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Asymptotic freedom predicts that the leading asymptotic behavior is $\\sim a^n [\\bar g^2(a^{-1})]^{\\hat\\gamma_1} \\sim\n  a^n \\left[\\frac{1}{-\\log(a\\Lambda)}\\right]^{\\hat\\gamma_1}$. For spectral quantities, $n=d$ is given in terms of the (lowest) canonical dimension, $d+4$, of the operators in the local effective Lagrangian and $\\hat\\gamma_1$ is proportional to the leading eigenvalue of their one-loop anomalous dimension matrix $\\gamma^{(0)}$. We determine $\\gamma^{(0)}$ for"},"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":"1912.08498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2019-12-18T10:23:01Z","cross_cats_sorted":[],"title_canon_sha256":"8649e006aaaca736ccfc8980414111db274fa5481065047b632d07808b10fb00","abstract_canon_sha256":"81d07eabdd7fefe9cf91e414f2532122ced4ad56fda704fcdaca1a6bf294abf7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:21.881348Z","signature_b64":"IpHwZLoDg+x09Vss0DK+TdTXfr9Sb3YSFrHrtyYFzS7TIrfloRxxJlokWFaiVVqy3VAWYikZvg5V7SpV9HHlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dccb901c433b23d56583bb85ea267b7e6580122e34684e574e09aeab3d6f4781","last_reissued_at":"2026-07-05T00:48:21.880886Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:21.880886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic behavior of cutoff effects in Yang-Mills theory and in Wilson's lattice QCD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Nikolai Husung, Peter Marquard, Rainer Sommer","submitted_at":"2019-12-18T10:23:01Z","abstract_excerpt":"Discretization effects of lattice QCD are described by Symanzik's effective theory when the lattice spacing, $a$, is small. Asymptotic freedom predicts that the leading asymptotic behavior is $\\sim a^n [\\bar g^2(a^{-1})]^{\\hat\\gamma_1} \\sim\n  a^n \\left[\\frac{1}{-\\log(a\\Lambda)}\\right]^{\\hat\\gamma_1}$. For spectral quantities, $n=d$ is given in terms of the (lowest) canonical dimension, $d+4$, of the operators in the local effective Lagrangian and $\\hat\\gamma_1$ is proportional to the leading eigenvalue of their one-loop anomalous dimension matrix $\\gamma^{(0)}$. 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