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In other words, such a link $L$ satisfies $s_{\\text{top}}=\\frac{n-\\chi(\\Sigma)}{2}=1$, and in addition $\\text{rk}\\:\\widehat{HFL}_{*}(L)[1]=2$ and $\\text{rk}\\:\\widehat{HFL}_{*}(L)[s]=0$ for every $s>1$. The proof of the main theorem is inspired by th"},"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":"2302.12365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-02-23T23:33:26Z","cross_cats_sorted":[],"title_canon_sha256":"39b7d8f560c8d2799ddbd644bbcc812ccc062c5516b9100624845b2be489c5de","abstract_canon_sha256":"f176149550bfff9745a804c1e7d2619aa8e6dbd51bc818a706fd19d0a936a03c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:00:21.383852Z","signature_b64":"oNXO2tnpkHMk2IAqTieDkCj15yO2eAqt1PGqF9DWEafd7BjAFF5bdPtTtZNrZCVwAt5xSlamR27WtoRERARAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"056b67f8ac8edce322f024ae42cf132f3f6e99e2bc63499d2db0560e362fe029","last_reissued_at":"2026-07-05T07:00:21.383391Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:00:21.383391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nearly fibered links with genus one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Alberto Cavallo, Irena Matkovi\\v{c}","submitted_at":"2023-02-23T23:33:26Z","abstract_excerpt":"We classify all the $n$-component links in the $3$-sphere that bound a Thurston norm minimizing Seifert surface $\\Sigma$ with Euler characteristic $\\chi(\\Sigma)=n-2$ and that are nearly fibered, which means that their rank of the maximal (collapsed) Alexander grading $s_{\\text{top}}$ of the link Floer homology group $\\widehat{HFL}$ is equal to two. 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