{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:Y2TOYEY4MMEM553QV2RMMA6TKX","short_pith_number":"pith:Y2TOYEY4","schema_version":"1.0","canonical_sha256":"c6a6ec131c6308cef770aea2c603d355d2a3e82c91fa6eb11a43b3b794aa9bdb","source":{"kind":"arxiv","id":"2501.06649","version":1},"attestation_state":"computed","paper":{"title":"Toric Mirror Symmetry for Homotopy Theorists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.AG","authors_text":"Qingyuan Bai, Yuxuan Hu","submitted_at":"2025-01-11T22:06:57Z","abstract_excerpt":"We construct functors sending torus-equivariant quasi-coherent sheaves on toric schemes over the sphere spectrum to constructible sheaves of spectra on real vector spaces. This provides a spectral lift of the toric homolgoical mirror symmetry theorem of Fang-Liu-Treumann-Zaslow (arXiv:1007.0053). Along the way, we obtain symmetric monoidal structures and functoriality results concerning those functors, which are new even over a field $k$. We also explain how the `non-equivariant' version of the theorem would follow from this functoriality via the de-equivariantization technique. As a concrete "},"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":"2501.06649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-11T22:06:57Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"bfe63df74389d068f947fa148f23bbe1914a1084a84448440aebf9297ac246bd","abstract_canon_sha256":"56b5f18b4c26c4934b926f8d1c4aed9d3f35b256fc75cf3130ec1ea9ac165571"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:00:07.821642Z","signature_b64":"QPDYbRhwyZ/qfytgczVD4Qc8GFg/3Kolomzw9AyyZi/4H5HXa/YSUWhDOc7arKEkz+QEbFEUiJ6TsAxTut//Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6a6ec131c6308cef770aea2c603d355d2a3e82c91fa6eb11a43b3b794aa9bdb","last_reissued_at":"2026-07-05T10:00:07.821176Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:00:07.821176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toric Mirror Symmetry for Homotopy Theorists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.AG","authors_text":"Qingyuan Bai, Yuxuan Hu","submitted_at":"2025-01-11T22:06:57Z","abstract_excerpt":"We construct functors sending torus-equivariant quasi-coherent sheaves on toric schemes over the sphere spectrum to constructible sheaves of spectra on real vector spaces. This provides a spectral lift of the toric homolgoical mirror symmetry theorem of Fang-Liu-Treumann-Zaslow (arXiv:1007.0053). Along the way, we obtain symmetric monoidal structures and functoriality results concerning those functors, which are new even over a field $k$. We also explain how the `non-equivariant' version of the theorem would follow from this functoriality via the de-equivariantization technique. As a concrete "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.06649","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/2501.06649/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":"2501.06649","created_at":"2026-07-05T10:00:07.821239+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.06649v1","created_at":"2026-07-05T10:00:07.821239+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.06649","created_at":"2026-07-05T10:00:07.821239+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2TOYEY4MMEM","created_at":"2026-07-05T10:00:07.821239+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2TOYEY4MMEM553Q","created_at":"2026-07-05T10:00:07.821239+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2TOYEY4","created_at":"2026-07-05T10:00:07.821239+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.11853","citing_title":"An obstruction to lifting schemes to spectral schemes","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX","json":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX.json","graph_json":"https://pith.science/api/pith-number/Y2TOYEY4MMEM553QV2RMMA6TKX/graph.json","events_json":"https://pith.science/api/pith-number/Y2TOYEY4MMEM553QV2RMMA6TKX/events.json","paper":"https://pith.science/paper/Y2TOYEY4"},"agent_actions":{"view_html":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX","download_json":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX.json","view_paper":"https://pith.science/paper/Y2TOYEY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.06649&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2TOYEY4MMEM553QV2RMMA6TKX/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2TOYEY4MMEM553QV2RMMA6TKX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX/action/storage_attestation","attest_author":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX/action/author_attestation","sign_citation":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX/action/citation_signature","submit_replication":"https://pith.science/pith/Y2TOYEY4MMEM553QV2RMMA6TKX/action/replication_record"}},"created_at":"2026-07-05T10:00:07.821239+00:00","updated_at":"2026-07-05T10:00:07.821239+00:00"}