{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OCFOFC6LRFMI5W2TIFDH3CVIE7","short_pith_number":"pith:OCFOFC6L","schema_version":"1.0","canonical_sha256":"708ae28bcb89588edb5341467d8aa827d7342b20b2e2b681b38e7aa67e195430","source":{"kind":"arxiv","id":"2503.06025","version":1},"attestation_state":"computed","paper":{"title":"$K$-theoretic pullbacks for Lagrangians on derived critical loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Gufang Zhao, Yalong Cao, Yukinobu Toda","submitted_at":"2025-03-08T02:57:37Z","abstract_excerpt":"Given a regular function $\\phi$ on a smooth stack, and a $(-1)$-shifted Lagrangian $M$ on the derived critical locus of $\\phi$, under fairly general hypotheses, we construct a pullback map from the Grothendieck group of coherent matrix factorizations of $\\phi$ to that of coherent sheaves on $M$. This map satisfies a functoriality property with respect to the composition of Lagrangian correspondences, as well as the usual bivariance and base-change properties.\n  We provide three applications of the construction, one in the definition of quantum $K$-theory of critical loci (Landau-Ginzburg model"},"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":"2503.06025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-03-08T02:57:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"f3d702abe6576d407488a21d9055de87345da9d51c8656a02cf63239f42596cd","abstract_canon_sha256":"241cdf083de4bd9e7b2cff8e49bf2fc780a576745c7cec8fafaa702344105236"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:51.985799Z","signature_b64":"UgMqrNrR9tZozjS1iKSINqU5I+BaBC/USLmxUGqVffuRusjFuiaXdBixEtiy6V6xh2ghrz/JknZUnlVym6pJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"708ae28bcb89588edb5341467d8aa827d7342b20b2e2b681b38e7aa67e195430","last_reissued_at":"2026-07-05T10:26:51.985123Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:51.985123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$K$-theoretic pullbacks for Lagrangians on derived critical loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Gufang Zhao, Yalong Cao, Yukinobu Toda","submitted_at":"2025-03-08T02:57:37Z","abstract_excerpt":"Given a regular function $\\phi$ on a smooth stack, and a $(-1)$-shifted Lagrangian $M$ on the derived critical locus of $\\phi$, under fairly general hypotheses, we construct a pullback map from the Grothendieck group of coherent matrix factorizations of $\\phi$ to that of coherent sheaves on $M$. This map satisfies a functoriality property with respect to the composition of Lagrangian correspondences, as well as the usual bivariance and base-change properties.\n  We provide three applications of the construction, one in the definition of quantum $K$-theory of critical loci (Landau-Ginzburg model"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06025","kind":"arxiv","version":1},"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/2503.06025/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":"2503.06025","created_at":"2026-07-05T10:26:51.985195+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.06025v1","created_at":"2026-07-05T10:26:51.985195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.06025","created_at":"2026-07-05T10:26:51.985195+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCFOFC6LRFMI","created_at":"2026-07-05T10:26:51.985195+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCFOFC6LRFMI5W2T","created_at":"2026-07-05T10:26:51.985195+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCFOFC6L","created_at":"2026-07-05T10:26:51.985195+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7","json":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7.json","graph_json":"https://pith.science/api/pith-number/OCFOFC6LRFMI5W2TIFDH3CVIE7/graph.json","events_json":"https://pith.science/api/pith-number/OCFOFC6LRFMI5W2TIFDH3CVIE7/events.json","paper":"https://pith.science/paper/OCFOFC6L"},"agent_actions":{"view_html":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7","download_json":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7.json","view_paper":"https://pith.science/paper/OCFOFC6L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.06025&json=true","fetch_graph":"https://pith.science/api/pith-number/OCFOFC6LRFMI5W2TIFDH3CVIE7/graph.json","fetch_events":"https://pith.science/api/pith-number/OCFOFC6LRFMI5W2TIFDH3CVIE7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7/action/storage_attestation","attest_author":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7/action/author_attestation","sign_citation":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7/action/citation_signature","submit_replication":"https://pith.science/pith/OCFOFC6LRFMI5W2TIFDH3CVIE7/action/replication_record"}},"created_at":"2026-07-05T10:26:51.985195+00:00","updated_at":"2026-07-05T10:26:51.985195+00:00"}