{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:D72JIJFDHSEXZ46XN6YG3NH7AS","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":"9ecb1ffcb0d723258d589addd605c779a85fa54acd17e70c0769ebbea1b65d24","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-07-16T16:07:13Z","title_canon_sha256":"821724e4d900701f927939544cedcbf36f1ba3a84d24b3cba344bb78eb7ad401"},"schema_version":"1.0","source":{"id":"0707.2348","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.2348","created_at":"2026-07-05T00:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"0707.2348v5","created_at":"2026-07-05T00:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.2348","created_at":"2026-07-05T00:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"D72JIJFDHSEX","created_at":"2026-07-05T00:23:45Z"},{"alias_kind":"pith_short_16","alias_value":"D72JIJFDHSEXZ46X","created_at":"2026-07-05T00:23:45Z"},{"alias_kind":"pith_short_8","alias_value":"D72JIJFD","created_at":"2026-07-05T00:23:45Z"}],"graph_snapshots":[{"event_id":"sha256:60a9b12fea036191fbb27a266e0e4d741077020db64555b12a8d51be00988cbc","target":"graph","created_at":"2026-07-05T00:23:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0707.2348/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\\subset X$ is an embedded curve and $D\\subset C$ is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of $X$. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of $X$. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing formula in the derived category.\n  Several calculations of the new invariants","authors_text":"R. Pandharipande, R. P. Thomas","cross_cats":["hep-th","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-07-16T16:07:13Z","title":"Curve counting via stable pairs in the derived category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2348","kind":"arxiv","version":5},"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:d625da523f056e7cbd91214315f93cd4ed1f093775501a27e69927c122faeebc","target":"record","created_at":"2026-07-05T00:23:45Z","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":"9ecb1ffcb0d723258d589addd605c779a85fa54acd17e70c0769ebbea1b65d24","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-07-16T16:07:13Z","title_canon_sha256":"821724e4d900701f927939544cedcbf36f1ba3a84d24b3cba344bb78eb7ad401"},"schema_version":"1.0","source":{"id":"0707.2348","kind":"arxiv","version":5}},"canonical_sha256":"1ff49424a33c897cf3d76fb06db4ff04bcd9f9b18c1729c85154d7d4de3fb3fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ff49424a33c897cf3d76fb06db4ff04bcd9f9b18c1729c85154d7d4de3fb3fc","first_computed_at":"2026-07-05T00:23:45.898550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:23:45.898550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bBufptuhob6fytDN5Y9zynGw8w6H6CtivhD1mBoLajY010MsHNnNGEe1LoQvGbGOMBeuxnIS8UNChmtJ99IRAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:23:45.899110Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.2348","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d625da523f056e7cbd91214315f93cd4ed1f093775501a27e69927c122faeebc","sha256:60a9b12fea036191fbb27a266e0e4d741077020db64555b12a8d51be00988cbc"],"state_sha256":"59c06dcb49264fdd7f08246f2aa153a6517d1c8c53a6aeb3fec807ae127a8fdf"}