{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KDARN6DFYIKWYMHE45EBOV55C5","short_pith_number":"pith:KDARN6DF","canonical_record":{"source":{"id":"1401.7507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-29T13:20:52Z","cross_cats_sorted":["math.MP","physics.atom-ph","physics.comp-ph"],"title_canon_sha256":"3cb736235edb856f0a2212f91fc508f5919a69982d08a9b60f1aa5b11aa35729","abstract_canon_sha256":"6f007494a806fe42721f67860e81aeed7bd4a17436fdda5c43036660887c5454"},"schema_version":"1.0"},"canonical_sha256":"50c116f865c2156c30e4e7481757bd177b84e3aaa2a9e9b499dc3fd4e5aa51d3","source":{"kind":"arxiv","id":"1401.7507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7507","created_at":"2026-05-18T01:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7507v1","created_at":"2026-05-18T01:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7507","created_at":"2026-05-18T01:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"KDARN6DFYIKW","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KDARN6DFYIKWYMHE","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KDARN6DF","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KDARN6DFYIKWYMHE45EBOV55C5","target":"record","payload":{"canonical_record":{"source":{"id":"1401.7507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-29T13:20:52Z","cross_cats_sorted":["math.MP","physics.atom-ph","physics.comp-ph"],"title_canon_sha256":"3cb736235edb856f0a2212f91fc508f5919a69982d08a9b60f1aa5b11aa35729","abstract_canon_sha256":"6f007494a806fe42721f67860e81aeed7bd4a17436fdda5c43036660887c5454"},"schema_version":"1.0"},"canonical_sha256":"50c116f865c2156c30e4e7481757bd177b84e3aaa2a9e9b499dc3fd4e5aa51d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:59.924550Z","signature_b64":"++qjUmNswT+Nyb1h3jg82w4vVGnfYhgQUoAYzjeDbYKxG8PRth7oIVs0Xjc3tnNmtulrtrpphKTsKTR1xiaODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50c116f865c2156c30e4e7481757bd177b84e3aaa2a9e9b499dc3fd4e5aa51d3","last_reissued_at":"2026-05-18T01:44:59.923925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:59.923925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.7507","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":"2026-05-18T01:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K0nhUhT35KiDi3H5Gh7BSSiD+S7tuyQqf7m9GNPbUJTd/dxqmw3ebpzdCSB3ZgkwInvDIrK3X1ds7VpP8ypdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T15:17:12.516379Z"},"content_sha256":"a3faef277579f4bc5448fc1daf71eaf7083e46397412148bd4ef61293291b5b1","schema_version":"1.0","event_id":"sha256:a3faef277579f4bc5448fc1daf71eaf7083e46397412148bd4ef61293291b5b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KDARN6DFYIKWYMHE45EBOV55C5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic matrix elements for the two-electron atomic basis with logarithmic terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.atom-ph","physics.comp-ph"],"primary_cat":"math-ph","authors_text":"Evgeny Z. Liverts, Nir Barnea","submitted_at":"2014-01-29T13:20:52Z","abstract_excerpt":"The two-electron problem for the helium-like atom/ions in $S$-state is considered. The basis containing the integer powers of $\\ln r$, where $r$ is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions for the matrix elements of the corresponding Hamiltonian are presented. These expressions include only special functions presented by the built-in $Mathematica$ codes, what enables very fast and accurate computation of the matrix elements. The decisive contribution of the correct logarithmic terms to the behavior of the two-electron wave function in the