{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:C2UIHRWMC6LFZECYODWANQ74QX","short_pith_number":"pith:C2UIHRWM","canonical_record":{"source":{"id":"1108.6165","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-31T08:59:26Z","cross_cats_sorted":[],"title_canon_sha256":"bd7a110d3025a3ce8b3e3e8b00a29b1a378144c4fd2eefef5d4da3877a5b7422","abstract_canon_sha256":"505cf37068e799235d9424880c1a0822c4560ef7c313a7e510d379013c9cf563"},"schema_version":"1.0"},"canonical_sha256":"16a883c6cc17965c905870ec06c3fc85e83c41a0413a9f42eab561ae4cd6aa05","source":{"kind":"arxiv","id":"1108.6165","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6165","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6165v2","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6165","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"C2UIHRWMC6LF","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C2UIHRWMC6LFZECY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C2UIHRWM","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:C2UIHRWMC6LFZECYODWANQ74QX","target":"record","payload":{"canonical_record":{"source":{"id":"1108.6165","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-31T08:59:26Z","cross_cats_sorted":[],"title_canon_sha256":"bd7a110d3025a3ce8b3e3e8b00a29b1a378144c4fd2eefef5d4da3877a5b7422","abstract_canon_sha256":"505cf37068e799235d9424880c1a0822c4560ef7c313a7e510d379013c9cf563"},"schema_version":"1.0"},"canonical_sha256":"16a883c6cc17965c905870ec06c3fc85e83c41a0413a9f42eab561ae4cd6aa05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:48.127642Z","signature_b64":"3Uw77K7Frr5zXrSZHgib7KbVnx3R6TcDIk1WGyGc2lSmqqwQHfQUihyoyQJi8TWt0249ZRffwVz21euuJPFmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16a883c6cc17965c905870ec06c3fc85e83c41a0413a9f42eab561ae4cd6aa05","last_reissued_at":"2026-05-18T02:20:48.126894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:48.126894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.6165","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":"2026-05-18T02:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ny/jKxjgikQUJPOGehxRBjBRHK3osiQluqW7A0jHBpT3SPO0G0zTDD2jG7yQofa1uAqWEfzbO2bCvX6BfmJSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:29:30.577753Z"},"content_sha256":"f2a970f515cb41c0d463dbb7a96ad2ba6bc1e9425236ce1d6eef113bffbe0e2c","schema_version":"1.0","event_id":"sha256:f2a970f515cb41c0d463dbb7a96ad2ba6bc1e9425236ce1d6eef113bffbe0e2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:C2UIHRWMC6LFZECYODWANQ74QX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moduli spaces of principal bundles on singular varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrian Langer","submitted_at":"2011-08-31T08:59:26Z","abstract_excerpt":"Let k be an algebraically closed field of characteristic zero. Let f:X-->S be a flat, projective morphism of k-schemes of finite type with integral geometric fibers. We prove existence of a projective relative moduli space for semistable singular principal bundles on the fibres of f. This generalizes the result of A. Schmitt who studied the case when X is a nodal curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6165","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":"2026-05-18T02:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aHJiy/4JcXkeOWSWhS3RM28dOYKnwpgfImZwPjX4rmDyAtp6z+/hifKSh/YcdwFsb1rwcXOcPV+uguQnkWTDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:29:30.578431Z"},"content_sha256":"ee275033503eeaf7b1a78f7a0361f9b332d9d45fb3e67856e3471b7bb204f9f5","schema_version":"1.0","event_id":"sha256:ee275033503eeaf7b1a78f7a0361f9b332d9d45fb3e67856e3471b7bb204f9f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C2UIHRWMC6LFZECYODWANQ74QX/bundle.json","state_url":"https://pith.science/pith/C2UIHRWMC6LFZECYODWANQ74QX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C2UIHRWMC6LFZECYODWANQ74QX/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":"2026-06-09T07:29:30Z","links":{"resolver":"https://pith.science/pith/C2UIHRWMC6LFZECYODWANQ74QX","bundle":"https://pith.science/pith/C2UIHRWMC6LFZECYODWANQ74QX/bundle.json","state":"https://pith.science/pith/C2UIHRWMC6LFZECYODWANQ74QX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C2UIHRWMC6LFZECYODWANQ74QX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C2UIHRWMC6LFZECYODWANQ74QX","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":"505cf37068e799235d9424880c1a0822c4560ef7c313a7e510d379013c9cf563","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-31T08:59:26Z","title_canon_sha256":"bd7a110d3025a3ce8b3e3e8b00a29b1a378144c4fd2eefef5d4da3877a5b7422"},"schema_version":"1.0","source":{"id":"1108.6165","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6165","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6165v2","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6165","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"C2UIHRWMC6LF","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C2UIHRWMC6LFZECY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C2UIHRWM","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:ee275033503eeaf7b1a78f7a0361f9b332d9d45fb3e67856e3471b7bb204f9f5","target":"graph","created_at":"2026-05-18T02:20:48Z","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 k be an algebraically closed field of characteristic zero. Let f:X-->S be a flat, projective morphism of k-schemes of finite type with integral geometric fibers. We prove existence of a projective relative moduli space for semistable singular principal bundles on the fibres of f. This generalizes the result of A. Schmitt who studied the case when X is a nodal curve.","authors_text":"Adrian Langer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-31T08:59:26Z","title":"Moduli spaces of principal bundles on singular varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6165","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:f2a970f515cb41c0d463dbb7a96ad2ba6bc1e9425236ce1d6eef113bffbe0e2c","target":"record","created_at":"2026-05-18T02:20:48Z","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":"505cf37068e799235d9424880c1a0822c4560ef7c313a7e510d379013c9cf563","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-31T08:59:26Z","title_canon_sha256":"bd7a110d3025a3ce8b3e3e8b00a29b1a378144c4fd2eefef5d4da3877a5b7422"},"schema_version":"1.0","source":{"id":"1108.6165","kind":"arxiv","version":2}},"canonical_sha256":"16a883c6cc17965c905870ec06c3fc85e83c41a0413a9f42eab561ae4cd6aa05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16a883c6cc17965c905870ec06c3fc85e83c41a0413a9f42eab561ae4cd6aa05","first_computed_at":"2026-05-18T02:20:48.126894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:48.126894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Uw77K7Frr5zXrSZHgib7KbVnx3R6TcDIk1WGyGc2lSmqqwQHfQUihyoyQJi8TWt0249ZRffwVz21euuJPFmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:48.127642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.6165","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2a970f515cb41c0d463dbb7a96ad2ba6bc1e9425236ce1d6eef113bffbe0e2c","sha256:ee275033503eeaf7b1a78f7a0361f9b332d9d45fb3e67856e3471b7bb204f9f5"],"state_sha256":"21d5b7522cb1c4f94ce7ac99acae041f26782266cfa4f3303f191afde5f49f92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHvlX4kgQHgqPO8Xwf7qCx+qpYgvFAb7Hc6IM4IDKE1MInk/jMqGFIMklD7qINFv0hzKmgZKB50sdPacHwiKBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:29:30.581245Z","bundle_sha256":"6e208dd049a76cc9a3b1966eee310fa13e512d1f5288e0e4a2c88f6761c4d22f"}}