{"paper":{"title":"Satellites and telescopes: a concordance Formula for bordered Floer homology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gary Guth, Sungkyung Kang","submitted_at":"2026-06-15T02:27:21Z","abstract_excerpt":"Given a knot $K$ in $S^3$, its knot Floer completely determines the bordered Floer homology of its complement by a work of Lipshitz--Ozsv\\'{a}th--Thurston, and the reverse is also true by a work of Kotelskiy--Watson--Zibrowius. Moreover, given a model for $CFK_{\\mathcal{R}}(S^3, K)$ there is a completely combinatorial method for producing a model for $\\widehat{CFD}(S^3 \\smallsetminus K)$. In this paper, we show that a similar formula holds between certain classes of chain endomorphisms of knot Floer chain complex and type D endomorphisms of bordered Floer homology, up to a 1-dimensional ambigu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.16120","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/2606.16120/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"}