{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:76W7IK5Y3JSBESOJOSJOKFDXHG","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":"38d8b4c536c14064a3e8abeac72f3cfa8b15abf2b7f5e4b250bfc9ea44166535","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-07-31T04:11:58Z","title_canon_sha256":"8c8f78df85c8916e8368d34fd78c54697da5a176d13454946b067fce610fdd4d"},"schema_version":"1.0","source":{"id":"0707.4528","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.4528","created_at":"2026-05-18T04:40:20Z"},{"alias_kind":"arxiv_version","alias_value":"0707.4528v2","created_at":"2026-05-18T04:40:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.4528","created_at":"2026-05-18T04:40:20Z"},{"alias_kind":"pith_short_12","alias_value":"76W7IK5Y3JSB","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"76W7IK5Y3JSBESOJ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"76W7IK5Y","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:6c04e597e79a15c01fa5e8561b5cce12217819469b11dbd46219fe70c9e3dea4","target":"graph","created_at":"2026-05-18T04:40:20Z","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":"Given a holomorphic vector bundle $\\cale$ on a connected compact complex manifold X, [FLS] construct a $\\compl$-linear functional $I_{\\cale}$ on $\\hh{2n}{\\compl}$. This is done by constructing a linear functional on the 0-th completed Hochschild homology $\\choch{0}{(\\dif(\\cale))}$ of the sheaf of holomorphic differential operators on $\\cale$ using topological quantum mechanics. They show that this functional is $\\int_X$ if $\\cale$ has non zero Euler characteristic. They conjecture that this functional is $\\int_X$ for all $\\cale$.\n  A subsequent work [Ram] by the author proved that the linear f","authors_text":"Ajay C. Ramadoss","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-07-31T04:11:58Z","title":"Integration over complex manifolds via Hochschild homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.4528","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:b549f24549cb286691879d8c6f87e142ac74246ca76168b43b0a9e108093e00a","target":"record","created_at":"2026-05-18T04:40:20Z","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":"38d8b4c536c14064a3e8abeac72f3cfa8b15abf2b7f5e4b250bfc9ea44166535","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-07-31T04:11:58Z","title_canon_sha256":"8c8f78df85c8916e8368d34fd78c54697da5a176d13454946b067fce610fdd4d"},"schema_version":"1.0","source":{"id":"0707.4528","kind":"arxiv","version":2}},"canonical_sha256":"ffadf42bb8da641249c97492e5147739adf5e1713fc99577143f9235d16536ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffadf42bb8da641249c97492e5147739adf5e1713fc99577143f9235d16536ad","first_computed_at":"2026-05-18T04:40:20.884011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:20.884011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lXAgnLu6NmEr4DLWPpUAZuZOLvLfLlN6vNzAsu6TWVVc1eKJr1ic8q3NV9Xvvetvf0nyeGYs58M8ZFecGLNPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:20.884502Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.4528","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b549f24549cb286691879d8c6f87e142ac74246ca76168b43b0a9e108093e00a","sha256:6c04e597e79a15c01fa5e8561b5cce12217819469b11dbd46219fe70c9e3dea4"],"state_sha256":"d4f98fabf3052d7f1b842b5f8645fd73c5dd5b7b8958511a684db12863a42367"}