{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:GQEVEXNCYDG4FUCB77ZUNBZI6A","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":"39cac8ea826a322b827e3b9d7fe76c0c8b7ff2d4e2c3a45ae7e15cfe8fedcf0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-12T07:03:40Z","title_canon_sha256":"5bb3695fa8a7903fe425060eeff3ef215f07c0b18311933bdbe869a04d4cd51d"},"schema_version":"1.0","source":{"id":"0911.2301","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2301","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2301v2","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2301","created_at":"2026-05-18T04:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"GQEVEXNCYDG4","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"GQEVEXNCYDG4FUCB","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"GQEVEXNC","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:e25fecb202b27140c6efc8ec33efd3e55526d3a0b339c70b890c49ff07181422","target":"graph","created_at":"2026-05-18T04:27:47Z","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":"Let X be a geometrically irreducible smooth projective curve over a field k. We describe the algebra of endomorphisms of indecomposable unstable vector bundles over X of rank 2 and degree d. Fixing some numerical invariants, namely the Harder-Narasimhan type and the dimension of the algebra of endomorphisms, we construct algebraic stacks and moduli schemes for such bundles.","authors_text":"L. Brambila-Paz, Nitin Nitsure, Osbaldo Mata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-12T07:03:40Z","title":"Moduli stacks and moduli schemes for rank 2 unstable bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2301","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":"sha256:1094f1563400e32955dde08eac800711018fedabb43a63a652cf9faefefcd2f1","target":"record","created_at":"2026-05-18T04:27:47Z","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":"39cac8ea826a322b827e3b9d7fe76c0c8b7ff2d4e2c3a45ae7e15cfe8fedcf0d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-12T07:03:40Z","title_canon_sha256":"5bb3695fa8a7903fe425060eeff3ef215f07c0b18311933bdbe869a04d4cd51d"},"schema_version":"1.0","source":{"id":"0911.2301","kind":"arxiv","version":2}},"canonical_sha256":"3409525da2c0cdc2d041fff3468728f02e5969eaaede31b7b2339a79ae09aec6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3409525da2c0cdc2d041fff3468728f02e5969eaaede31b7b2339a79ae09aec6","first_computed_at":"2026-05-18T04:27:47.815388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:47.815388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZQVmSmfUk9nMUimuoQ6JFRd22ug5k4krty9drd08X61VRQxvJZr1l2CkUwm/nzRRumnGQtp5pkrWjizVOR7dDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:47.815901Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2301","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1094f1563400e32955dde08eac800711018fedabb43a63a652cf9faefefcd2f1","sha256:e25fecb202b27140c6efc8ec33efd3e55526d3a0b339c70b890c49ff07181422"],"state_sha256":"390942238c7d11736cb1f1e2fba437e45c51581eee2ea4bed70899e9b0d33c55"}