{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QNYWKGUGYVDIHKANRR5TK2DIHS","short_pith_number":"pith:QNYWKGUG","canonical_record":{"source":{"id":"1410.6113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-10-22T17:26:37Z","cross_cats_sorted":["physics.chem-ph"],"title_canon_sha256":"465f2840b6ed65f4f1c1a884b289b7b5e506afc57074a8917af87427eb5a86b2","abstract_canon_sha256":"d83c93b287b382e76f1fb0b84c807be436b71421346bedc16b6c8bbd365748a7"},"schema_version":"1.0"},"canonical_sha256":"8371651a86c54683a80d8c7b3568683cbbb29ce7840838ac1b1a8b5e15f88545","source":{"kind":"arxiv","id":"1410.6113","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6113","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6113v2","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6113","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"pith_short_12","alias_value":"QNYWKGUGYVDI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QNYWKGUGYVDIHKAN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QNYWKGUG","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QNYWKGUGYVDIHKANRR5TK2DIHS","target":"record","payload":{"canonical_record":{"source":{"id":"1410.6113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-10-22T17:26:37Z","cross_cats_sorted":["physics.chem-ph"],"title_canon_sha256":"465f2840b6ed65f4f1c1a884b289b7b5e506afc57074a8917af87427eb5a86b2","abstract_canon_sha256":"d83c93b287b382e76f1fb0b84c807be436b71421346bedc16b6c8bbd365748a7"},"schema_version":"1.0"},"canonical_sha256":"8371651a86c54683a80d8c7b3568683cbbb29ce7840838ac1b1a8b5e15f88545","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:20.182483Z","signature_b64":"Rj4zIfaIDCPKj4rKolRhEZwOv48T4aywSSfA4QaMheIWjCe9jwFU0Bqs0WX76G46qvwVZUe27OFFGnSBF29XAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8371651a86c54683a80d8c7b3568683cbbb29ce7840838ac1b1a8b5e15f88545","last_reissued_at":"2026-05-18T01:00:20.181784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:20.181784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.6113","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBNgJJrK+hg7WgGUMkF0IFgG1F0wTfE+5UVHx50LBYBZy6ZY179q7MzGxD9qMGvP70lGW/TAhHZ/eLVK3HNjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T11:45:26.710652Z"},"content_sha256":"3f438f0f130e5e2300d59da182c69503469ae4391598258f94ef8d03e4303df6","schema_version":"1.0","event_id":"sha256:3f438f0f130e5e2300d59da182c69503469ae4391598258f94ef8d03e4303df6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QNYWKGUGYVDIHKANRR5TK2DIHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. II. Neumann expansion of the exchange integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Micha{\\l} Lesiuk, Robert Moszynski","submitted_at":"2014-10-22T17:26:37Z","abstract_excerpt":"In this paper we consider calculation of two-centre exchange integrals over Slater-type orbitals (STOs). We apply the Neumann expansion of the Coulomb interaction potential and consider calculation of all basic quantities which appear in the resulting expression. Analytical closed-form equations for all auxiliary quantities have already been known but they suffer from large digital erosion when some of the parameters are large or small. We derive two differential equations which are obeyed by the most difficult basic integrals. Taking them as a starting point, useful series expansions for smal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6113","kind":"arxiv","version":2},"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":"2026-05-18T01:00:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MyX7IYYwaTPtBpgmzRgpo8A014NxvZgP5+Q206tjHaTHOb0B05zPJ5b2zvgO/KviT46AYZCMfswowlbZSg6yBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T11:45:26.711000Z"},"content_sha256":"8dc203ab2a7f1404f6a6f4625d246956ea3ee0de5ad099c7206ad26276a60341","schema_version":"1.0","event_id":"sha256:8dc203ab2a7f1404f6a6f4625d246956ea3ee0de5ad099c7206ad26276a60341"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QNYWKGUGYVDIHKANRR5TK2DIHS/bundle.json","state_url":"https://pith.science/pith/QNYWKGUGYVDIHKANRR5TK2DIHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