{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QPG35UDMMYVYFKRQSYULP3EUAH","short_pith_number":"pith:QPG35UDM","canonical_record":{"source":{"id":"1503.00319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-01T18:09:39Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4da421b0fcb4ab48cef9a38cc9c7355d1ad26c043775b60183cbc9e4e22269c5","abstract_canon_sha256":"ed6dc2a1bcc9d742a051dc63fdfa3a3b769ffc397dded35f7c37664a789c9227"},"schema_version":"1.0"},"canonical_sha256":"83cdbed06c662b82aa309628b7ec9401fefe8d38c7c1e42ae6603915310a7921","source":{"kind":"arxiv","id":"1503.00319","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00319","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00319v2","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00319","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"pith_short_12","alias_value":"QPG35UDMMYVY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QPG35UDMMYVYFKRQ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QPG35UDM","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QPG35UDMMYVYFKRQSYULP3EUAH","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-01T18:09:39Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4da421b0fcb4ab48cef9a38cc9c7355d1ad26c043775b60183cbc9e4e22269c5","abstract_canon_sha256":"ed6dc2a1bcc9d742a051dc63fdfa3a3b769ffc397dded35f7c37664a789c9227"},"schema_version":"1.0"},"canonical_sha256":"83cdbed06c662b82aa309628b7ec9401fefe8d38c7c1e42ae6603915310a7921","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:10.044476Z","signature_b64":"mk8HasXzGdfKccgnrjsJxlZj/x4AUiUnCVbbDHGKg8ts5dOzzqrWFvtXKPjbEqJo0xiU9hsg4T3h92zGiDh/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83cdbed06c662b82aa309628b7ec9401fefe8d38c7c1e42ae6603915310a7921","last_reissued_at":"2026-05-18T00:18:10.043863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:10.043863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00319","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":"2026-05-18T00:18:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bU5WzcWU0mlfnH+7eA159zInsNZtxoOtzZow/twqN30MW3wkgtmtUiwQXlS8IkDKwfdmOu9r0wULB9nxy0EgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:18:29.283040Z"},"content_sha256":"2a73a296c14543bc2f11cea7e9ac7aca931cf34921de90d2215bdb06b78b0601","schema_version":"1.0","event_id":"sha256:2a73a296c14543bc2f11cea7e9ac7aca931cf34921de90d2215bdb06b78b0601"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QPG35UDMMYVYFKRQSYULP3EUAH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moduli of vector bundles on higher-dimensional base manifolds - Construction and Variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Daniel Greb, Julius Ross, Matei Toma","submitted_at":"2015-03-01T18:09:39Z","abstract_excerpt":"We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson-Uhlenbeck compactification and explain how to use moduli spaces of quiver representations to show that Gieseker-Maruyama moduli spaces with respect to two different chosen polarisations are related via Thaddeus-flips through other \"multi-Gieseker\"-moduli spaces of sheaves. Moreover, as a new result, we show the existence of a natural morphism from a multi-Gieseker moduli space to the corresponding D"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00319","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":"2026-05-18T00:18:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ovkM/wqGf6QbK8rWkmQywQlGo1GECDURWwq9je6SZEOxRpC3gqQ7CFKlP/6+NO+DTMI77+sP4kFzOEo0EzQnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:18:29.283401Z"},"content_sha256":"dcac96ff6ff37ef4e991a291e1af7cf117adf9b46da4859b32a4a59679555ea4","schema_version":"1.0","event_id":"sha256:dcac96ff6ff37ef4e991a291e1af7cf117adf9b46da4859b32a4a59679555ea4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPG35UDMMYVYFKRQSYULP3EUAH/bundle.json","state_url":"https://pith.science/pith/QPG35UDMMYVYFKRQSYULP3EUAH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPG35UDMMYVYFKRQSYULP3EUAH/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":"2026-06-03T21:18:29Z","links":{"resolver":"https://pith.science/pith/QPG35UDMMYVYFKRQSYULP3EUAH","bundle":"https://pith.science/pith/QPG35UDMMYVYFKRQSYULP3EUAH/bundle.json","state":"https://pith.science/pith/QPG35UDMMYVYFKRQSYULP3EUAH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPG35UDMMYVYFKRQSYULP3EUAH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QPG35UDMMYVYFKRQSYULP3EUAH","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":"ed6dc2a1bcc9d742a051dc63fdfa3a3b769ffc397dded35f7c37664a789c9227","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-01T18:09:39Z","title_canon_sha256":"4da421b0fcb4ab48cef9a38cc9c7355d1ad26c043775b60183cbc9e4e22269c5"},"schema_version":"1.0","source":{"id":"1503.00319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00319","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00319v2","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00319","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"pith_short_12","alias_value":"QPG35UDMMYVY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QPG35UDMMYVYFKRQ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QPG35UDM","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:dcac96ff6ff37ef4e991a291e1af7cf117adf9b46da4859b32a4a59679555ea4","target":"graph","created_at":"2026-05-18T00:18:10Z","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":"We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson-Uhlenbeck compactification and explain how to use moduli spaces of quiver representations to show that Gieseker-Maruyama moduli spaces with respect to two different chosen polarisations are related via Thaddeus-flips through other \"multi-Gieseker\"-moduli spaces of sheaves. Moreover, as a new result, we show the existence of a natural morphism from a multi-Gieseker moduli space to the corresponding D","authors_text":"Daniel Greb, Julius Ross, Matei Toma","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-01T18:09:39Z","title":"Moduli of vector bundles on higher-dimensional base manifolds - Construction and Variation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00319","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":"sha256:2a73a296c14543bc2f11cea7e9ac7aca931cf34921de90d2215bdb06b78b0601","target":"record","created_at":"2026-05-18T00:18:10Z","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":"ed6dc2a1bcc9d742a051dc63fdfa3a3b769ffc397dded35f7c37664a789c9227","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-01T18:09:39Z","title_canon_sha256":"4da421b0fcb4ab48cef9a38cc9c7355d1ad26c043775b60183cbc9e4e22269c5"},"schema_version":"1.0","source":{"id":"1503.00319","kind":"arxiv","version":2}},"canonical_sha256":"83cdbed06c662b82aa309628b7ec9401fefe8d38c7c1e42ae6603915310a7921","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83cdbed06c662b82aa309628b7ec9401fefe8d38c7c1e42ae6603915310a7921","first_computed_at":"2026-05-18T00:18:10.043863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:10.043863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mk8HasXzGdfKccgnrjsJxlZj/x4AUiUnCVbbDHGKg8ts5dOzzqrWFvtXKPjbEqJo0xiU9hsg4T3h92zGiDh/Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:10.044476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a73a296c14543bc2f11cea7e9ac7aca931cf34921de90d2215bdb06b78b0601","sha256:dcac96ff6ff37ef4e991a291e1af7cf117adf9b46da4859b32a4a59679555ea4"],"state_sha256":"7cbb0033331a20a4ed1787c3ccd462608ca383fe0c3dcf09842beb7c283ea6a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xRjTn63+GD9YFXhhhoW4SrGal8bf1Jaue54E2Mvm8i/dLRYlB4eMchozHhhVHln5mMbdIHSAHtVTAocmpOACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:18:29.285388Z","bundle_sha256":"bdde4487d488ba8224943ed59798a8d376c8b8db5fddb53d954d1a34284a2b5a"}}