{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:RZ664PPY2RNQL5DOSUP4WYC3FG","short_pith_number":"pith:RZ664PPY","schema_version":"1.0","canonical_sha256":"8e7dee3df8d45b05f46e951fcb605b29ac362864aa84b6b5c342f87df7f01603","source":{"kind":"arxiv","id":"0904.3001","version":2},"attestation_state":"computed","paper":{"title":"Complexity of D-dimensional hydrogenic systems in position and momentum spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"D. Manzano, J. S. Dehesa, S. Lopez-Rosa","submitted_at":"2009-04-20T11:04:28Z","abstract_excerpt":"The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal spaces. This quantity, which is the product of the disequilibrium or averaging density and the Shannon entropic power, is mathematically expressed for both ground and excited stationary states in terms of certain entropic functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. We emphasize the ground and circular states, where the complexity "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0904.3001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-04-20T11:04:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9640b11fb41f190fa1f9ed97a5c8460a8558df2ec3b7b85dcdbb583ebe3df9bc","abstract_canon_sha256":"68940ddd2694bcd1ceff05d3ed9c5ed6f392aac4578446c4959d6d908f6130bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:58.904817Z","signature_b64":"SSLor3wlOfKOXzZ99P6vRgP2kaNzs+khTT8euatl0zXhShWx0b4fCnUvQKoJbljO+3vTmFIdeDzFdt4YLBoCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e7dee3df8d45b05f46e951fcb605b29ac362864aa84b6b5c342f87df7f01603","last_reissued_at":"2026-05-18T02:13:58.904071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:58.904071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complexity of D-dimensional hydrogenic systems in position and momentum spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"D. Manzano, J. S. Dehesa, S. Lopez-Rosa","submitted_at":"2009-04-20T11:04:28Z","abstract_excerpt":"The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal spaces. This quantity, which is the product of the disequilibrium or averaging density and the Shannon entropic power, is mathematically expressed for both ground and excited stationary states in terms of certain entropic functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. We emphasize the ground and circular states, where the complexity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.3001","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0904.3001","created_at":"2026-05-18T02:13:58.904207+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.3001v2","created_at":"2026-05-18T02:13:58.904207+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.3001","created_at":"2026-05-18T02:13:58.904207+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZ664PPY2RNQ","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZ664PPY2RNQL5DO","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZ664PPY","created_at":"2026-05-18T12:26:01.383474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG","json":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG.json","graph_json":"https://pith.science/api/pith-number/RZ664PPY2RNQL5DOSUP4WYC3FG/graph.json","events_json":"https://pith.science/api/pith-number/RZ664PPY2RNQL5DOSUP4WYC3FG/events.json","paper":"https://pith.science/paper/RZ664PPY"},"agent_actions":{"view_html":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG","download_json":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG.json","view_paper":"https://pith.science/paper/RZ664PPY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.3001&json=true","fetch_graph":"https://pith.science/api/pith-number/RZ664PPY2RNQL5DOSUP4WYC3FG/graph.json","fetch_events":"https://pith.science/api/pith-number/RZ664PPY2RNQL5DOSUP4WYC3FG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG/action/storage_attestation","attest_author":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG/action/author_attestation","sign_citation":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG/action/citation_signature","submit_replication":"https://pith.science/pith/RZ664PPY2RNQL5DOSUP4WYC3FG/action/replication_record"}},"created_at":"2026-05-18T02:13:58.904207+00:00","updated_at":"2026-05-18T02:13:58.904207+00:00"}