{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:5TB2X2B2GHSHORFCXNHKNQAPQT","short_pith_number":"pith:5TB2X2B2","canonical_record":{"source":{"id":"math/0402447","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2004-02-27T05:57:01Z","cross_cats_sorted":[],"title_canon_sha256":"d1f6fae4241c8a40d455fca18174561694e3fcca9f7a734e58c2ddc9fe49d07a","abstract_canon_sha256":"eb84756bd80b82b51d298178553ab8097d5d99fca07051e4b1fe15a5f3754ea0"},"schema_version":"1.0"},"canonical_sha256":"ecc3abe83a31e47744a2bb4ea6c00f84cce9df43fcda4c2edff1074a4eb2719b","source":{"kind":"arxiv","id":"math/0402447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402447","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402447v1","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402447","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"5TB2X2B2GHSH","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"pith_short_16","alias_value":"5TB2X2B2GHSHORFC","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"pith_short_8","alias_value":"5TB2X2B2","created_at":"2026-07-04T14:38:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:5TB2X2B2GHSHORFCXNHKNQAPQT","target":"record","payload":{"canonical_record":{"source":{"id":"math/0402447","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2004-02-27T05:57:01Z","cross_cats_sorted":[],"title_canon_sha256":"d1f6fae4241c8a40d455fca18174561694e3fcca9f7a734e58c2ddc9fe49d07a","abstract_canon_sha256":"eb84756bd80b82b51d298178553ab8097d5d99fca07051e4b1fe15a5f3754ea0"},"schema_version":"1.0"},"canonical_sha256":"ecc3abe83a31e47744a2bb4ea6c00f84cce9df43fcda4c2edff1074a4eb2719b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:16.363555Z","signature_b64":"XuSsqRRPNIyw/MvUhrh7nw/khh4b8G6WhpUNaxbNi5mCXwdvcx8nVoGuNNK30LAXZ0HY0jjwqcfSZsgnB3niBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecc3abe83a31e47744a2bb4ea6c00f84cce9df43fcda4c2edff1074a4eb2719b","last_reissued_at":"2026-07-04T14:38:16.363160Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:16.363160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0402447","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:38:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8VqmQvQiAoJMGsf8mq4y5zYJaXOqoCMd2hHR6pyj9oUQBPJ7UUQ6JACUPbGNg8pA4EG/VzHK/zSpuZRl+XeUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:00:54.048111Z"},"content_sha256":"5be66cb6dd38af21fb21dd82c1317655d3ce1a15ad4c39935a8cfeea94c28bc0","schema_version":"1.0","event_id":"sha256:5be66cb6dd38af21fb21dd82c1317655d3ce1a15ad4c39935a8cfeea94c28bc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:5TB2X2B2GHSHORFCXNHKNQAPQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Desingularizations of the moduli space of rank 2 bundles over a curve","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jun Li, Young-Hoon Kiem","submitted_at":"2004-02-27T05:57:01Z","abstract_excerpt":"Let $X$ be a smooth projective curve of genus $g\\ge 3$ and $M_0$ be the moduli space of rank 2 semistable bundles over $X$ with trivial determinant. There are three desingularizations of this singular moduli space constructed by Narasimhan-Ramanan \\cite{NR}, Seshadri \\cite{Se1} and Kirwan \\cite{k5} respectively. The relationship between them has not been understood so far. The purpose of this paper is to show that there is a morphism from Kirwan's desingularization to Seshadri's, which turns out to be the composition of two blow-downs. In doing so, we will show that the singularities of $M_0$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402447","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0402447/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:38:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"igs8enl+vl7XQLEkvMZAFtoLN9iuAplpX6QFY8GCiY1q5WBCo99u3sscoJc89CPzNXbJCR7UqsTyvSXRbfBpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:00:54.049049Z"},"content_sha256":"cb9c0a3c1b62fd49d196e6092fdb43bf39ccc0a48cb333b586e13b93b5962076","schema_version":"1.0","event_id":"sha256:cb9c0a3c1b62fd49d196e6092fdb43bf39ccc0a48cb333b586e13b93b5962076"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5TB2X2B2GHSHORFCXNHKNQAPQT/bundle.json","state_url":"https://pith.science/pith/5TB2X2B2GHSHORFCXNHKNQAPQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5TB2X2B2GHSHORFCXNHKNQAPQT/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":"2026-08-04T21:00:54Z","links":{"resolver":"https://pith.science/pith/5TB2X2B2GHSHORFCXNHKNQAPQT","bundle":"https://pith.science/pith/5TB2X2B2GHSHORFCXNHKNQAPQT/bundle.json","state":"https://pith.science/pith/5TB2X2B2GHSHORFCXNHKNQAPQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5TB2X2B2GHSHORFCXNHKNQAPQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:5TB2X2B2GHSHORFCXNHKNQAPQT","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":"eb84756bd80b82b51d298178553ab8097d5d99fca07051e4b1fe15a5f3754ea0","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2004-02-27T05:57:01Z","title_canon_sha256":"d1f6fae4241c8a40d455fca18174561694e3fcca9f7a734e58c2ddc9fe49d07a"},"schema_version":"1.0","source":{"id":"math/0402447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402447","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402447v1","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402447","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"5TB2X2B2GHSH","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"pith_short_16","alias_value":"5TB2X2B2GHSHORFC","created_at":"2026-07-04T14:38:16Z"},{"alias_kind":"pith_short_8","alias_value":"5TB2X2B2","created_at":"2026-07-04T14:38:16Z"}],"graph_snapshots":[{"event_id":"sha256:cb9c0a3c1b62fd49d196e6092fdb43bf39ccc0a48cb333b586e13b93b5962076","target":"graph","created_at":"2026-07-04T14:38:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0402447/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a smooth projective curve of genus $g\\ge 3$ and $M_0$ be the moduli space of rank 2 semistable bundles over $X$ with trivial determinant. There are three desingularizations of this singular moduli space constructed by Narasimhan-Ramanan \\cite{NR}, Seshadri \\cite{Se1} and Kirwan \\cite{k5} respectively. The relationship between them has not been understood so far. The purpose of this paper is to show that there is a morphism from Kirwan's desingularization to Seshadri's, which turns out to be the composition of two blow-downs. In doing so, we will show that the singularities of $M_0$ ","authors_text":"Jun Li, Young-Hoon Kiem","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2004-02-27T05:57:01Z","title":"Desingularizations of the moduli space of rank 2 bundles over a curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402447","kind":"arxiv","version":1},"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":"sha256:5be66cb6dd38af21fb21dd82c1317655d3ce1a15ad4c39935a8cfeea94c28bc0","target":"record","created_at":"2026-07-04T14:38:16Z","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":"eb84756bd80b82b51d298178553ab8097d5d99fca07051e4b1fe15a5f3754ea0","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2004-02-27T05:57:01Z","title_canon_sha256":"d1f6fae4241c8a40d455fca18174561694e3fcca9f7a734e58c2ddc9fe49d07a"},"schema_version":"1.0","source":{"id":"math/0402447","kind":"arxiv","version":1}},"canonical_sha256":"ecc3abe83a31e47744a2bb4ea6c00f84cce9df43fcda4c2edff1074a4eb2719b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecc3abe83a31e47744a2bb4ea6c00f84cce9df43fcda4c2edff1074a4eb2719b","first_computed_at":"2026-07-04T14:38:16.363160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:16.363160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XuSsqRRPNIyw/MvUhrh7nw/khh4b8G6WhpUNaxbNi5mCXwdvcx8nVoGuNNK30LAXZ0HY0jjwqcfSZsgnB3niBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:16.363555Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0402447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5be66cb6dd38af21fb21dd82c1317655d3ce1a15ad4c39935a8cfeea94c28bc0","sha256:cb9c0a3c1b62fd49d196e6092fdb43bf39ccc0a48cb333b586e13b93b5962076"],"state_sha256":"3e51815f944cd449b7c9b000ac3e4ff516b2b7497fdef9e71a47fb09672a0f02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5jtOhgT/IQD1OUo95k3+2V7n2vwLxaWwBUdD3fuHfey9GLXBGtW9PYMpAH/DOyKnngP0arhRljAsEOYe2TIQAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T21:00:54.054375Z","bundle_sha256":"e4799e6bffe06b4ffac0d62ea57002346dae0350c47947255f158d67c94c5c34"}}