{"paper":{"title":"The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Pandharipande-Thomas invariants have rational generating functions for superpositive curve classes on 3-manifolds","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dominic Joyce, Reginald Anderson","submitted_at":"2026-04-07T10:05:56Z","abstract_excerpt":"Let $X$ be a projective complex 3-manifold. An effective curve class $\\beta\\in H_2(X,\\mathbb Z)$ is called positive if $c_1(X)\\cdot\\beta>0$, and superpositive if all the effective summands of $\\beta$ are positive. If $X$ is Fano then all curve classes are superpositive. In arXiv:2111.04694 the second author developed a theory of enumerative invariants in abelian categories and wall-crossing formulae. We use this theory to prove conjectures by Pandharipande and Thomas on the rationality and poles of generating functions of Pandharipande-Thomas invariants of $X$ with descendent insertions, for s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We use this theory to prove conjectures by Pandharipande and Thomas on the rationality and poles of generating functions of Pandharipande-Thomas invariants of X with descendent insertions, for superpositive curve classes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the enumerative invariants and wall-crossing formulae developed in arXiv:2111.04694 apply without additional obstructions to the superpositive curve classes on any projective complex 3-manifold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Pandharipande-Thomas invariants have rational generating functions for superpositive curve classes on 3-manifolds","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8ed6187d81a5309a2a0cd3f8ce87117df56cef32f544afcfe3f9dd79e622d09f"},"source":{"id":"2604.05664","kind":"arxiv","version":2},"verdict":{"id":"2995c114-1a23-4f3d-ab35-60db5bc1d07e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T19:13:50.369019Z","strongest_claim":"We use this theory to prove conjectures by Pandharipande and Thomas on the rationality and poles of generating functions of Pandharipande-Thomas invariants of X with descendent insertions, for superpositive curve classes.","one_line_summary":"Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the enumerative invariants and wall-crossing formulae developed in arXiv:2111.04694 apply without additional obstructions to the superpositive curve classes on any projective complex 3-manifold.","pith_extraction_headline":"Pandharipande-Thomas invariants have rational generating functions for superpositive curve classes on 3-manifolds"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.05664/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a1a923bd5211b2a42a967a2b90eace547f23b849af173035f4dac1cb56b6a58e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}