{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3TBTA2AWD3BDYJ64CZVYTWO4UE","short_pith_number":"pith:3TBTA2AW","schema_version":"1.0","canonical_sha256":"dcc33068161ec23c27dc166b89d9dca116c07f6632b0cb554c37f792d8c69261","source":{"kind":"arxiv","id":"2604.05664","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2604.05664","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-04-07T10:05:56Z","cross_cats_sorted":[],"title_canon_sha256":"a13a66c0de07833a3f67d0111e83aae18f2d41ac0fa878ab567ac6434630926b","abstract_canon_sha256":"6aeb190aa81a8e70678a56986aa92f1ac68eb6eec580c260de5775c8a4228dbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:09:57.931112Z","signature_b64":"0SPIy13mHrHZxP/Ae56nB8RDipbVMkapBnk7g9M37qjbHy6UpBghykfJGYppw4GSfKbJPDSsKxzLH6/dCPqxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcc33068161ec23c27dc166b89d9dca116c07f6632b0cb554c37f792d8c69261","last_reissued_at":"2026-06-19T16:09:57.930645Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:09:57.930645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2604.05664","created_at":"2026-06-19T16:09:57.930702+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.05664v2","created_at":"2026-06-19T16:09:57.930702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.05664","created_at":"2026-06-19T16:09:57.930702+00:00"},{"alias_kind":"pith_short_12","alias_value":"3TBTA2AWD3BD","created_at":"2026-06-19T16:09:57.930702+00:00"},{"alias_kind":"pith_short_16","alias_value":"3TBTA2AWD3BDYJ64","created_at":"2026-06-19T16:09:57.930702+00:00"},{"alias_kind":"pith_short_8","alias_value":"3TBTA2AW","created_at":"2026-06-19T16:09:57.930702+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE","json":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE.json","graph_json":"https://pith.science/api/pith-number/3TBTA2AWD3BDYJ64CZVYTWO4UE/graph.json","events_json":"https://pith.science/api/pith-number/3TBTA2AWD3BDYJ64CZVYTWO4UE/events.json","paper":"https://pith.science/paper/3TBTA2AW"},"agent_actions":{"view_html":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE","download_json":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE.json","view_paper":"https://pith.science/paper/3TBTA2AW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.05664&json=true","fetch_graph":"https://pith.science/api/pith-number/3TBTA2AWD3BDYJ64CZVYTWO4UE/graph.json","fetch_events":"https://pith.science/api/pith-number/3TBTA2AWD3BDYJ64CZVYTWO4UE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE/action/storage_attestation","attest_author":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE/action/author_attestation","sign_citation":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE/action/citation_signature","submit_replication":"https://pith.science/pith/3TBTA2AWD3BDYJ64CZVYTWO4UE/action/replication_record"}},"created_at":"2026-06-19T16:09:57.930702+00:00","updated_at":"2026-06-19T16:09:57.930702+00:00"}