{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y7FWVHZNYZXBRLK5XVBZPR45D5","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":"26db405a7575c95f2010ceb15be2968254f1e90fde55024f60950bfd0ee33a91","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-09-06T11:33:14Z","title_canon_sha256":"bb124e8df8996b18e45f296e9b8e59681855b2e857be0d7d0ef8768e224813c9"},"schema_version":"1.0","source":{"id":"1209.1258","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1258","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1258v3","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1258","created_at":"2026-05-18T01:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"Y7FWVHZNYZXB","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y7FWVHZNYZXBRLK5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y7FWVHZN","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:889165466b212cdf8498b68200aa1164d400a482579229504aab69ec4b93ac0c","target":"graph","created_at":"2026-05-18T01:54:39Z","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":"Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional integral representation is found, which is suited for the numerical evaluation. Together with recurrence relations, it makes possible the calculation of the two-center two-electron integral with arbitrary powers of electron distances. Alternative approach via the Taylor series in the internuclear distance is also investigated. Although numerically slower, it can ","authors_text":"Krzysztof Pachucki","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-09-06T11:33:14Z","title":"Correlated exponential functions in high precision calculations for diatomic molecules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1258","kind":"arxiv","version":3},"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:d77df1207d756b7816ff2258ed93c11a2eccdd83429b82d02dfaf700798f92f2","target":"record","created_at":"2026-05-18T01:54:39Z","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":"26db405a7575c95f2010ceb15be2968254f1e90fde55024f60950bfd0ee33a91","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-09-06T11:33:14Z","title_canon_sha256":"bb124e8df8996b18e45f296e9b8e59681855b2e857be0d7d0ef8768e224813c9"},"schema_version":"1.0","source":{"id":"1209.1258","kind":"arxiv","version":3}},"canonical_sha256":"c7cb6a9f2dc66e18ad5dbd4397c79d1f7490933246430797d4cd4910fec5a92d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7cb6a9f2dc66e18ad5dbd4397c79d1f7490933246430797d4cd4910fec5a92d","first_computed_at":"2026-05-18T01:54:39.376288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:54:39.376288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"db3YXxGqrdpQWRpewOqkCCJsdK7xZYbVMdQ0bCSRQ1DFEfeozHJEpCC/cp6wf96Axc9qy9FAEKwcaOjqNgqfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:54:39.377042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1258","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d77df1207d756b7816ff2258ed93c11a2eccdd83429b82d02dfaf700798f92f2","sha256:889165466b212cdf8498b68200aa1164d400a482579229504aab69ec4b93ac0c"],"state_sha256":"f1c2dcf4d5cfdfd29da2656c9095c08fc81c2b722c1d33df8d1ec0ee709f845c"}