QNYWKGUGYVDIHKANRR5TK2DIHS/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":"2026-06-23T11:45:26Z","links":{"resolver":"https://pith.science/pith/QNYWKGUGYVDIHKANRR5TK2DIHS","bundle":"https://pith.science/pith/QNYWKGUGYVDIHKANRR5TK2DIHS/bundle.json","state":"https://pith.science/pith/QNYWKGUGYVDIHKANRR5TK2DIHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QNYWKGUGYVDIHKANRR5TK2DIHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QNYWKGUGYVDIHKANRR5TK2DIHS","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":"d83c93b287b382e76f1fb0b84c807be436b71421346bedc16b6c8bbd365748a7","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-10-22T17:26:37Z","title_canon_sha256":"465f2840b6ed65f4f1c1a884b289b7b5e506afc57074a8917af87427eb5a86b2"},"schema_version":"1.0","source":{"id":"1410.6113","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6113","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6113v2","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6113","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"pith_short_12","alias_value":"QNYWKGUGYVDI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QNYWKGUGYVDIHKAN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QNYWKGUG","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:8dc203ab2a7f1404f6a6f4625d246956ea3ee0de5ad099c7206ad26276a60341","target":"graph","created_at":"2026-05-18T01:00:20Z","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":"In this paper we consider calculation of two-centre exchange integrals over Slater-type orbitals (STOs). We apply the Neumann expansion of the Coulomb interaction potential and consider calculation of all basic quantities which appear in the resulting expression. Analytical closed-form equations for all auxiliary quantities have already been known but they suffer from large digital erosion when some of the parameters are large or small. We derive two differential equations which are obeyed by the most difficult basic integrals. Taking them as a starting point, useful series expansions for smal","authors_text":"Micha{\\l} Lesiuk, Robert Moszynski","cross_cats":["physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-10-22T17:26:37Z","title":"Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. II. Neumann expansion of the exchange integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6113","kind":"arxiv","version":2},"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":"sha256:3f438f0f130e5e2300d59da182c69503469ae4391598258f94ef8d03e4303df6","target":"record","created_at":"2026-05-18T01:00:20Z","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":"d83c93b287b382e76f1fb0b84c807be436b71421346bedc16b6c8bbd365748a7","cross_cats_sorted":["physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-10-22T17:26:37Z","title_canon_sha256":"465f2840b6ed65f4f1c1a884b289b7b5e506afc57074a8917af87427eb5a86b2"},"schema_version":"1.0","source":{"id":"1410.6113","kind":"arxiv","version":2}},"canonical_sha256":"8371651a86c54683a80d8c7b3568683cbbb29ce7840838ac1b1a8b5e15f88545","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8371651a86c54683a80d8c7b3568683cbbb29ce7840838ac1b1a8b5e15f88545","first_computed_at":"2026-05-18T01:00:20.181784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:20.181784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rj4zIfaIDCPKj4rKolRhEZwOv48T4aywSSfA4QaMheIWjCe9jwFU0Bqs0WX76G46qvwVZUe27OFFGnSBF29XAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:20.182483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6113","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f438f0f130e5e2300d59da182c69503469ae4391598258f94ef8d03e4303df6","sha256:8dc203ab2a7f1404f6a6f4625d246956ea3ee0de5ad099c7206ad26276a60341"],"state_sha256":"26c8488008e6368519ad28d843b81c84b2c52a4c7fd2437e28378ca500022b89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Db6MplTrDo1WC/XFxb30grxO0udz0MoJ4UMn3cTPNhEW1kT6k/fgx53C5Y0HUPXLcTGaVp3z/FYs0YKFaLVXDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T11:45:26.713141Z","bundle_sha256":"2a10c7eb9930028df22a2ac7d4a61d60a164791b75bed6a31f965d21b8363f02"}}