{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:MVERRT6BIYUMHTYKB6SR2U3G5G","short_pith_number":"pith:MVERRT6B","schema_version":"1.0","canonical_sha256":"654918cfc14628c3cf0a0fa51d5366e9aef5d8b19fcae33fb73ceff6bf86e408","source":{"kind":"arxiv","id":"hep-ph/0112267","version":1},"attestation_state":"computed","paper":{"title":"Expansion of bound state energies in powers of m/M and (1-m/M)","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Andrzej Czarnecki, Ian Blokland, Kirill Melnikov","submitted_at":"2001-12-19T22:30:15Z","abstract_excerpt":"Elaborating on a previous letter, we use a new approach to compute energy levels of a non-relativistic bound-state of two constituents, with masses m and M, by systematic expansions - one in powers of m/M and another in powers of (1-m/M). Technical aspects of the calculations are described in detail. Theoretical predictions are given for O(alpha(Z*alpha)^5) radiative recoil and O((Z*alpha)^6) pure recoil corrections to the average energy shift and hyperfine splitting relevant for hydrogen, muonic hydrogen, and muonium."},"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/0112267","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2001-12-19T22:30:15Z","cross_cats_sorted":[],"title_canon_sha256":"d5ef0f6800e845a2b2bed756d850a8bddebe7c82e4b2a40e164f1b150310d23e","abstract_canon_sha256":"1923049df38bb93b50851ba2825124f7fbcbeda0225b234441cfe928dc2ccda8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:26:41.767715Z","signature_b64":"5FimRdVZ0KTC0fuyDQlPMKnyxpxm9DF6l1OlmFZd+dgBsCDW2l3W5w0ItnU48rZygbgynAEKzp5X1rSvtrz8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"654918cfc14628c3cf0a0fa51d5366e9aef5d8b19fcae33fb73ceff6bf86e408","last_reissued_at":"2026-07-04T15:26:41.767305Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:26:41.767305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expansion of bound state energies in powers of m/M and (1-m/M)","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Andrzej Czarnecki, Ian Blokland, Kirill Melnikov","submitted_at":"2001-12-19T22:30:15Z","abstract_excerpt":"Elaborating on a previous letter, we use a new approach to compute energy levels of a non-relativistic bound-state of two constituents, with masses m and M, by systematic expansions - one in powers of m/M and another in powers of (1-m/M). Technical aspects of the calculations are described in detail. Theoretical predictions are given for O(alpha(Z*alpha)^5) radiative recoil and O((Z*alpha)^6) pure recoil corrections to the average energy shift and hyperfine splitting relevant for hydrogen, muonic hydrogen, and muonium."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0112267","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-ph/0112267/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0112267","created_at":"2026-07-04T15:26:41.767375+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0112267v1","created_at":"2026-07-04T15:26:41.767375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0112267","created_at":"2026-07-04T15:26:41.767375+00:00"},{"alias_kind":"pith_short_12","alias_value":"MVERRT6BIYUM","created_at":"2026-07-04T15:26:41.767375+00:00"},{"alias_kind":"pith_short_16","alias_value":"MVERRT6BIYUMHTYK","created_at":"2026-07-04T15:26:41.767375+00:00"},{"alias_kind":"pith_short_8","alias_value":"MVERRT6B","created_at":"2026-07-04T15:26:41.767375+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G","json":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G.json","graph_json":"https://pith.science/api/pith-number/MVERRT6BIYUMHTYKB6SR2U3G5G/graph.json","events_json":"https://pith.science/api/pith-number/MVERRT6BIYUMHTYKB6SR2U3G5G/events.json","paper":"https://pith.science/paper/MVERRT6B"},"agent_actions":{"view_html":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G","download_json":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G.json","view_paper":"https://pith.science/paper/MVERRT6B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-ph/0112267&json=true","fetch_graph":"https://pith.science/api/pith-number/MVERRT6BIYUMHTYKB6SR2U3G5G/graph.json","fetch_events":"https://pith.science/api/pith-number/MVERRT6BIYUMHTYKB6SR2U3G5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G/action/storage_attestation","attest_author":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G/action/author_attestation","sign_citation":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G/action/citation_signature","submit_replication":"https://pith.science/pith/MVERRT6BIYUMHTYKB6SR2U3G5G/action/replication_record"}},"created_at":"2026-07-04T15:26:41.767375+00:00","updated_at":"2026-07-04T15:26:41.767375+00:00"}