{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:US6CBDHZMCGCFQIESSVKN6X6E4","short_pith_number":"pith:US6CBDHZ","canonical_record":{"source":{"id":"0712.4021","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-12-24T20:18:06Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.SG"],"title_canon_sha256":"88fab655ce71100b2f2b026517f6736c37691f96a2e5a6fa89c6aa39810c8791","abstract_canon_sha256":"63e722e790198a8e3dd3ef7f2b5f33ade263fa186c10a519fb1317f433991815"},"schema_version":"1.0"},"canonical_sha256":"a4bc208cf9608c22c10494aaa6fafe2703f1a9cdac12922728b6e681e138f9a1","source":{"kind":"arxiv","id":"0712.4021","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4021","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4021v4","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4021","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"US6CBDHZMCGC","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"US6CBDHZMCGCFQIE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"US6CBDHZ","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:US6CBDHZMCGCFQIESSVKN6X6E4","target":"record","payload":{"canonical_record":{"source":{"id":"0712.4021","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-12-24T20:18:06Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.SG"],"title_canon_sha256":"88fab655ce71100b2f2b026517f6736c37691f96a2e5a6fa89c6aa39810c8791","abstract_canon_sha256":"63e722e790198a8e3dd3ef7f2b5f33ade263fa186c10a519fb1317f433991815"},"schema_version":"1.0"},"canonical_sha256":"a4bc208cf9608c22c10494aaa6fafe2703f1a9cdac12922728b6e681e138f9a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:09.425840Z","signature_b64":"9VR38tuhoTgkR2Hgx0CoGwgvEofpumlA0GF/5jQjuUjdwnk4Bd79DjV/XQAHcrrRgQ6g7UeV16Pb0cen3TsxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4bc208cf9608c22c10494aaa6fafe2703f1a9cdac12922728b6e681e138f9a1","last_reissued_at":"2026-05-18T03:50:09.425142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:09.425142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.4021","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":"2026-05-18T03:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06bC2LdkbLjyHnsOlRGZDY0ZEKeK09zAET+0E/slQ65K6AQ5kBqTtIR7oMhzZkKnnMe7J8vAx9H1k66pE979AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:53:03.087672Z"},"content_sha256":"1a5346f97c67327a7c5cea2abeff5e27a4cea0c29dfb4d72affb4c40390536a4","schema_version":"1.0","event_id":"sha256:1a5346f97c67327a7c5cea2abeff5e27a4cea0c29dfb4d72affb4c40390536a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:US6CBDHZMCGCFQIESSVKN6X6E4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Witten equation, mirror symmetry and quantum singularity theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.SG"],"primary_cat":"math.AG","authors_text":"Huijun Fan, Tyler J. Jarvis, Yongbin Ruan","submitted_at":"2007-12-24T20:18:06Z","abstract_excerpt":"For any non-degenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the singularity. This theory is analogous to Gromov-Witten theory and generalizes the theory of r-spin curves, which corresponds to the simple singularity A_{r-1}.\n  We also resolve two outstanding conjectures of Witten. The first conjecture is that ADE-singularities are self-dual; and the second conjecture is that the total potential functions of ADE-singularities satisfy corresponding ADE-integrable hierarchie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4021","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":"2026-05-18T03:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lemg8ZGjPkcDsR2nOE81gfXV+FGYdOl421pU+ieVDf5USZSsVbICKLmk5oCNRhld5uhHAD7ev8DMyiWXf6aBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:53:03.088313Z"},"content_sha256":"81214123fb5b971f8dbfef8e39ee732603e14abc896ce44c7422cdfb12497d8d","schema_version":"1.0","event_id":"sha256:81214123fb5b971f8dbfef8e39ee732603e14abc896ce44c7422cdfb12497d8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/US6CBDHZMCGCFQIESSVKN6X6E4/bundle.json","state_url":"https://pith.science/pith/US6CBDHZMCGCFQIESSVKN6X6E4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/US6CBDHZMCGCFQIESSVKN6X6E4/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":"2026-05-27T05:53:03Z","links":{"resolver":"https://pith.science/pith/US6CBDHZMCGCFQIESSVKN6X6E4","bundle":"https://pith.science/pith/US6CBDHZMCGCFQIESSVKN6X6E4/bundle.json","state":"https://pith.science/pith/US6CBDHZMCGCFQIESSVKN6X6E4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/US6CBDHZMCGCFQIESSVKN6X6E4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:US6CBDHZMCGCFQIESSVKN6X6E4","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":"63e722e790198a8e3dd3ef7f2b5f33ade263fa186c10a519fb1317f433991815","cross_cats_sorted":["hep-th","math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-12-24T20:18:06Z","title_canon_sha256":"88fab655ce71100b2f2b026517f6736c37691f96a2e5a6fa89c6aa39810c8791"},"schema_version":"1.0","source":{"id":"0712.4021","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4021","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4021v4","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4021","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"US6CBDHZMCGC","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"US6CBDHZMCGCFQIE","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"US6CBDHZ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:81214123fb5b971f8dbfef8e39ee732603e14abc896ce44c7422cdfb12497d8d","target":"graph","created_at":"2026-05-18T03:50:09Z","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":"For any non-degenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the singularity. This theory is analogous to Gromov-Witten theory and generalizes the theory of r-spin curves, which corresponds to the simple singularity A_{r-1}.\n  We also resolve two outstanding conjectures of Witten. The first conjecture is that ADE-singularities are self-dual; and the second conjecture is that the total potential functions of ADE-singularities satisfy corresponding ADE-integrable hierarchie","authors_text":"Huijun Fan, Tyler J. Jarvis, Yongbin Ruan","cross_cats":["hep-th","math-ph","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-12-24T20:18:06Z","title":"The Witten equation, mirror symmetry and quantum singularity theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4021","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":"sha256:1a5346f97c67327a7c5cea2abeff5e27a4cea0c29dfb4d72affb4c40390536a4","target":"record","created_at":"2026-05-18T03:50:09Z","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":"63e722e790198a8e3dd3ef7f2b5f33ade263fa186c10a519fb1317f433991815","cross_cats_sorted":["hep-th","math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-12-24T20:18:06Z","title_canon_sha256":"88fab655ce71100b2f2b026517f6736c37691f96a2e5a6fa89c6aa39810c8791"},"schema_version":"1.0","source":{"id":"0712.4021","kind":"arxiv","version":4}},"canonical_sha256":"a4bc208cf9608c22c10494aaa6fafe2703f1a9cdac12922728b6e681e138f9a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4bc208cf9608c22c10494aaa6fafe2703f1a9cdac12922728b6e681e138f9a1","first_computed_at":"2026-05-18T03:50:09.425142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:09.425142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9VR38tuhoTgkR2Hgx0CoGwgvEofpumlA0GF/5jQjuUjdwnk4Bd79DjV/XQAHcrrRgQ6g7UeV16Pb0cen3TsxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:09.425840Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.4021","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a5346f97c67327a7c5cea2abeff5e27a4cea0c29dfb4d72affb4c40390536a4","sha256:81214123fb5b971f8dbfef8e39ee732603e14abc896ce44c7422cdfb12497d8d"],"state_sha256":"3c6e63f91fefd7efb60eb8ca092b92e2518e703c910c2f2ec442a629fe8aad82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mA/whu5bEgrZTxDdQTRzbq0DEfGRyZnj1SumQovJOZiCD7IBTj82cYqNaJthZ4xq8OpWthATXtbyhwo0kL+yCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:53:03.091911Z","bundle_sha256":"e2c35e7837ccdcddc734099c898c511a0c43f92210d1454ed70ccb34f03e6005"}}