{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VUJW4MBPCOESYN3EHCVAFTBXTA","short_pith_number":"pith:VUJW4MBP","canonical_record":{"source":{"id":"0905.4047","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-05-25T16:34:06Z","cross_cats_sorted":[],"title_canon_sha256":"d004094b52f45ad4a46dc9bf6e534a3b16c85947fab833c9f61fad9fd054df8c","abstract_canon_sha256":"3d479d6343d613edc4b7ece403939b86c75ed05dbfa68a8b5e759383f184a02d"},"schema_version":"1.0"},"canonical_sha256":"ad136e302f13892c376438aa02cc379827f6c9e6cfb73d96ce52326291635c9a","source":{"kind":"arxiv","id":"0905.4047","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4047","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4047v2","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4047","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"pith_short_12","alias_value":"VUJW4MBPCOES","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VUJW4MBPCOESYN3E","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VUJW4MBP","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VUJW4MBPCOESYN3EHCVAFTBXTA","target":"record","payload":{"canonical_record":{"source":{"id":"0905.4047","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-05-25T16:34:06Z","cross_cats_sorted":[],"title_canon_sha256":"d004094b52f45ad4a46dc9bf6e534a3b16c85947fab833c9f61fad9fd054df8c","abstract_canon_sha256":"3d479d6343d613edc4b7ece403939b86c75ed05dbfa68a8b5e759383f184a02d"},"schema_version":"1.0"},"canonical_sha256":"ad136e302f13892c376438aa02cc379827f6c9e6cfb73d96ce52326291635c9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:36.620665Z","signature_b64":"ZHPiXQ5qoI0VB6hg9wM3C07Mi8d6v2tMkZ8Yn/kDPwc3J5L6ZR+NAD/PppFq1zfWIdffT/wI5q7znVCVQypXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad136e302f13892c376438aa02cc379827f6c9e6cfb73d96ce52326291635c9a","last_reissued_at":"2026-05-18T03:44:36.619900Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:36.619900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.4047","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":"2026-05-18T03:44:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvMisG7bmZ/pV9BDd/TpPaEn0dXgp0EvfrQb0uk54pC7V4DVBMWi7jUVie2cQQROorSLk+1wW04NpCyf5m1kCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:54:05.067301Z"},"content_sha256":"4cd235d469856e08fec8d1ff326e981dbe924829ca3e835ef3e03c4bd5224e27","schema_version":"1.0","event_id":"sha256:4cd235d469856e08fec8d1ff326e981dbe924829ca3e835ef3e03c4bd5224e27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VUJW4MBPCOESYN3EHCVAFTBXTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Quantum Kirwan Map, I: Fredholm Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Fabian Ziltener","submitted_at":"2009-05-25T16:34:06Z","abstract_excerpt":"Consider a Hamiltonian action of a compact connected Lie group $G$ on an aspherical symplectic manifold $(M,\\omega)$. Under some assumptions on $(M,\\omega)$ and the action, D. A. Salamon conjectured that counting gauge equivalence classes of symplectic vortices on the plane $R^2$ gives rise to a quantum deformation $Q\\kappa_G$ of the Kirwan map. This article is the first of three, whose goal is to define $Q\\kappa_G$ rigorously. Its main result is that the vertical differential of the vortex equations over $R^2$ (at the level of gauge equivalence) is a Fredholm operator of a specified index. Po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4047","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":"2026-05-18T03:44:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9k0vNiYgbtBYcBTCO/qjFtxrCgv2OLChpyRtVymfg8/cvfOXdDVljODlFt8/HlfoHgRPy5PjdJaGsZJf8n9tCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:54:05.067965Z"},"content_sha256":"b064ab2e45af3894c39d41b624e8f4c15c1a26b1d95d8e9fb13973d53389f9e8","schema_version":"1.0","event_id":"sha256:b064ab2e45af3894c39d41b624e8f4c15c1a26b1d95d8e9fb13973d53389f9e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VUJW4MBPCOESYN3EHCVAFTBXTA/bundle.json","state_url":"https://pith.science/pith