{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CV7GUPBBY4USVRDIPPNBVEUPA7","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":"e0284358616e90cf85853b28fe3d9bab52bcc4cd2068e26e5837961417fe2600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-10-09T20:49:33Z","title_canon_sha256":"962c63787fab9c988ad92a79cd1caaf1c4a6bf560617e454e697a6f6ede1231f"},"schema_version":"1.0","source":{"id":"0910.1855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1855","created_at":"2026-05-18T04:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1855v1","created_at":"2026-05-18T04:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1855","created_at":"2026-05-18T04:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"CV7GUPBBY4US","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CV7GUPBBY4USVRDI","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CV7GUPBB","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:5233b9c6ce5861d52342d685c74a3c0b53cd0759b97b238c07654c841eee283f","target":"graph","created_at":"2026-05-18T04:37:33Z","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 derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for Hartree-Fock and Hartree-Fock-Bogoliubov calculations in deformed nuclei using realistic, finite-range effective interactions between nucleons. The results given here are also relevant for microscopic many-body calculations in atomic and molecular physics, as the formalism can be applied to other types of interactions beyond the Gaussian form. The derivation is pre","authors_text":"W. Younes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-10-09T20:49:33Z","title":"Gaussian matrix elements in a cylindrical harmonic oscillator basis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1855","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":"sha256:11bcfa3352c5803cf92de30b582aae771c9f8ff3b502318c88453372f037c73e","target":"record","created_at":"2026-05-18T04:37:33Z","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":"e0284358616e90cf85853b28fe3d9bab52bcc4cd2068e26e5837961417fe2600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-10-09T20:49:33Z","title_canon_sha256":"962c63787fab9c988ad92a79cd1caaf1c4a6bf560617e454e697a6f6ede1231f"},"schema_version":"1.0","source":{"id":"0910.1855","kind":"arxiv","version":1}},"canonical_sha256":"157e6a3c21c7292ac4687bda1a928f07ff541ec0f396befad598983a13dcd920","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"157e6a3c21c7292ac4687bda1a928f07ff541ec0f396befad598983a13dcd920","first_computed_at":"2026-05-18T04:37:33.634784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:33.634784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KC/CyP+bk2//Sc+7NABvRiQ5P5FL8X2n75q3wx/JHCF0+TGWgCWBNvJOAtCl6M+wBAs1SMvlqSy94mCHbryCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:33.635447Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11bcfa3352c5803cf92de30b582aae771c9f8ff3b502318c88453372f037c73e","sha256:5233b9c6ce5861d52342d685c74a3c0b53cd0759b97b238c07654c841eee283f"],"state_sha256":"fb83212d0d077def99265dd612c2693dedac64ae8823631be406635c89dc1b5d"}