{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BGMZR2JJQUNB637RCSRNNQXAWJ","short_pith_number":"pith:BGMZR2JJ","canonical_record":{"source":{"id":"1404.5409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-04-22T07:48:21Z","cross_cats_sorted":[],"title_canon_sha256":"8c9fcfb51ecde09e5915dbfe5db3e7e98690d9eb400aa2b74195b73482acf79e","abstract_canon_sha256":"8d549111c7d95f8bede29a14157f5d3cb459ebb8093e4b141b18a71f5524c55c"},"schema_version":"1.0"},"canonical_sha256":"099998e929851a1f6ff114a2d6c2e0b269c7dcc52596fdc44bb47c5aaff2fa0c","source":{"kind":"arxiv","id":"1404.5409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5409","created_at":"2026-05-18T02:53:31Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5409v1","created_at":"2026-05-18T02:53:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5409","created_at":"2026-05-18T02:53:31Z"},{"alias_kind":"pith_short_12","alias_value":"BGMZR2JJQUNB","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BGMZR2JJQUNB637R","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BGMZR2JJ","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BGMZR2JJQUNB637RCSRNNQXAWJ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-04-22T07:48:21Z","cross_cats_sorted":[],"title_canon_sha256":"8c9fcfb51ecde09e5915dbfe5db3e7e98690d9eb400aa2b74195b73482acf79e","abstract_canon_sha256":"8d549111c7d95f8bede29a14157f5d3cb459ebb8093e4b141b18a71f5524c55c"},"schema_version":"1.0"},"canonical_sha256":"099998e929851a1f6ff114a2d6c2e0b269c7dcc52596fdc44bb47c5aaff2fa0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:31.553926Z","signature_b64":"urXtdohTuhvLymv3JRd+1XjuusuEY2QZBA2NbqWPZtVR5lbzNGBs4tKNLyQF0rgXp/9F57nC8zMw8js19jxwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"099998e929851a1f6ff114a2d6c2e0b269c7dcc52596fdc44bb47c5aaff2fa0c","last_reissued_at":"2026-05-18T02:53:31.553345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:31.553345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5409","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:53:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fJVPJFPdwtrpJR8JnwkFPJ1U2G30hUSgsc+UZwR92koOUqHmyJ1V/balX3XDQGHUq0YEr6vFue1IeOBjp3ToCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:03:42.944717Z"},"content_sha256":"c40b859b13f5f287842847369783fab13af619b4a7971eba6a23a0eceec4b016","schema_version":"1.0","event_id":"sha256:c40b859b13f5f287842847369783fab13af619b4a7971eba6a23a0eceec4b016"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BGMZR2JJQUNB637RCSRNNQXAWJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Accurate solution of the Dirac equation on Lagrange meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.atom-ph","authors_text":"Daniel Baye, Livio Filippin, Michel Godefroid","submitted_at":"2014-04-22T07:48:21Z","abstract_excerpt":"The Lagrange-mesh method is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. With a basis of Lagrange functions involving associated Laguerre polynomials related to the Gauss quadrature, the method is applied to the Dirac equation. The potential may possess a $1/r$ singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers $n+1$ of mesh points, where $n$ is the principal quantum number. Numerically exact mean values of powers $-2$ to 3 of the radial coordinate $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5409","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":""},"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":"2026-05-18T02:53:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0UHUVKEd7T0th43sNm7Ld520eKcbkB6vgxBd0xrr2lD4U0gQaslAaA1mtLxxM0LaWbvVlGl7+7Y4KUFm8OtYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:03:42.945150Z"},"content_sha256":"fde80eb962c41969f408efc2d73435df067ea1d80d96ca5e2b6d73ec98f3a16f","schema_version":"1.0","event_id":"sha256:fde80eb962c41969f408efc2d73435df067ea1d80d96ca5e2b6d73ec98f3a16f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGMZR2JJQUNB637RCSRNNQXAWJ/bundle.json","state_url":"https://