{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:ENIO6SSKRVBZ4RW6P3WHOPYKTJ","short_pith_number":"pith:ENIO6SSK","canonical_record":{"source":{"id":"math/0112160","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2001-12-16T12:00:50Z","cross_cats_sorted":["hep-th","math.AG"],"title_canon_sha256":"b34e2b124db2f33972b63cb7cf5a677133a525c6977c8b1f54621b0fd31f84be","abstract_canon_sha256":"81b1910a8b4b0b9460c1bda6fbb115836fa8022e2bd005d9d91b7fe5a03a9a48"},"schema_version":"1.0"},"canonical_sha256":"2350ef4a4a8d439e46de7eec773f0a9a62a68f458fe43f8cdb9b4a391b693c63","source":{"kind":"arxiv","id":"math/0112160","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0112160","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0112160v2","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0112160","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"ENIO6SSKRVBZ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"ENIO6SSKRVBZ4RW6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"ENIO6SSK","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:ENIO6SSKRVBZ4RW6P3WHOPYKTJ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0112160","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2001-12-16T12:00:50Z","cross_cats_sorted":["hep-th","math.AG"],"title_canon_sha256":"b34e2b124db2f33972b63cb7cf5a677133a525c6977c8b1f54621b0fd31f84be","abstract_canon_sha256":"81b1910a8b4b0b9460c1bda6fbb115836fa8022e2bd005d9d91b7fe5a03a9a48"},"schema_version":"1.0"},"canonical_sha256":"2350ef4a4a8d439e46de7eec773f0a9a62a68f458fe43f8cdb9b4a391b693c63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:07.791767Z","signature_b64":"2WazqaMQ3fx4lKNnHaH+gmZK2S00o4mBMy2efYMaJHltTuSV4ZNcvO0ogWUFOmpi4HO6uL0nvwO0tLsVNQCJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2350ef4a4a8d439e46de7eec773f0a9a62a68f458fe43f8cdb9b4a391b693c63","last_reissued_at":"2026-05-18T01:09:07.791347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:07.791347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0112160","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":"2026-05-18T01:09:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uBaOo4DER3sLJZ+zWlnysc6EI5FTr5gjCVSu1VbuN3xed3bseBswSutc9lvpH823qDcHhQ0NQgJDrQYgS/51BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:56:58.716611Z"},"content_sha256":"aed1f27ec491bb06a71ba1e3fdb2805b29b23f29c21dece59d73596e88a1502b","schema_version":"1.0","event_id":"sha256:aed1f27ec491bb06a71ba1e3fdb2805b29b23f29c21dece59d73596e88a1502b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:ENIO6SSKRVBZ4RW6P3WHOPYKTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimensional reduction and quiver bundles","license":"","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.DG","authors_text":"Luis \\'Alvarez-C\\'onsul, Oscar Garc\\'ia-Prada","submitted_at":"2001-12-16T12:00:50Z","abstract_excerpt":"The so-called Hitchin-Kobayashi correspondence, proved by Donaldson, Uhlenbeck and Yau, establishes that an indecomposable holomorphic vector bundle over a compact Kahler manifold admits a Hermitian-Einstein metric if and only if the bundle satisfies the Mumford-Takemoto stability condition. In this paper we consider a variant of this correspondence for G-equivariant vector bundles on the product of a compact Kahler manifold X by a flag manifold G/P, where G is a complex semisimple Lie group and P is a parabolic subgroup. The modification that we consider is determined by a filtration of the v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0112160","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":"2026-05-18T01:09:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VgxsB/oiILUJd5+UFtTWuU1w9LsWa3GOuT/5JVttUWJdC8G3EV2OJrxDvu9QAQYIHB50313bZnAOas6YLaOuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:56:58.716957Z"},"content_sha256":"13b5eb01f9c45927574f4da2168937f11a89e1987c921dbb86e5e08d26d3ce96","schema_version":"1.0","event_id":"sha256:13b5eb01f9c45927574f4da2168937f11a89e1987c921dbb86e5e08d26d3ce96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ENIO6SSKRVBZ4RW6P3WHOPYKTJ/bundle.json","state_url":"https://pith.science/pith/ENIO6SSKRVBZ4RW6P3WHOPYKTