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In particular, for any number of particles $N$ and large enough $\\alpha$ we provide a bound of the form $-C\\alpha^2 N^3\\log^2(\\alpha N)$, where $C$ is an explicit positive numerical constant; and if $\\alpha$ is sufficiently small, we give one of the form $-C\\alpha^2 N^3\\log^2 N$ for $N \\geq 2$, and $-C\\alpha^2$ for $N = 1$. Whereas it is known that the renormalized"},"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":"1609.08590","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-09-27T19:30:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"134ff77c3ce0d4a46cfc4d949e97f8aedf2f6334f82bb5ea666df988418a2358","abstract_canon_sha256":"f7e0ffd3a3925aa52f6ceceb43abaf7804470d4a99e9e4c8d2a4a8a5ac029cf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:23.991290Z","signature_b64":"mDstiytXPnQSKJIGTQ6Vvh7zJs6bdT00FsUff9T4G5joK63R3ozPaVryxPE54D1jqNsq4x4/8/sKw7oNyCKEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c987fd79ca06ea91b1421e0c3414f6285c40c33beddfc6338127959fd47664e","last_reissued_at":"2026-05-18T00:31:23.990763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:23.990763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Lower Bound on the Renormalized Nelson Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Gonzalo A. Bley","submitted_at":"2016-09-27T19:30:39Z","abstract_excerpt":"We provide explicit lower bounds for the ground-state energy of the renormalized Nelson model in terms of the coupling constant $\\alpha$ and the number of particles $N$, uniform in the meson mass and valid even in the massless case. In particular, for any number of particles $N$ and large enough $\\alpha$ we provide a bound of the form $-C\\alpha^2 N^3\\log^2(\\alpha N)$, where $C$ is an explicit positive numerical constant; and if $\\alpha$ is sufficiently small, we give one of the form $-C\\alpha^2 N^3\\log^2 N$ for $N \\geq 2$, and $-C\\alpha^2$ for $N = 1$. 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