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We prove two versions of homological mirror symmetry for these Stein $3$-folds.\n  (i) The uncompleted version: there is an equivalence $D^\\mathit{perf}\\mathcal{W}(W_f^\\circ)\\simeq D^b\\mathit{Coh}(Y^\\circ_f)$ between the derived wrapped Fukaya category and the bounded derived category of coherent sheaves on some divisor complement $Y^\\circ_f=Y_f\\setminus D$.\n  (ii) The completed ver"},"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":"2511.22837","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-11-28T02:02:50Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5c92dbcc4c5123a5e523daaa477ea5f721ddc3fd4384ab9edf9bfe143222d231","abstract_canon_sha256":"9fce9da02ea377e54896bc495aff389ea13bbcc61ececa53644f91bdc690fb98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:04:53.077528Z","signature_b64":"K8FFUF1+4UgpNAJaF75Y2eLnUHfPOsfQS7cpFTCQtVUfqn3h8hhZjkocSweDqSnnt6V3AXD+rSsFZrJKEfoSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b7104d9c9d120d92d9f9917ebfbbd824d45762c1ded57af111f688f2290c877","last_reissued_at":"2026-05-27T01:04:53.076842Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:04:53.076842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Plumbings of lens spaces and crepant resolutions of compound $A_n$ singularities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Bilun Xie, Yin Li","submitted_at":"2025-11-28T02:02:50Z","abstract_excerpt":"For many compound $A_n$ ($cA_n$) singularities $R_f=\\mathbb{C}[u,v,x,y]/(uv-f(x,y))$ with crepant resolutions $Y_f$, their mirrors are affine $A_n$ plumbings $W^\\circ_f$ of $3$-dimensional lens spaces along circles. We prove two versions of homological mirror symmetry for these Stein $3$-folds.\n  (i) The uncompleted version: there is an equivalence $D^\\mathit{perf}\\mathcal{W}(W_f^\\circ)\\simeq D^b\\mathit{Coh}(Y^\\circ_f)$ between the derived wrapped Fukaya category and the bounded derived category of coherent sheaves on some divisor complement $Y^\\circ_f=Y_f\\setminus D$.\n  (ii) The completed ver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.22837","kind":"arxiv","version":2},"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/2511.22837/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":"2511.22837","created_at":"2026-05-27T01:04:53.076923+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.22837v2","created_at":"2026-05-27T01:04:53.076923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.22837","created_at":"2026-05-27T01:04:53.076923+00:00"},{"alias_kind":"pith_short_12","alias_value":"DNYQJWOJ2EQN","created_at":"2026-05-27T01:04:53.076923+00:00"},{"alias_kind":"pith_short_16","alias_value":"DNYQJWOJ2EQNSLM7","created_at":"2026-05-27T01:04:53.076923+00:00"},{"alias_kind":"pith_short_8","alias_value":"DNYQJWOJ","created_at":"2026-05-27T01:04:53.076923+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2512.24382","citing_title":"Equivariant Partially Wrapped Fukaya Categories on Liouville Sectors","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ","json":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ.json","graph_json":"https://pith.science/api/pith-number/DNYQJWOJ2EQNSLM7TEL6X655QJ/graph.json","events_json":"https://pith.science/api/pith-number/DNYQJWOJ2EQNSLM7TEL6X655QJ/events.json","paper":"https://pith.science/paper/DNYQJWOJ"},"agent_actions":{"view_html":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ","download_json":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ.json","view_paper":"https://pith.science/paper/DNYQJWOJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.22837&json=true","fetch_graph":"https://pith.science/api/pith-number/DNYQJWOJ2EQNSLM7TEL6X655QJ/graph.json","fetch_events":"https://pith.science/api/pith-number/DNYQJWOJ2EQNSLM7TEL6X655QJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ/action/storage_attestation","attest_author":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ/action/author_attestation","sign_citation":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ/action/citation_signature","submit_replication":"https://pith.science/pith/DNYQJWOJ2EQNSLM7TEL6X655QJ/action/replication_record"}},"created_at":"2026-05-27T01:04:53.076923+00:00","updated_at":"2026-05-27T01:04:53.076923+00:00"}