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We show that if $V_D(R)$ is confining, $\\lim_{R \\to \\infty}V_D(R) = + \\infty$, then the inequality $V_D(R) \\leq - C_D V_{\\rm coul}(R)$ holds asymptotically at large $R$, where $C_D > 0$ is the Casimir in the representation $D$. This implies that $ - V_{\\rm coul}(R)$ is a"},"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":"hep-lat/0209105","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-lat","submitted_at":"2002-09-10T19:35:22Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"0c47829d25bb1dad8411cf323b8950af23b1b03ffd971e54b4777fdc9c10f66f","abstract_canon_sha256":"30e341e78e2f20bf45b5639bd4c888c8f2c45160880ff6f7eb80e2589d8928be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:26:38.220930Z","signature_b64":"nI6GzwFiVGc/LpsqeBXuF7Ln9jrqj4SU1Id87w3K3dZQ1KCcM49/RqvTkU31NyY/5oGd1K2eL7fJMlt+KiCODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8a0511db0b03191ad604480b6ea952801f596a66748535435f4600418ad09e5","last_reissued_at":"2026-07-04T15:26:38.220522Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:26:38.220522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"No confinement without Coulomb confinement","license":"","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-lat","authors_text":"Daniel Zwanziger","submitted_at":"2002-09-10T19:35:22Z","abstract_excerpt":"We compare the physical potential $V_D(R)$ of an external quark-antiquark pair in the representation $D$ of SU(N), to the color-Coulomb potential $V_{\\rm coul}(R)$ which is the instantaneous part of the 44-component of the gluon propagator in Coulomb gauge, $D_{44}(\\vx,t) = V_{\\rm coul}(|\\vx|) \\delta(t)$ + (non-instantaneous). We show that if $V_D(R)$ is confining, $\\lim_{R \\to \\infty}V_D(R) = + \\infty$, then the inequality $V_D(R) \\leq - C_D V_{\\rm coul}(R)$ holds asymptotically at large $R$, where $C_D > 0$ is the Casimir in the representation $D$. 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