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ENIO6SSKRVBZ4RW6P3WHOPYKTJ/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":"2026-05-31T02:56:58Z","links":{"resolver":"https://pith.science/pith/ENIO6SSKRVBZ4RW6P3WHOPYKTJ","bundle":"https://pith.science/pith/ENIO6SSKRVBZ4RW6P3WHOPYKTJ/bundle.json","state":"https://pith.science/pith/ENIO6SSKRVBZ4RW6P3WHOPYKTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ENIO6SSKRVBZ4RW6P3WHOPYKTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:ENIO6SSKRVBZ4RW6P3WHOPYKTJ","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":"81b1910a8b4b0b9460c1bda6fbb115836fa8022e2bd005d9d91b7fe5a03a9a48","cross_cats_sorted":["hep-th","math.AG"],"license":"","primary_cat":"math.DG","submitted_at":"2001-12-16T12:00:50Z","title_canon_sha256":"b34e2b124db2f33972b63cb7cf5a677133a525c6977c8b1f54621b0fd31f84be"},"schema_version":"1.0","source":{"id":"math/0112160","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0112160","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0112160v2","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0112160","created_at":"2026-05-18T01:09:07Z"},{"alias_kind":"pith_short_12","alias_value":"ENIO6SSKRVBZ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"ENIO6SSKRVBZ4RW6","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"ENIO6SSK","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:13b5eb01f9c45927574f4da2168937f11a89e1987c921dbb86e5e08d26d3ce96","target":"graph","created_at":"2026-05-18T01:09:07Z","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":"The so-called Hitchin-Kobayashi correspondence, proved by Donaldson, Uhlenbeck and Yau, establishes that an indecomposable holomorphic vector bundle over a compact Kahler manifold admits a Hermitian-Einstein metric if and only if the bundle satisfies the Mumford-Takemoto stability condition. In this paper we consider a variant of this correspondence for G-equivariant vector bundles on the product of a compact Kahler manifold X by a flag manifold G/P, where G is a complex semisimple Lie group and P is a parabolic subgroup. The modification that we consider is determined by a filtration of the v","authors_text":"Luis \\'Alvarez-C\\'onsul, Oscar Garc\\'ia-Prada","cross_cats":["hep-th","math.AG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2001-12-16T12:00:50Z","title":"Dimensional reduction and quiver bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0112160","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:aed1f27ec491bb06a71ba1e3fdb2805b29b23f29c21dece59d73596e88a1502b","target":"record","created_at":"2026-05-18T01:09:07Z","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":"81b1910a8b4b0b9460c1bda6fbb115836fa8022e2bd005d9d91b7fe5a03a9a48","cross_cats_sorted":["hep-th","math.AG"],"license":"","primary_cat":"math.DG","submitted_at":"2001-12-16T12:00:50Z","title_canon_sha256":"b34e2b124db2f33972b63cb7cf5a677133a525c6977c8b1f54621b0fd31f84be"},"schema_version":"1.0","source":{"id":"math/0112160","kind":"arxiv","version":2}},"canonical_sha256":"2350ef4a4a8d439e46de7eec773f0a9a62a68f458fe43f8cdb9b4a391b693c63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2350ef4a4a8d439e46de7eec773f0a9a62a68f458fe43f8cdb9b4a391b693c63","first_computed_at":"2026-05-18T01:09:07.791347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:07.791347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2WazqaMQ3fx4lKNnHaH+gmZK2S00o4mBMy2efYMaJHltTuSV4ZNcvO0ogWUFOmpi4HO6uL0nvwO0tLsVNQCJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:07.791767Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0112160","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aed1f27ec491bb06a71ba1e3fdb2805b29b23f29c21dece59d73596e88a1502b","sha256:13b5eb01f9c45927574f4da2168937f11a89e1987c921dbb86e5e08d26d3ce96"],"state_sha256":"0f07a7aba72fe50f108d8bed0622ad6ae7bbd57f25127b0f5ce1e29e0e031861"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w03hzgK3uQf4t0uU1N7Rm7SbSSGMOwtBfVMKaAMRlJFDXp8NvqyT+6Rf4UqV7nTHkOj7hzxwOZkg7Q/tm+vMDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:56:58.718932Z","bundle_sha256":"164dc44e766ed8ccc53c24f7aad5fd3fc1c3702ec495bf072eb302bcda7e2237"}}