{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:NTGLJ2JSDKTC26VWZAM7BWPO22","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5c7d973502264d6de0096ddf5ac6c34cccbf3fde58915a238022f1cc76acf5d5","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1998-09-11T13:27:40Z","title_canon_sha256":"e4a43086f8bb70a0582feab1c235d4bb521fd4fecbc99a1cb0a77922b0b87648"},"schema_version":"1.0","source":{"id":"hep-ph/9809341","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9809341","created_at":"2026-07-04T16:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9809341v1","created_at":"2026-07-04T16:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9809341","created_at":"2026-07-04T16:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"NTGLJ2JSDKTC","created_at":"2026-07-04T16:09:24Z"},{"alias_kind":"pith_short_16","alias_value":"NTGLJ2JSDKTC26VW","created_at":"2026-07-04T16:09:24Z"},{"alias_kind":"pith_short_8","alias_value":"NTGLJ2JS","created_at":"2026-07-04T16:09:24Z"}],"graph_snapshots":[{"event_id":"sha256:4146c7782e10da5cd502dddd5f2bba07b155c7ad21980a1c15e360e946b35883","target":"graph","created_at":"2026-07-04T16:09:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-ph/9809341/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an analytic calculation of the m*alpha^6 recoil corrections to the hyperfine splitting (HFS) of the ground state energy levels in positronium. 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 ","authors_text":"A. Czarnecki, A. Yelkhovsky, K. Melnikov","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"1998-09-11T13:27:40Z","title":"Positronium hyperfine splitting: analytical value at m*alpha^6"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9809341","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8fa22aaa2b18bb36abaf5be524d694df7bb0c7e6aaa0812987092db0653898a3","target":"record","created_at":"2026-07-04T16:09:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5c7d973502264d6de0096ddf5ac6c34cccbf3fde58915a238022f1cc76acf5d5","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1998-09-11T13:27:40Z","title_canon_sha256":"e4a43086f8bb70a0582feab1c235d4bb521fd4fecbc99a1cb0a77922b0b87648"},"schema_version":"1.0","source":{"id":"hep-ph/9809341","kind":"arxiv","version":1}},"canonical_sha256":"6cccb4e9321aa62d7ab6c819f0d9eed6b903a8b0c9e50e95c5b5ebe26073d631","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cccb4e9321aa62d7ab6c819f0d9eed6b903a8b0c9e50e95c5b5ebe26073d631","first_computed_at":"2026-07-04T16:09:24.507036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:09:24.507036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5zMYpg1oRH0KWDGDfdZ0323bjeDGerX0KGJ3cZp4Hk9gE7kBsZ/Qg/0HDhNkj9k+Oek7/Na9wxIkG8ktr8JDw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:09:24.507485Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/9809341","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fa22aaa2b18bb36abaf5be524d694df7bb0c7e6aaa0812987092db0653898a3","sha256:4146c7782e10da5cd502dddd5f2bba07b155c7ad21980a1c15e360e946b35883"],"state_sha256":"3846cf39ebfedf84f0af2f1c92402ad66b8d73e1ad4652948878d6b4a21e1715"}