{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:MFDK6NJMQI2NH4Q5FH5KQSQYKA","short_pith_number":"pith:MFDK6NJM","canonical_record":{"source":{"id":"hep-th/9605225","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1996-05-31T02:42:12Z","cross_cats_sorted":[],"title_canon_sha256":"abdcf8a0be77218c334965b12d134a1ba5db9d9dc71d074c18b058213c3a22a3","abstract_canon_sha256":"cb529b02e86d32fe2765083810d27adfcc919d729b3c9259d03a297f15068944"},"schema_version":"1.0"},"canonical_sha256":"6146af352c8234d3f21d29faa84a18500858bf5f00b1850058dbf38276a52d3e","source":{"kind":"arxiv","id":"hep-th/9605225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9605225","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9605225v1","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9605225","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"MFDK6NJMQI2N","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MFDK6NJMQI2NH4Q5","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MFDK6NJM","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:MFDK6NJMQI2NH4Q5FH5KQSQYKA","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9605225","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1996-05-31T02:42:12Z","cross_cats_sorted":[],"title_canon_sha256":"abdcf8a0be77218c334965b12d134a1ba5db9d9dc71d074c18b058213c3a22a3","abstract_canon_sha256":"cb529b02e86d32fe2765083810d27adfcc919d729b3c9259d03a297f15068944"},"schema_version":"1.0"},"canonical_sha256":"6146af352c8234d3f21d29faa84a18500858bf5f00b1850058dbf38276a52d3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:38.017055Z","signature_b64":"hDG0IwIq3BOA4jOPbd7wodQzFCKHAf0lB0ZPyM/+IVrwVCHjWAx0AkCCk0vROwRh/V/bwDN5XG3s07AL0/ZYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6146af352c8234d3f21d29faa84a18500858bf5f00b1850058dbf38276a52d3e","last_reissued_at":"2026-05-18T01:38:38.016628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:38.016628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9605225","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wLnmvfkJf8K4WGeKX9PFt0MBqAl1ZpaxEpq5uB/nI8CBLT3Fysl82vot/cfiezbRwhb4tFdNcip+iu44KViMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:51:23.267576Z"},"content_sha256":"f15e92621b853bf95e8227c49a8bf01bb62da4f7931a565cd553ccc89e4dc9a2","schema_version":"1.0","event_id":"sha256:f15e92621b853bf95e8227c49a8bf01bb62da4f7931a565cd553ccc89e4dc9a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:MFDK6NJMQI2NH4Q5FH5KQSQYKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational Quantum Cohomology","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Chuan-Sheng Xiong, Kentaro Hori, Tohru Eguchi","submitted_at":"1996-05-31T02:42:12Z","abstract_excerpt":"We discuss how the theory of quantum cohomology may be generalized to ``gravitational quantum cohomology'' by studying topological sigma models coupled to two-dimensional gravity. We first consider sigma models defined on a general Fano manifold $M$ (manifold with a positive first Chern class) and derive new recursion relations for its two point functions. We then derive bi-Hamiltonian structures of the theories and show that they are completely integrable at least at the level of genus $0$. We next consider the subspace of the phase space where only a marginal perturbation (with a parameter $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9605225","kind":"arxiv","version":1},"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":"2026-05-18T01:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/HFh65d8YdbaOl2/zGNO0En2/iit2cgOkaC9vET1pRPcxTx9GEhd6LybKLJAYdTEZCnlxzv92BelS/Ugc/lCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:51:23.267931Z"},"content_sha256":"d66c914c3543d7e43f70834bfade53551a1d635224e1de8823f3c0a147d4e26c","schema_version":"1.0","event_id":"sha256:d66c914c3543d7e43f70834bfade53551a1d635224e1de8823f3c0a147d4e26c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFDK6NJMQI2NH4Q5FH5KQSQYKA/bundle.json","state_url":"https://pith.science/pith/MFDK6NJMQI2NH4Q5FH5KQSQYKