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We find \\Delta E_{\\rm rec} = m alpha^6 (-1/6 ln(alpha) + 331/432 -ln(2)/4 - 17 Zeta(3)/(8 pi^2) + 5/(12 pi^2)) \\approx m alpha^6 (- 1/6 ln(alpha) + 0.37632), confirming Pachucki's numerical result \\cite{Ph}. We present a complete analytic formula for the m*alpha^6 HFS of the positronium ground state and, including m*alpha^7*ln^2(alpha) effects, find E(1^3S_1)-E(1^1S_0))_{theory} = 203 392(1) MHz. This differs from the experimental results by "},"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-ph/9809341","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"1998-09-11T13:27:40Z","cross_cats_sorted":[],"title_canon_sha256":"e4a43086f8bb70a0582feab1c235d4bb521fd4fecbc99a1cb0a77922b0b87648","abstract_canon_sha256":"5c7d973502264d6de0096ddf5ac6c34cccbf3fde58915a238022f1cc76acf5d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:09:24.507485Z","signature_b64":"O5zMYpg1oRH0KWDGDfdZ0323bjeDGerX0KGJ3cZp4Hk9gE7kBsZ/Qg/0HDhNkj9k+Oek7/Na9wxIkG8ktr8JDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cccb4e9321aa62d7ab6c819f0d9eed6b903a8b0c9e50e95c5b5ebe26073d631","last_reissued_at":"2026-07-04T16:09:24.507036Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:09:24.507036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positronium hyperfine splitting: analytical value at m*alpha^6","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. 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