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Here we report on the complete result in the case of two equal masses $m_1 = m_2$ for the massive operator matrix element $A_{gg,Q}^{(3)}$, which contributes to the corresponding heavy flavor transition matrix element in the variable flavor number scheme. Nested finite binomial sums and iterated integrals over square-root valued alphabets emerge in the result for this quantity in $N$ and $x$-space, respectively. We also prese"},"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":"1407.2821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2014-07-10T15:05:24Z","cross_cats_sorted":[],"title_canon_sha256":"19992e6c58b96ceac01131de5c7d86191c7f8849f94c9228594d593fa8f299a1","abstract_canon_sha256":"b93d86cc2bd99cfd487906da63a31aec8b15aa7db9b483a0d4e6ef17a5c70e5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:53.594486Z","signature_b64":"gXlWMn+LtjPl6PeLNIwrjWT3ZDIE9ydSXqnzD7P1rjh5LBfJ9uhagiDB0sBsyPBbdfaxN9LoTpT8jNiixqXLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7c7a08b42103c6e1bf7ec9b05811184dfe0357788d3e2684c20858458e56349","last_reissued_at":"2026-05-18T02:47:53.593961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:53.593961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. De Freitas, A. Hasselhuhn, A. von Manteuffel, C. Schneider, F. Wi{\\ss}brock, J. Ablinger, J. Bl\\\"umlein, M. Round","submitted_at":"2014-07-10T15:05:24Z","abstract_excerpt":"We consider gluonic contributions to the heavy flavor Wilson coefficients at 3-loop order in QCD with two heavy quark lines in the asymptotic region $Q^2 \\gg m_{1(2)}^2$. Here we report on the complete result in the case of two equal masses $m_1 = m_2$ for the massive operator matrix element $A_{gg,Q}^{(3)}$, which contributes to the corresponding heavy flavor transition matrix element in the variable flavor number scheme. Nested finite binomial sums and iterated integrals over square-root valued alphabets emerge in the result for this quantity in $N$ and $x$-space, respectively. 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