pith.science/pith/BGMZR2JJQUNB637RCSRNNQXAWJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGMZR2JJQUNB637RCSRNNQXAWJ/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":"2026-05-31T08:03:42Z","links":{"resolver":"https://pith.science/pith/BGMZR2JJQUNB637RCSRNNQXAWJ","bundle":"https://pith.science/pith/BGMZR2JJQUNB637RCSRNNQXAWJ/bundle.json","state":"https://pith.science/pith/BGMZR2JJQUNB637RCSRNNQXAWJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGMZR2JJQUNB637RCSRNNQXAWJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BGMZR2JJQUNB637RCSRNNQXAWJ","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":"8d549111c7d95f8bede29a14157f5d3cb459ebb8093e4b141b18a71f5524c55c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-04-22T07:48:21Z","title_canon_sha256":"8c9fcfb51ecde09e5915dbfe5db3e7e98690d9eb400aa2b74195b73482acf79e"},"schema_version":"1.0","source":{"id":"1404.5409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5409","created_at":"2026-05-18T02:53:31Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5409v1","created_at":"2026-05-18T02:53:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5409","created_at":"2026-05-18T02:53:31Z"},{"alias_kind":"pith_short_12","alias_value":"BGMZR2JJQUNB","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BGMZR2JJQUNB637R","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BGMZR2JJ","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:fde80eb962c41969f408efc2d73435df067ea1d80d96ca5e2b6d73ec98f3a16f","target":"graph","created_at":"2026-05-18T02:53:31Z","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":"The Lagrange-mesh method is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. With a basis of Lagrange functions involving associated Laguerre polynomials related to the Gauss quadrature, the method is applied to the Dirac equation. The potential may possess a $1/r$ singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers $n+1$ of mesh points, where $n$ is the principal quantum number. Numerically exact mean values of powers $-2$ to 3 of the radial coordinate $","authors_text":"Daniel Baye, Livio Filippin, Michel Godefroid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-04-22T07:48:21Z","title":"Accurate solution of the Dirac equation on Lagrange meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5409","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:c40b859b13f5f287842847369783fab13af619b4a7971eba6a23a0eceec4b016","target":"record","created_at":"2026-05-18T02:53:31Z","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":"8d549111c7d95f8bede29a14157f5d3cb459ebb8093e4b141b18a71f5524c55c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.atom-ph","submitted_at":"2014-04-22T07:48:21Z","title_canon_sha256":"8c9fcfb51ecde09e5915dbfe5db3e7e98690d9eb400aa2b74195b73482acf79e"},"schema_version":"1.0","source":{"id":"1404.5409","kind":"arxiv","version":1}},"canonical_sha256":"099998e929851a1f6ff114a2d6c2e0b269c7dcc52596fdc44bb47c5aaff2fa0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"099998e929851a1f6ff114a2d6c2e0b269c7dcc52596fdc44bb47c5aaff2fa0c","first_computed_at":"2026-05-18T02:53:31.553345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:31.553345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"urXtdohTuhvLymv3JRd+1XjuusuEY2QZBA2NbqWPZtVR5lbzNGBs4tKNLyQF0rgXp/9F57nC8zMw8js19jxwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:31.553926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c40b859b13f5f287842847369783fab13af619b4a7971eba6a23a0eceec4b016","sha256:fde80eb962c41969f408efc2d73435df067ea1d80d96ca5e2b6d73ec98f3a16f"],"state_sha256":"63c26d10f5266dbd44ca060e6aeb4357165a2140a7efc61bae71ccd53394df2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Ek/TYQf2a0aPGWUJLy7bl3lXJl7qpK3p8SNKuxzO3PeRQPmtNCkEL7KArSbktoFYUNtv8kbQBreka9oBI5vAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:03:42.947753Z","bundle_sha256":"038b0a6a9becfe8d38a3e68a46898d0dfc4f97e9407c11019205a437a7544a8d"}}