonsingular complex projective surface and $\\bM(c)$ on its one point blow-up. They are moduli spaces of perverse coherent sheaves on the blow-up.\n  In this paper we study how Donaldson-type invariants (integrals of cohomology classes given by universal sheaves) change from $\\bM^m(c)$ to $\\bM^{m+1}(c)$, and then from $M(c)$ to $\\bM(c)$.\n  As an application we prove that Nekrasov-type partition fu","authors_text":"Hiraku Nakajima, Kota Yoshioka","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-09T21:13:08Z","title":"Perverse coherent sheaves on blow-up. III. Blow-up formula from wall-crossing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1773","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:e07678d12a53606b8744b04744bed5583cefc5d7088e899e6dd08add3998afa3","target":"record","created_at":"2026-05-18T02:29:30Z","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":"68c15c5246d96d221ac20a0695e3b0c116ba7717ed1e283da6de1921e4016c93","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-09T21:13:08Z","title_canon_sha256":"815d0d7d09f11274214d5fb5a5aacecfc81258020dcc34ee32f4110ca7bec629"},"schema_version":"1.0","source":{"id":"0911.1773","kind":"arxiv","version":3}},"canonical_sha256":"f735693efad2e3ea88ea613106f79401293f0e71f1c0a05489b02758f5d99a9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f735693efad2e3ea88ea613106f79401293f0e71f1c0a05489b02758f5d99a9c","first_computed_at":"2026-05-18T02:29:30.367024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:30.367024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zo9lTil4u5IXp3V65KaeLBC7uyXAt+bMW+pUuEJ0+DcmieotzDCqf1TmT7YaS1snXLXeq07t6YHO8VwZLcU9BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:30.367462Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1773","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e07678d12a53606b8744b04744bed5583cefc5d7088e899e6dd08add3998afa3","sha256:75d447dc16d201fe1ba5c237ec6a98f533c930b8d3b91038a43f715ee8d2fe5b"],"state_sha256":"4af7f469055510399e3f572df01f5926b4c42c5116c2ee9593f57bd918308c43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBqTz0H7z65BrUggUGChJPC2yvromYvcSU9g16o36ac5V9XDtPfCLftjdqC0zSMsdqXsw8WaTUe6A6oQNl6FDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T19:45:23.028543Z","bundle_sha256":"6069ef208a57ec93b5dbbefde95c7a3fe86a122a56b885d7728427f374debc74"}}