{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4THOHKMNEN4SDBJPH44BZ44MVG","short_pith_number":"pith:4THOHKMN","canonical_record":{"source":{"id":"1408.5864","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T19:00:16Z","cross_cats_sorted":[],"title_canon_sha256":"35a71cf4c5f4efcb37c9b48302f0da438d85b443c9635c1160939e631fe043a2","abstract_canon_sha256":"7773f620a41c938277461e5ef9f98eed104926cc1e16f96cadbf0a4efc782866"},"schema_version":"1.0"},"canonical_sha256":"e4cee3a98d237921852f3f381cf38ca9af2cd54dc2070bc96d6ffcefbf6dcf05","source":{"kind":"arxiv","id":"1408.5864","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5864","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5864v4","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5864","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"4THOHKMNEN4S","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4THOHKMNEN4SDBJP","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4THOHKMN","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4THOHKMNEN4SDBJPH44BZ44MVG","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5864","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T19:00:16Z","cross_cats_sorted":[],"title_canon_sha256":"35a71cf4c5f4efcb37c9b48302f0da438d85b443c9635c1160939e631fe043a2","abstract_canon_sha256":"7773f620a41c938277461e5ef9f98eed104926cc1e16f96cadbf0a4efc782866"},"schema_version":"1.0"},"canonical_sha256":"e4cee3a98d237921852f3f381cf38ca9af2cd54dc2070bc96d6ffcefbf6dcf05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:18.159968Z","signature_b64":"KsfUc7Y48Qonp0NDCY1X2BKTqqbfRQKZc34gk16nKNz9Zp4KoF0kdpBFFyXduDA7mUzsbY/2KwOcEqjnhsVnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4cee3a98d237921852f3f381cf38ca9af2cd54dc2070bc96d6ffcefbf6dcf05","last_reissued_at":"2026-05-18T00:44:18.159299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:18.159299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5864","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jnSEnOq+ZwrLizglkUJfGX+qOIGOtZKrBMBzKzWkOOA8JHL6P2TRdQb1Ry13vYyNmea0QLWqSiYuxES59AAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:15:01.412447Z"},"content_sha256":"19f80a6c4f4f6a5e95dadc8579fe92d918a817e56dfc7f4981fb01dd0de9ead5","schema_version":"1.0","event_id":"sha256:19f80a6c4f4f6a5e95dadc8579fe92d918a817e56dfc7f4981fb01dd0de9ead5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4THOHKMNEN4SDBJPH44BZ44MVG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Kirwan morphism and Gromov-Witten invariants of quotients II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chris T. Woodward","submitted_at":"2014-08-25T19:00:16Z","abstract_excerpt":"This is the second in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology of a smooth polarized complex projective variety with the action of a connected complex reductive group to the orbifold quantum cohomology of its geometric invariant theory quotient, and prove that it intertwines the genus zero gauged Gromov-Witten potential with the genus zero Gromov-Witten graph potential. In this part we construct virtual fundamental classes on the moduli spaces used in the construction of the quantum Kirwan map and the gauged Gromov-W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5864","kind":"arxiv","version":4},"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":"2026-05-18T00:44:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aYRaYzGCj5DtzgQs/AEQ92ke4gBxpXll6hq2xaOOmqz6DtjzxPqJwhLzlfOz7nLFi1xv10hnnCfUMmpjyNWLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:15:01.412805Z"},"content_sha256":"3ef0df5e19f948524fe2c50a48d5c3b49da6e4ec7c70600def0289a95259f5db","schema_version":"1.0","event_id":"sha256:3ef0df5e19f948524fe2c50a48d5c3b49da6e4ec7c70600def0289a95259f5db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4THOHKMNEN4SDBJPH44BZ44MVG/bundle.json","state_url":"https://pith.science/pith/4THOHKMNEN4SDBJPH44BZ44MVG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4THOHKMNEN4SDBJPH44BZ44MVG/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":"2026-05-30T06:15:01Z","links":{"resolver":"https://pith.science/pith/4THOHKMNEN4SDBJPH44BZ44MVG","bundle":"https://pith.science/pith/4THOHKMNEN4SDBJPH44BZ44MVG/bundle.json","state":"https://pith.science/pith/4THOHKMNEN4SDBJPH44BZ44MVG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4THOHKMNEN4SDBJPH44BZ44MVG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4THOHKMNEN4SDBJPH44BZ44MVG","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":"7773f620a41c938277461e5ef9f98eed104926cc1e16f96cadbf0a4efc782866","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T19:00:16Z","title_canon_sha256":"35a71cf4c5f4efcb37c9b48302f0da438d85b443c9635c1160939e631fe043a2"},"schema_version":"1.0","source":{"id":"1408.5864","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5864","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5864v4","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5864","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"4THOHKMNEN4S","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4THOHKMNEN4SDBJP","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4THOHKMN","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:3ef0df5e19f948524fe2c50a48d5c3b49da6e4ec7c70600def0289a95259f5db","target":"graph","created_at":"2026-05-18T00:44:18Z","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":"This is the second in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology of a smooth polarized complex projective variety with the action of a connected complex reductive group to the orbifold quantum cohomology of its geometric invariant theory quotient, and prove that it intertwines the genus zero gauged Gromov-Witten potential with the genus zero Gromov-Witten graph potential. In this part we construct virtual fundamental classes on the moduli spaces used in the construction of the quantum Kirwan map and the gauged Gromov-W","authors_text":"Chris T. Woodward","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T19:00:16Z","title":"Quantum Kirwan morphism and Gromov-Witten invariants of quotients II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5864","kind":"arxiv","version":4},"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":"sha256:19f80a6c4f4f6a5e95dadc8579fe92d918a817e56dfc7f4981fb01dd0de9ead5","target":"record","created_at":"2026-05-18T00:44:18Z","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":"7773f620a41c938277461e5ef9f98eed104926cc1e16f96cadbf0a4efc782866","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-25T19:00:16Z","title_canon_sha256":"35a71cf4c5f4efcb37c9b48302f0da438d85b443c9635c1160939e631fe043a2"},"schema_version":"1.0","source":{"id":"1408.5864","kind":"arxiv","version":4}},"canonical_sha256":"e4cee3a98d237921852f3f381cf38ca9af2cd54dc2070bc96d6ffcefbf6dcf05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4cee3a98d237921852f3f381cf38ca9af2cd54dc2070bc96d6ffcefbf6dcf05","first_computed_at":"2026-05-18T00:44:18.159299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:18.159299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KsfUc7Y48Qonp0NDCY1X2BKTqqbfRQKZc34gk16nKNz9Zp4KoF0kdpBFFyXduDA7mUzsbY/2KwOcEqjnhsVnDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:18.159968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5864","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19f80a6c4f4f6a5e95dadc8579fe92d918a817e56dfc7f4981fb01dd0de9ead5","sha256:3ef0df5e19f948524fe2c50a48d5c3b49da6e4ec7c70600def0289a95259f5db"],"state_sha256":"5748895760fd6b581631abfb61426796996c2aa03a75750ffefea8539a4601cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lTQQnGUnx+inJrx6NCI7ns9CkY6OZ36+cSIvWMK81THpd7+Om6neR2V8TZggSvrAVloZsrQqNaSmdRyW5HFOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:15:01.415935Z","bundle_sha256":"25c88d393be635409f9c3bf10e8e46d2eace36831a2d21d8b033612f2cde4bb8"}}