{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:O2IDLDKKPPLELTJPMSHRS6WPRZ","short_pith_number":"pith:O2IDLDKK","schema_version":"1.0","canonical_sha256":"7690358d4a7bd645cd2f648f197acf8e596a035202de5ac3de0f72a3b945303f","source":{"kind":"arxiv","id":"1910.02987","version":1},"attestation_state":"computed","paper":{"title":"Semi-analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian expansion of Distance Operators W= R$_{C1}^{-n}$R$_{D1}^{-m}$, R$_{C1}^{-n}$r$_{12}^{-m}$, r$_{12}^{-n}$r$_{13}^{-m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Sandor Kristyan","submitted_at":"2019-08-16T12:48:18Z","abstract_excerpt":"The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)...rho(rk) W(r1,...,rk) dr1...drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expres"},"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":"1910.02987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2019-08-16T12:48:18Z","cross_cats_sorted":[],"title_canon_sha256":"152534379d28d08be720ce3d748b87875e1738b7a647d28cca54639528d96249","abstract_canon_sha256":"f6026d88213da6bdea7b29a5a2e0d8f6b3f07a4bc340ead119d269892ca94246"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:11:39.143565Z","signature_b64":"2fTw+GxTfBBr8I96wDdcYj2su/SxbVbBAsS4d7QKw7RnfLOwbJuHW+w6yQIxLLCsT3XV0wBEo8yYCU214AIOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7690358d4a7bd645cd2f648f197acf8e596a035202de5ac3de0f72a3b945303f","last_reissued_at":"2026-07-05T02:11:39.143118Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:11:39.143118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semi-analytic Evaluation of 1, 2 and 3-Electron Coulomb Integrals with Gaussian expansion of Distance Operators W= R$_{C1}^{-n}$R$_{D1}^{-m}$, R$_{C1}^{-n}$r$_{12}^{-m}$, r$_{12}^{-n}$r$_{13}^{-m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Sandor Kristyan","submitted_at":"2019-08-16T12:48:18Z","abstract_excerpt":"The equations derived help to evaluate semi-analytically (mostly for k=1,2 or 3) the important Coulomb integrals Int rho(r1)...rho(rk) W(r1,...,rk) dr1...drk, where the one-electron density, rho(r1), is a linear combination (LC) of Gaussian functions of position vector variable r1. It is capable to describe the electron clouds in molecules, solids or any media/ensemble of materials, weight W is the distance operator indicated in the title. R stands for nucleus-electron and r for electron-electron distances. The n=m=0 case is trivial, the (n,m)=(1,0) and (0,1) cases, for which analytical expres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.02987","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/1910.02987/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":"1910.02987","created_at":"2026-07-05T02:11:39.143176+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.02987v1","created_at":"2026-07-05T02:11:39.143176+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.02987","created_at":"2026-07-05T02:11:39.143176+00:00"},{"alias_kind":"pith_short_12","alias_value":"O2IDLDKKPPLE","created_at":"2026-07-05T02:11:39.143176+00:00"},{"alias_kind":"pith_short_16","alias_value":"O2IDLDKKPPLELTJP","created_at":"2026-07-05T02:11:39.143176+00:00"},{"alias_kind":"pith_short_8","alias_value":"O2IDLDKK","created_at":"2026-07-05T02:11:39.143176+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/O2IDLDKKPPLELTJPMSHRS6WPRZ","json":"https://pith.science/pith/O2IDLDKKPPLELTJPMSHRS6WPRZ.json","graph_json":"https://pith.science/api/pith-number/O2IDLDKKPPLELTJPMSHRS6WPRZ/graph.json","events_json":"https://pith.science/api/pith-number/O2IDLDKKPPLELTJPMSHRS6WPRZ/events.json","paper":"https://pith.science/paper/O2IDLDKK"},"agent_actions":{"view_html":"https://pith.science/pith/O2IDLDKKPPLELTJPMSHRS6WPRZ","download_json":"https://pith.science/pith/O2IDLDKKPPLELTJPMSHRS6WPRZ.json","view_paper":"https://pith.science/paper/O2IDLDKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.02987&json=true","fetch_graph":"https://pith.science/api/pith-number/O2IDLDKKPPLELTJPMSHRS6WPRZ/graph.json","fetch_events":"https://pith.science/api/pith-number/O2IDLDKKPPLELTJPMSHRS6WPRZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O2IDLDKKPPLELTJPMSHRS6WPRZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O2IDLDKKPPLELTJPMSHRS6WPRZ/action/storage_attestation","attest_author":"https://pith.science/pith/O2IDLDKKPPLELTJPMSHRS6WPRZ/action/author_attestation","sign_citation":"https://pith.science/pith/O2IDLDKKPPLELTJPMSHRS6WPRZ/action/citation_signature","submit_replication":"https://pith.science/pith/O2IDLDKKPPLELTJPMSHRS6WPRZ/action/replication_record"}},"created_at":"2026-07-05T02:11:39.143176+00:00","updated_at":"2026-07-05T02:11:39.143176+00:00"}