/VUJW4MBPCOESYN3EHCVAFTBXTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VUJW4MBPCOESYN3EHCVAFTBXTA/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":"2026-05-28T22:54:05Z","links":{"resolver":"https://pith.science/pith/VUJW4MBPCOESYN3EHCVAFTBXTA","bundle":"https://pith.science/pith/VUJW4MBPCOESYN3EHCVAFTBXTA/bundle.json","state":"https://pith.science/pith/VUJW4MBPCOESYN3EHCVAFTBXTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VUJW4MBPCOESYN3EHCVAFTBXTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VUJW4MBPCOESYN3EHCVAFTBXTA","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":"3d479d6343d613edc4b7ece403939b86c75ed05dbfa68a8b5e759383f184a02d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-05-25T16:34:06Z","title_canon_sha256":"d004094b52f45ad4a46dc9bf6e534a3b16c85947fab833c9f61fad9fd054df8c"},"schema_version":"1.0","source":{"id":"0905.4047","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4047","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4047v2","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4047","created_at":"2026-05-18T03:44:36Z"},{"alias_kind":"pith_short_12","alias_value":"VUJW4MBPCOES","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VUJW4MBPCOESYN3E","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VUJW4MBP","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:b064ab2e45af3894c39d41b624e8f4c15c1a26b1d95d8e9fb13973d53389f9e8","target":"graph","created_at":"2026-05-18T03:44:36Z","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":"Consider a Hamiltonian action of a compact connected Lie group $G$ on an aspherical symplectic manifold $(M,\\omega)$. Under some assumptions on $(M,\\omega)$ and the action, D. A. Salamon conjectured that counting gauge equivalence classes of symplectic vortices on the plane $R^2$ gives rise to a quantum deformation $Q\\kappa_G$ of the Kirwan map. This article is the first of three, whose goal is to define $Q\\kappa_G$ rigorously. Its main result is that the vertical differential of the vortex equations over $R^2$ (at the level of gauge equivalence) is a Fredholm operator of a specified index. Po","authors_text":"Fabian Ziltener","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-05-25T16:34:06Z","title":"A Quantum Kirwan Map, I: Fredholm Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4047","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":"sha256:4cd235d469856e08fec8d1ff326e981dbe924829ca3e835ef3e03c4bd5224e27","target":"record","created_at":"2026-05-18T03:44:36Z","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":"3d479d6343d613edc4b7ece403939b86c75ed05dbfa68a8b5e759383f184a02d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2009-05-25T16:34:06Z","title_canon_sha256":"d004094b52f45ad4a46dc9bf6e534a3b16c85947fab833c9f61fad9fd054df8c"},"schema_version":"1.0","source":{"id":"0905.4047","kind":"arxiv","version":2}},"canonical_sha256":"ad136e302f13892c376438aa02cc379827f6c9e6cfb73d96ce52326291635c9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad136e302f13892c376438aa02cc379827f6c9e6cfb73d96ce52326291635c9a","first_computed_at":"2026-05-18T03:44:36.619900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:36.619900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZHPiXQ5qoI0VB6hg9wM3C07Mi8d6v2tMkZ8Yn/kDPwc3J5L6ZR+NAD/PppFq1zfWIdffT/wI5q7znVCVQypXBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:36.620665Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4047","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cd235d469856e08fec8d1ff326e981dbe924829ca3e835ef3e03c4bd5224e27","sha256:b064ab2e45af3894c39d41b624e8f4c15c1a26b1d95d8e9fb13973d53389f9e8"],"state_sha256":"f9fb21b37a81a251e098dac895b545440fad1e72e8cbf775dd7017b215db8a0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NoomzWwk1kQh+6y6kgcRevuxCNAD3UdpOuBJqRWl9A5TN2xyqY05BLptijLQ8Bd6HvEVEVtEbYcvir1R/N9hBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:54:05.071379Z","bundle_sha256":"43e6fc9f1b12716d1a541be735762407f9b1f09b787ca251cbe1611c93062689"}}