{"paper":{"title":"Spectral Sidorenko inequalities and edge-spectral supersaturation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hong Liu, Shengtong Zhang, Wilson Lin, Yongtao Li","submitted_at":"2026-05-26T06:51:18Z","abstract_excerpt":"We develop a spectral approach to Sidorenko-type inequalities and apply it to establish sharp edge-spectral supersaturation results. Let $H$ be a bipartite graph with $v$ vertices and $e$ edges, where $v\\le e$, and write $M(G)=2e(G)$. We prove that Sidorenko's conjecture is equivalent to a spectral strengthening: \\[\n  \\hom(H,G)\\ge M(G)^e |V(G)|^{v-2e} \\quad \\text{ if and only if }\\quad \\hom(H,G)\\ge \\lambda(G)^{2e-v}M(G)^{v-e}. \\] We also introduce an operator-norm certificate which, via the Riesz--Thorin interpolation, gives direct proofs of the spectral Sidorenko inequality in several cases. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26614","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/2605.26614/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"}