{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VILHXU4ZMC7AJJB5GZFVQCDH3Y","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":"f4e16d3734d1aa0e15c07652056b9f4310513699f08521050babdfa72e5d764b","cross_cats_sorted":["physics.atom-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-05T01:20:33Z","title_canon_sha256":"667c0d38d05f7257c0837153bb3450d9524aa39a81765f4da5a531d646a39ae8"},"schema_version":"1.0","source":{"id":"1209.0839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0839","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0839v2","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0839","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"VILHXU4ZMC7A","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VILHXU4ZMC7AJJB5","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VILHXU4Z","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:5f1c4e8692a21fc960cf39a698dcffacaf68bbaca706c9203bb225f5fe745d00","target":"graph","created_at":"2026-05-18T03:39:04Z","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":"We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the int","authors_text":"Micha{\\l} Lesiuk, Robert Moszynski","cross_cats":["physics.atom-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-05T01:20:33Z","title":"Analytical two-center integrals over Slater geminal functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0839","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":"sha256:83facfa2cd179b173b8c02118db4ce8b1984018ad56be70078bf648147df6db5","target":"record","created_at":"2026-05-18T03:39:04Z","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":"f4e16d3734d1aa0e15c07652056b9f4310513699f08521050babdfa72e5d764b","cross_cats_sorted":["physics.atom-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-05T01:20:33Z","title_canon_sha256":"667c0d38d05f7257c0837153bb3450d9524aa39a81765f4da5a531d646a39ae8"},"schema_version":"1.0","source":{"id":"1209.0839","kind":"arxiv","version":2}},"canonical_sha256":"aa167bd39960be04a43d364b580867de15932157f6a6a12269e67add7baa90e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa167bd39960be04a43d364b580867de15932157f6a6a12269e67add7baa90e6","first_computed_at":"2026-05-18T03:39:04.904264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:04.904264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"05O+OZtXrqT5Vb1d4fBCEyYQGepnXl9PEBFLM3gxUoyf/Dm+OF/812j1abqED7ysRYB5j1R5wr/0+aP5/8PiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:04.904717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83facfa2cd179b173b8c02118db4ce8b1984018ad56be70078bf648147df6db5","sha256:5f1c4e8692a21fc960cf39a698dcffacaf68bbaca706c9203bb225f5fe745d00"],"state_sha256":"5d01fdf36f4fe505cd57ff3658cdbf3b90bae7280f6cb2888cae303db71f3a52"}