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFDK6NJMQI2NH4Q5FH5KQSQYKA/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":"2026-06-21T14:51:23Z","links":{"resolver":"https://pith.science/pith/MFDK6NJMQI2NH4Q5FH5KQSQYKA","bundle":"https://pith.science/pith/MFDK6NJMQI2NH4Q5FH5KQSQYKA/bundle.json","state":"https://pith.science/pith/MFDK6NJMQI2NH4Q5FH5KQSQYKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFDK6NJMQI2NH4Q5FH5KQSQYKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:MFDK6NJMQI2NH4Q5FH5KQSQYKA","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":"cb529b02e86d32fe2765083810d27adfcc919d729b3c9259d03a297f15068944","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1996-05-31T02:42:12Z","title_canon_sha256":"abdcf8a0be77218c334965b12d134a1ba5db9d9dc71d074c18b058213c3a22a3"},"schema_version":"1.0","source":{"id":"hep-th/9605225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9605225","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9605225v1","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9605225","created_at":"2026-05-18T01:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"MFDK6NJMQI2N","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MFDK6NJMQI2NH4Q5","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MFDK6NJM","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:d66c914c3543d7e43f70834bfade53551a1d635224e1de8823f3c0a147d4e26c","target":"graph","created_at":"2026-05-18T01:38:38Z","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 discuss how the theory of quantum cohomology may be generalized to ``gravitational quantum cohomology'' by studying topological sigma models coupled to two-dimensional gravity. We first consider sigma models defined on a general Fano manifold $M$ (manifold with a positive first Chern class) and derive new recursion relations for its two point functions. We then derive bi-Hamiltonian structures of the theories and show that they are completely integrable at least at the level of genus $0$. We next consider the subspace of the phase space where only a marginal perturbation (with a parameter $","authors_text":"Chuan-Sheng Xiong, Kentaro Hori, Tohru Eguchi","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1996-05-31T02:42:12Z","title":"Gravitational Quantum Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9605225","kind":"arxiv","version":1},"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:f15e92621b853bf95e8227c49a8bf01bb62da4f7931a565cd553ccc89e4dc9a2","target":"record","created_at":"2026-05-18T01:38:38Z","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":"cb529b02e86d32fe2765083810d27adfcc919d729b3c9259d03a297f15068944","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1996-05-31T02:42:12Z","title_canon_sha256":"abdcf8a0be77218c334965b12d134a1ba5db9d9dc71d074c18b058213c3a22a3"},"schema_version":"1.0","source":{"id":"hep-th/9605225","kind":"arxiv","version":1}},"canonical_sha256":"6146af352c8234d3f21d29faa84a18500858bf5f00b1850058dbf38276a52d3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6146af352c8234d3f21d29faa84a18500858bf5f00b1850058dbf38276a52d3e","first_computed_at":"2026-05-18T01:38:38.016628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:38.016628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hDG0IwIq3BOA4jOPbd7wodQzFCKHAf0lB0ZPyM/+IVrwVCHjWAx0AkCCk0vROwRh/V/bwDN5XG3s07AL0/ZYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:38.017055Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9605225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f15e92621b853bf95e8227c49a8bf01bb62da4f7931a565cd553ccc89e4dc9a2","sha256:d66c914c3543d7e43f70834bfade53551a1d635224e1de8823f3c0a147d4e26c"],"state_sha256":"11e70fdd05523d78ada73d7c775a7d80ccad6402e62b08a6ea891d4caf5ad1bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IKD7cNCmwNefDYnIZMv/4qZGF0v7QIw8Hatu5LfFD8B54SuOaITIz9YQcLmBgpn0qqPA1jJEyXT9x86vgPMqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:51:23.269942Z","bundle_sha256":"e1095aa61619a31c3fbea529318dd6f85938f07326911d1f7c0b96b96842f2ab"}}