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Hence, $h_G$ is tightly controlled by $\\lambda_1$ to within a quadratic factor.\n  We give an alternative Cheeger Inequality where we consider the $\\infty$-norm of the corresponding eigenvector in addition to $\\lambda_1$. This inequality controls $h_G$ to within a linear factor of $\\lambda_1$ thereby providing an improvement to the previous quadrati"},"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":"1412.3195","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-10T04:33:32Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"688d37321260dc616dab7e173e96a0f6c54fce23fcd169025e5992cd18f7b252","abstract_canon_sha256":"98fc453756c5f9ca7d062816a9f1eb030a103fc5511aa410d5a61177299a97b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:37.308897Z","signature_b64":"tGrw74v02FXwbT3wgD7pdMTZLshGTfQYP3LQreSkIEI6yai0TQmRwhLvxYyq0OhMlrWGAvchaJK5O5YZctwpBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"770bf484f3d47fbe0120ae018d901e9293843e7bf739973e3165c9cddd6aeb5b","last_reissued_at":"2026-05-18T02:31:37.308292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:37.308292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Linear Cheeger Inequality using Eigenvector Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Franklin H. 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