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We obtain, in this world where all pions have the mass of the $\\pi^0$, $10^{10} a_\\mu^{ll}({\\rm conn.}) = 637.8\\,(8.8)$, in agreement with indep"},"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":"1902.04223","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-lat","submitted_at":"2019-02-12T03:09:07Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"011d0b6fd7c326c5fb23c61c5ac9f9be6d88e1da6d78cd0eb91654322d693a3e","abstract_canon_sha256":"f47a3cf87a48b024859e56c3f805afdda3a9ec15b6dad0e1e2befa23322dc9c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:45:50.399310Z","signature_b64":"R77T6GV3sD2OfuzNLiXTIubI4behv39x7nk8gTvpRGpTP6Q6iXcDKPDJpaSlBFHRrVB4qLUwoldS0xYs/dmyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c44d22948f24fae7e2c623429096f3403bfcf4a456ee79705c5c7f7d0eb34e8","last_reissued_at":"2026-07-05T00:45:50.398833Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:45:50.398833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment from four-flavor lattice QCD","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-lat","authors_text":"A. S. Kronfeld, A. Vaquero, A. X. El-Khadra, C. DeTar, C. McNeile, C. T. H. Davies, D. Hatton, D. Toussaint, E. Gamiz, E. T. Neil, G. P. Lepage, J. Laiho, J. N. Simone, P. B. Mackenzie, R. S. Van de Water, Steven Gottlieb, T. Primer, Yuzhi Liu","submitted_at":"2019-02-12T03:09:07Z","abstract_excerpt":"We calculate the contribution to the muon anomalous magnetic moment hadronic vacuum polarization from {the} connected diagrams of up and down quarks, omitting electromagnetism. We employ QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks and the physical pion mass, and analyze five ensembles with lattice spacings ranging from $a \\approx 0.06$ to~0.15~fm. The up- and down-quark masses in our simulations have equal masses $m_l$. 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