{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WTBYEI5HH2X6JFORR2ACU2QILT","short_pith_number":"pith:WTBYEI5H","schema_version":"1.0","canonical_sha256":"b4c38223a73eafe495d18e802a6a085cd6123a1704f8cc0c71c4500b94a4eccf","source":{"kind":"arxiv","id":"1710.11158","version":4},"attestation_state":"computed","paper":{"title":"Relative quasimaps and mirror formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Battistella, Navid Nabijou","submitted_at":"2017-10-30T18:10:57Z","abstract_excerpt":"We construct and study the theory of relative quasimaps in genus zero, in the spirit of Gathmann. When $X$ is a smooth toric variety and $Y$ is a smooth very ample hypersurface in $X$, we produce a virtual class on the moduli space of relative quasimaps to $(X,Y)$, which we use to define relative quasimap invariants. We obtain a recursion formula which expresses each relative invariant in terms of invariants of lower tangency, and apply this formula to derive a quantum Lefschetz theorem for quasimaps, expressing the restricted quasimap invariants of $Y$ in terms of those of $X$. Finally, we sh"},"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":false},"canonical_record":{"source":{"id":"1710.11158","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-30T18:10:57Z","cross_cats_sorted":[],"title_canon_sha256":"1311f6dd4970bbe24449c994daa14b2f385681046f3f4a3196db889501e23fe1","abstract_canon_sha256":"fdcfa3186c66f8f5607754a00c05c74547b23b287c40cf5b88fe134a805fa5e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:44:30.351246Z","signature_b64":"C9bUyDIyEb+sWCGhhsWpvyqUrofJaDPByiXX6KC02UlpSRjpa03B8UZ9Ub6fjglNfielC12TzyTq0rK3YztFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4c38223a73eafe495d18e802a6a085cd6123a1704f8cc0c71c4500b94a4eccf","last_reissued_at":"2026-07-05T02:44:30.350690Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:44:30.350690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative quasimaps and mirror formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Battistella, Navid Nabijou","submitted_at":"2017-10-30T18:10:57Z","abstract_excerpt":"We construct and study the theory of relative quasimaps in genus zero, in the spirit of Gathmann. When $X$ is a smooth toric variety and $Y$ is a smooth very ample hypersurface in $X$, we produce a virtual class on the moduli space of relative quasimaps to $(X,Y)$, which we use to define relative quasimap invariants. We obtain a recursion formula which expresses each relative invariant in terms of invariants of lower tangency, and apply this formula to derive a quantum Lefschetz theorem for quasimaps, expressing the restricted quasimap invariants of $Y$ in terms of those of $X$. Finally, we sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11158","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1710.11158/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"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":"1710.11158","created_at":"2026-07-05T02:44:30.350751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.11158v4","created_at":"2026-07-05T02:44:30.350751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11158","created_at":"2026-07-05T02:44:30.350751+00:00"},{"alias_kind":"pith_short_12","alias_value":"WTBYEI5HH2X6","created_at":"2026-07-05T02:44:30.350751+00:00"},{"alias_kind":"pith_short_16","alias_value":"WTBYEI5HH2X6JFOR","created_at":"2026-07-05T02:44:30.350751+00:00"},{"alias_kind":"pith_short_8","alias_value":"WTBYEI5H","created_at":"2026-07-05T02:44:30.350751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.19713","citing_title":"The integral Chow ring of $\\mathscr{M}_{0}(\\mathbb{P}^r, 2)$","ref_index":31,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT","json":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT.json","graph_json":"https://pith.science/api/pith-number/WTBYEI5HH2X6JFORR2ACU2QILT/graph.json","events_json":"https://pith.science/api/pith-number/WTBYEI5HH2X6JFORR2ACU2QILT/events.json","paper":"https://pith.science/paper/WTBYEI5H"},"agent_actions":{"view_html":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT","download_json":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT.json","view_paper":"https://pith.science/paper/WTBYEI5H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.11158&json=true","fetch_graph":"https://pith.science/api/pith-number/WTBYEI5HH2X6JFORR2ACU2QILT/graph.json","fetch_events":"https://pith.science/api/pith-number/WTBYEI5HH2X6JFORR2ACU2QILT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT/action/storage_attestation","attest_author":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT/action/author_attestation","sign_citation":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT/action/citation_signature","submit_replication":"https://pith.science/pith/WTBYEI5HH2X6JFORR2ACU2QILT/action/replication_record"}},"created_at":"2026-07-05T02:44:30.350751+00:00","updated_at":"2026-07-05T02:44:30.350751+00:00"}