{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:BMNLGX2SSW4PLXKPD6P4GHSCER","short_pith_number":"pith:BMNLGX2S","canonical_record":{"source":{"id":"0908.3021","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-08-20T21:30:36Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4af37b6288b262faeec5b263548d78b5991b17889974486739618c62cf1205bf","abstract_canon_sha256":"036a719e0b1f7b5b95fa5e5bbd24bfe58fbdeb1e8590e64a5437d50835844977"},"schema_version":"1.0"},"canonical_sha256":"0b1ab35f5295b8f5dd4f1f9fc31e42245f149867700a82396687c604495b1ed0","source":{"kind":"arxiv","id":"0908.3021","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3021","created_at":"2026-05-18T02:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3021v5","created_at":"2026-05-18T02:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3021","created_at":"2026-05-18T02:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"BMNLGX2SSW4P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BMNLGX2SSW4PLXKP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BMNLGX2S","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:BMNLGX2SSW4PLXKPD6P4GHSCER","target":"record","payload":{"canonical_record":{"source":{"id":"0908.3021","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-08-20T21:30:36Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4af37b6288b262faeec5b263548d78b5991b17889974486739618c62cf1205bf","abstract_canon_sha256":"036a719e0b1f7b5b95fa5e5bbd24bfe58fbdeb1e8590e64a5437d50835844977"},"schema_version":"1.0"},"canonical_sha256":"0b1ab35f5295b8f5dd4f1f9fc31e42245f149867700a82396687c604495b1ed0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:24.506397Z","signature_b64":"v0Q2z0VXEsGKvXul8HGaJ9i/H+slhHOxkF3FG2uATfZcpCI21JhipvGbN/l20RrymXwlgENQW1YMJsLdsA6hDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b1ab35f5295b8f5dd4f1f9fc31e42245f149867700a82396687c604495b1ed0","last_reissued_at":"2026-05-18T02:12:24.505567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:24.505567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.3021","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kJqi+uhu8HUhjQUSvltlwBmWUwQwpN7rmztW8hcsrvv+m4RZa11OVFn1eC/fIb7dwVxwuk0v7OG8rBtE//5XDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:38:51.612714Z"},"content_sha256":"206bc6a2c9b76789c855fdde18765cf5d5739388aa65601b25d16322e84990aa","schema_version":"1.0","event_id":"sha256:206bc6a2c9b76789c855fdde18765cf5d5739388aa65601b25d16322e84990aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:BMNLGX2SSW4PLXKPD6P4GHSCER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relativistic Kramers-Pasternack Recurrence Relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Sergei K. Suslov","submitted_at":"2009-08-20T21:30:36Z","abstract_excerpt":"Recently we have evaluated the matrix elements $<Or^{p}>$,$ where $O$ $={1,\\beta, i\\mathbf{\\alpha n}\\beta} $ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions $_{3}F_{2}(1) $ for all suitable powers and established two sets of Pasternack-type matrix identities for these integrals. The corresponding Kramers--Pasternack three-term vector recurrence relations are derived here."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3021","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bnmaMlBEZLXulNvvSvEhMJO0DKBqBy3Ij0byphjh+y/zDq8KWIbuTCW2PYPnEyKcEnDVK40QuRFD3pD1maMTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T05:38:51.613362Z"},"content_sha256":"e9ae4987eea158f18b307dff9944ea87afa77bd4a67ef273f9974aed294cbfec","schema_version":"1.0","event_id":"sha256:e9ae4987eea158f18b307dff9944ea87afa77bd4a67ef273f9974aed294cbfec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BMNLGX2SSW4PLXKPD6P4GHSCER/bundle.json","state_url":"https://pith.science/pith/BMNLGX2SSW4PLXKPD6P4GHSCER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BMNLGX2SSW4PLXKPD6P4GHSCER/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T05:38:51Z","links":{"resolver":"https://pith.science/pith/BMNLGX2SSW4PLXKPD6P4GHSCER","bundle":"https://pith.science/pith/BMNLGX2SSW4PLXKPD6P4GHSCER/bundle.json","state":"https://pith.science/pith/BMNLGX2SSW4PLXKPD6P4GHSCER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BMNLGX2SSW4PLXKPD6P4GHSCER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BMNLGX2SSW4PLXKPD6P4GHSCER","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":"036a719e0b1f7b5b95fa5e5bbd24bfe58fbdeb1e8590e64a5437d50835844977","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-08-20T21:30:36Z","title_canon_sha256":"4af37b6288b262faeec5b263548d78b5991b17889974486739618c62cf1205bf"},"schema_version":"1.0","source":{"id":"0908.3021","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.3021","created_at":"2026-05-18T02:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"0908.3021v5","created_at":"2026-05-18T02:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3021","created_at":"2026-05-18T02:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"BMNLGX2SSW4P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BMNLGX2SSW4PLXKP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BMNLGX2S","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:e9ae4987eea158f18b307dff9944ea87afa77bd4a67ef273f9974aed294cbfec","target":"graph","created_at":"2026-05-18T02:12:24Z","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"},"paper":{"abstract_excerpt":"Recently we have evaluated the matrix elements $<Or^{p}>$,$ where $O$ $={1,\\beta, i\\mathbf{\\alpha n}\\beta} $ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions $_{3}F_{2}(1) $ for all suitable powers and established two sets of Pasternack-type matrix identities for these integrals. The corresponding Kramers--Pasternack three-term vector recurrence relations are derived here.","authors_text":"Sergei K. Suslov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-08-20T21:30:36Z","title":"Relativistic Kramers-Pasternack Recurrence Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3021","kind":"arxiv","version":5},"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":"sha256:206bc6a2c9b76789c855fdde18765cf5d5739388aa65601b25d16322e84990aa","target":"record","created_at":"2026-05-18T02:12:24Z","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":"036a719e0b1f7b5b95fa5e5bbd24bfe58fbdeb1e8590e64a5437d50835844977","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-08-20T21:30:36Z","title_canon_sha256":"4af37b6288b262faeec5b263548d78b5991b17889974486739618c62cf1205bf"},"schema_version":"1.0","source":{"id":"0908.3021","kind":"arxiv","version":5}},"canonical_sha256":"0b1ab35f5295b8f5dd4f1f9fc31e42245f149867700a82396687c604495b1ed0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b1ab35f5295b8f5dd4f1f9fc31e42245f149867700a82396687c604495b1ed0","first_computed_at":"2026-05-18T02:12:24.505567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:24.505567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v0Q2z0VXEsGKvXul8HGaJ9i/H+slhHOxkF3FG2uATfZcpCI21JhipvGbN/l20RrymXwlgENQW1YMJsLdsA6hDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:24.506397Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.3021","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:206bc6a2c9b76789c855fdde18765cf5d5739388aa65601b25d16322e84990aa","sha256:e9ae4987eea158f18b307dff9944ea87afa77bd4a67ef273f9974aed294cbfec"],"state_sha256":"0040c217d6721e255a8c5b5cbb44b6a6dd8e1f73476711e89f50c193dd44671a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3f6haDG0byRSDK1yUJwnn80WynoxgRlC1Jg8iu0wQR66+POv/m17vAd8KtK3iTUV6dWL0+R95IEucGGCeJqzBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T05:38:51.616578Z","bundle_sha256":"645800acfcf11f84de33ccb1dee8ac2cd69f0b91444d2f3445452b014dc05c41"}}