{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:75PJGXPSTJSHV5XWERQPLPK3OQ","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":"713d5390216795d79f64e0dfa1d01d59b27a72106b35b429ff49b9e3f0c2e4f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2013-11-22T17:15:33Z","title_canon_sha256":"663005095d29d850f89aafec647d8397e02f02d96ad803e298b092e2953e44a8"},"schema_version":"1.0","source":{"id":"1311.5822","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5822","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5822v3","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5822","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"75PJGXPSTJSH","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"75PJGXPSTJSHV5XW","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"75PJGXPS","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:4028a66a615f6d31df5ff4fe700a8e95db86dfce66f0d0f3b389d248fa432ac5","target":"graph","created_at":"2026-05-18T02:38:53Z","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"},"paper":{"abstract_excerpt":"Adjusting a previously developed Grotch-type approach to a perturbative calculation of the electronic vacuum-polarization effects in muonic atoms, we find here the two-loop vacuum polarization relativistic recoil correction of order $\\alpha^2(Z\\alpha)^4m^2/M$ in light muonic atoms. The result is in perfect agreement with the one previously obtained within the Breit-type approach. We also discuss here simple approximations of the irreducible part of the two-loop vacuum-polarization dispersion density, which was applied to test our calculations and can be useful for other evaluations with an unc","authors_text":"Evgeny Yu. Korzinin, Savely G. Karshenboim, Vladimir G. Ivanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2013-11-22T17:15:33Z","title":"Relativistic recoil effects to energy levels in a muonic atom: a Grotch-type calculation of the second-order vacuum-polarization contributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5822","kind":"arxiv","version":3},"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:d9b33ba8547edc9802185d5196d955464389d82809b58e637e6d8c22d53cc3bd","target":"record","created_at":"2026-05-18T02:38:53Z","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":"713d5390216795d79f64e0dfa1d01d59b27a72106b35b429ff49b9e3f0c2e4f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2013-11-22T17:15:33Z","title_canon_sha256":"663005095d29d850f89aafec647d8397e02f02d96ad803e298b092e2953e44a8"},"schema_version":"1.0","source":{"id":"1311.5822","kind":"arxiv","version":3}},"canonical_sha256":"ff5e935df29a647af6f62460f5bd5b7430d6b6d28ffc1ffc7e5ac18b735fd6c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff5e935df29a647af6f62460f5bd5b7430d6b6d28ffc1ffc7e5ac18b735fd6c8","first_computed_at":"2026-05-18T02:38:53.083098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:53.083098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lF+7ZtQT9848Rs0p8I4yYbTWd+V3gu4/B+gwk6yWb1M6Yp37e95HWysmmgVKqbgx0kAFOKtYlkDUAURmEw5EBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:53.083434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5822","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9b33ba8547edc9802185d5196d955464389d82809b58e637e6d8c22d53cc3bd","sha256:4028a66a615f6d31df5ff4fe700a8e95db86dfce66f0d0f3b389d248fa432ac5"],"state_sha256":"3c86ff55e8ef2f801a552aeba3aa1014caf296ae6b4356a2db8434819dd7d100"}