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There is a universal constant $C$ such that \\[\\gamma_{div}(\\Gamma) \\geq C \\frac{\\mu(\\Gamma) . \\ell_{\\min}^{\\mathrm{geo}}(\\Gamma). \\lambda_1(\\Gamma)}{d_{\\max}},\\] where the volume $\\mu(\\Gamma)$ is the total length of the edges in $\\Gamma$, $\\ell_{\\min}^{\\mathrm{geo}}$ is the minimum length of all the geodesic paths between points of $\\Gamma$ of valen"},"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":"1407.5614","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-21T19:56:17Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"8a97c4d701dedcc26785870128aaa22ac15e931fa225d4fa1e88c55692889a29","abstract_canon_sha256":"fa7e1e15d8e9eef33db271d6dd0c1b6ff96c2338051c5ca43de4db9edc1369ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:23.559729Z","signature_b64":"wjyXduwOvMTLVCoZGCd8SQsCxN0Nsa2VUr8UjwWDttfoUPWA5RzFgavu98lNk+1zs7iZQKmMt+sgeJKskSVLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"989e4918adea322a9a850b3938d15ba634c42ee9a53ed8e907e0fe04bda9b950","last_reissued_at":"2026-05-18T02:39:23.559253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:23.559253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A spectral lower bound for the divisorial gonality of metric graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.AG","authors_text":"Janne Kool, Omid Amini","submitted_at":"2014-07-21T19:56:17Z","abstract_excerpt":"Let $\\Gamma$ be a compact metric graph, and denote by $\\Delta$ the Laplace operator on $\\Gamma$ with the first non-trivial eigenvalue $\\lambda_1$. 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