vic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7507","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":"2026-05-18T01:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9h3lLNymF1pUjQ4B+y/RFX1okPFIBHfa1obVCSgeYm2FTTLnqlr94ALzd75AbcmR3nIPc/qH7xagNqANpHEtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T15:17:12.516735Z"},"content_sha256":"ca99e4d5fae9b9bd70c9d9c8f996fd9d17607bc4391e0809058315af2c0e6ae4","schema_version":"1.0","event_id":"sha256:ca99e4d5fae9b9bd70c9d9c8f996fd9d17607bc4391e0809058315af2c0e6ae4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KDARN6DFYIKWYMHE45EBOV55C5/bundle.json","state_url":"https://pith.science/pith/KDARN6DFYIKWYMHE45EBOV55C5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KDARN6DFYIKWYMHE45EBOV55C5/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":"2026-06-30T15:17:12Z","links":{"resolver":"https://pith.science/pith/KDARN6DFYIKWYMHE45EBOV55C5","bundle":"https://pith.science/pith/KDARN6DFYIKWYMHE45EBOV55C5/bundle.json","state":"https://pith.science/pith/KDARN6DFYIKWYMHE45EBOV55C5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KDARN6DFYIKWYMHE45EBOV55C5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KDARN6DFYIKWYMHE45EBOV55C5","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":"6f007494a806fe42721f67860e81aeed7bd4a17436fdda5c43036660887c5454","cross_cats_sorted":["math.MP","physics.atom-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-29T13:20:52Z","title_canon_sha256":"3cb736235edb856f0a2212f91fc508f5919a69982d08a9b60f1aa5b11aa35729"},"schema_version":"1.0","source":{"id":"1401.7507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7507","created_at":"2026-05-18T01:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7507v1","created_at":"2026-05-18T01:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7507","created_at":"2026-05-18T01:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"KDARN6DFYIKW","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KDARN6DFYIKWYMHE","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KDARN6DF","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:ca99e4d5fae9b9bd70c9d9c8f996fd9d17607bc4391e0809058315af2c0e6ae4","target":"graph","created_at":"2026-05-18T01:44:59Z","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 two-electron problem for the helium-like atom/ions in $S$-state is considered. The basis containing the integer powers of $\\ln r$, where $r$ is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions for the matrix elements of the corresponding Hamiltonian are presented. These expressions include only special functions presented by the built-in $Mathematica$ codes, what enables very fast and accurate computation of the matrix elements. The decisive contribution of the correct logarithmic terms to the behavior of the two-electron wave function in the vic","authors_text":"Evgeny Z. Liverts, Nir Barnea","cross_cats":["math.MP","physics.atom-ph","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-29T13:20:52Z","title":"Analytic matrix elements for the two-electron atomic basis with logarithmic terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7507","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:a3faef277579f4bc5448fc1daf71eaf7083e46397412148bd4ef61293291b5b1","target":"record","created_at":"2026-05-18T01:44:59Z","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":"6f007494a806fe42721f67860e81aeed7bd4a17436fdda5c43036660887c5454","cross_cats_sorted":["math.MP","physics.atom-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-01-29T13:20:52Z","title_canon_sha256":"3cb736235edb856f0a2212f91fc508f5919a69982d08a9b60f1aa5b11aa35729"},"schema_version":"1.0","source":{"id":"1401.7507","kind":"arxiv","version":1}},"canonical_sha256":"50c116f865c2156c30e4e7481757bd177b84e3aaa2a9e9b499dc3fd4e5aa51d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50c116f865c2156c30e4e7481757bd177b84e3aaa2a9e9b499dc3fd4e5aa51d3","first_computed_at":"2026-05-18T01:44:59.923925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:59.923925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"++qjUmNswT+Nyb1h3jg82w4vVGnfYhgQUoAYzjeDbYKxG8PRth7oIVs0Xjc3tnNmtulrtrpphKTsKTR1xiaODg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:59.924550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3faef277579f4bc5448fc1daf71eaf7083e46397412148bd4ef61293291b5b1","sha256:ca99e4d5fae9b9bd70c9d9c8f996fd9d17607bc4391e0809058315af2c0e6ae4"],"state_sha256":"2c13e34188149af431fc353c997d1a4dc6d7a1bfc345f30c3b65b41ba94fe985"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FkxPQaxLg8sbxvEwHsyCy0we54u2OMorr3KZLysftQDGiMPbZUPi7Uzqmil8a3hviR+90wzvO7Mm0S4WFAusCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T15:17:12.518709Z","bundle_sha256":"6ed8ec15027e510bcd8a9e5a765fb6f7c84725dd0fdbf4c2368e9078247268ad"}}