{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FLHUJIWI4JSNPHETKSA2K25C35","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":"5812dfd4d5554fdc97a14a3b4100afab572d848d034c3ad1c017ddbd9f07913b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-11T09:19:08Z","title_canon_sha256":"eeb2353c827bbf65cb741307ca944db07ffb72ae37f03818877e83c9e437a671"},"schema_version":"1.0","source":{"id":"1807.04797","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04797","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04797v1","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04797","created_at":"2026-05-18T00:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"FLHUJIWI4JSN","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FLHUJIWI4JSNPHET","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FLHUJIWI","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:48d1eea7c64a8bf31bb0e1e9ecfc360d7b86ac43be267edfd985236e4bab7609","target":"graph","created_at":"2026-05-18T00:10:21Z","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":"The R\\'enyi entropies of Coulomb systems $R_{p}[\\rho], 0 < p < \\infty$ are logarithms of power functionals of the electron density $\\rho(\\vec{r})$ which quantify most appropriately the electron uncertainty and describe numerous physical observables. However, its analytical determination is a hard issue not yet solved except for the first lowest-lying energetic states of some specific systems. This is so even for the $D$-dimensional hydrogenic system, which is the main prototype of the multidimensional Coulomb many-body systems. Recently, the R\\'enyi entropies of this system have been found in ","authors_text":"D. Puertas-Centeno, I.V. Toranzo, J.S. Dehesa","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-11T09:19:08Z","title":"R\\'enyi entropies for multidimensional hydrogenic systems in position and momentum spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04797","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":"sha256:50d507709e0e0c91b73de185594b6c4e1a2d061ba6bfa4da74cf94ef67efdf8c","target":"record","created_at":"2026-05-18T00:10:21Z","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":"5812dfd4d5554fdc97a14a3b4100afab572d848d034c3ad1c017ddbd9f07913b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-11T09:19:08Z","title_canon_sha256":"eeb2353c827bbf65cb741307ca944db07ffb72ae37f03818877e83c9e437a671"},"schema_version":"1.0","source":{"id":"1807.04797","kind":"arxiv","version":1}},"canonical_sha256":"2acf44a2c8e264d79c935481a56ba2df6c6a5cb3042d482431dc1b0399dfb8c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2acf44a2c8e264d79c935481a56ba2df6c6a5cb3042d482431dc1b0399dfb8c0","first_computed_at":"2026-05-18T00:10:21.476311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:21.476311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+zsTTnqJZu0HU52/sYTmGMhgnjATi5pEhbBHjB4psViQPzpk7Ydqn7o253OC2nMDklMmTr9l5WxGZ+AvytWiCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:21.476915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04797","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50d507709e0e0c91b73de185594b6c4e1a2d061ba6bfa4da74cf94ef67efdf8c","sha256:48d1eea7c64a8bf31bb0e1e9ecfc360d7b86ac43be267edfd985236e4bab7609"],"state_sha256":"3532aa640a06a7f70108571714d2cd99b1176bce334edd4a40e0c26d00f6ad0f"}