{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FO3S36ARFNSJ7KYAI6I5P73UXK","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":"17da2dc867490294417153843a24ecae99f0c26423b0b63c61fc03c1168382f4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2025-06-19T09:51:48Z","title_canon_sha256":"2493bbc00ac350a4b9a7b3d3328f59e683bb629b2730b8d14d63ec0d1773ad12"},"schema_version":"1.0","source":{"id":"2506.16178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.16178","created_at":"2026-07-05T11:24:32Z"},{"alias_kind":"arxiv_version","alias_value":"2506.16178v1","created_at":"2026-07-05T11:24:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.16178","created_at":"2026-07-05T11:24:32Z"},{"alias_kind":"pith_short_12","alias_value":"FO3S36ARFNSJ","created_at":"2026-07-05T11:24:32Z"},{"alias_kind":"pith_short_16","alias_value":"FO3S36ARFNSJ7KYA","created_at":"2026-07-05T11:24:32Z"},{"alias_kind":"pith_short_8","alias_value":"FO3S36AR","created_at":"2026-07-05T11:24:32Z"}],"graph_snapshots":[{"event_id":"sha256:783a6780811c290c2acc97f08e21b68ce84218d518f96b37faaa07a787b27b97","target":"graph","created_at":"2026-07-05T11:24:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.16178/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a bound state (an eigenfunction) $\\psi$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $\\gamma$ and of the one-particle kinetic energy density matrix $\\tau$ associated with $\\psi$. The paper contains two results. First, we obtain the bounds $\\lambda_k(\\gamma)\\le C_1 k^{-8/3}$ and $\\lambda_k(\\tau)\\le C_2 k^{-2}$ with some positive constants $C_1, C_2$ that depend explicitly on the eigenfunction $\\psi$. The sharpness of these bounds is confirmed by the asymptotic results obtained by the author in earlier papers. The advantage of these bounds over ","authors_text":"Alexander V. Sobolev","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2025-06-19T09:51:48Z","title":"Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16178","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:a42dc633b169916c7947bcf8afa20ddaa85aacddef85c1ee358de904e6b62608","target":"record","created_at":"2026-07-05T11:24:32Z","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":"17da2dc867490294417153843a24ecae99f0c26423b0b63c61fc03c1168382f4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2025-06-19T09:51:48Z","title_canon_sha256":"2493bbc00ac350a4b9a7b3d3328f59e683bb629b2730b8d14d63ec0d1773ad12"},"schema_version":"1.0","source":{"id":"2506.16178","kind":"arxiv","version":1}},"canonical_sha256":"2bb72df8112b649fab004791d7ff74babc2beb91d3523b83b08396f2cfd599f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bb72df8112b649fab004791d7ff74babc2beb91d3523b83b08396f2cfd599f2","first_computed_at":"2026-07-05T11:24:32.210459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:24:32.210459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9A+yqn+zn8mPj2a7Z9EcS4eWeEv3w7q99fBD8ILOr7681cwOmX8CXnX21egAQETuubTBYGUEq906FwovIw1VCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:24:32.210937Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.16178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a42dc633b169916c7947bcf8afa20ddaa85aacddef85c1ee358de904e6b62608","sha256:783a6780811c290c2acc97f08e21b68ce84218d518f96b37faaa07a787b27b97"],"state_sha256":"87ccf0a4ece0ec493aae09b4eaa7b3b344f2bb59820e37314266e72968b5f188"}