{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NS5IWP3ONKCNJGHU2LSBMZEMO4","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":"9f7c8022bb2377e3fa2776477fc95b8b478babab8918fc977714c81448b17fd1","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-29T15:58:42Z","title_canon_sha256":"3318f0c6bf5e13966274c37421d0eba90b7419609fe4857003840de52788189b"},"schema_version":"1.0","source":{"id":"1505.08100","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.08100","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1505.08100v1","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.08100","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"NS5IWP3ONKCN","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NS5IWP3ONKCNJGHU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NS5IWP3O","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:c91a230b326c5f27bed0254d4abbcd3361efa41a0eb87228ac65b4561dac37dd","target":"graph","created_at":"2026-05-18T01:59:59Z","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 investigate the consequences of one extra compactified dimension for the energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to $1/|x|^2$ in non-compactified 4d space. The calculations were performed numerically by diagonalizing the Hamiltonian in two different sets of basis vectors. The energy levels and electron probability density are plotted as a function of the compactification radius. The occurrence of several physical effects is discussed and interpreted.","authors_text":"Martin Bure\\v{s}","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-29T15:58:42Z","title":"Energy spectrum of the hydrogen atom in a space with one compactified extra dimension, $\\mathbb{R}^3 \\times S^1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08100","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":"sha256:855250b9e2207338177665e80b8501ea97a789585dfcb15108dfb005ca29d072","target":"record","created_at":"2026-05-18T01:59:59Z","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":"9f7c8022bb2377e3fa2776477fc95b8b478babab8918fc977714c81448b17fd1","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-05-29T15:58:42Z","title_canon_sha256":"3318f0c6bf5e13966274c37421d0eba90b7419609fe4857003840de52788189b"},"schema_version":"1.0","source":{"id":"1505.08100","kind":"arxiv","version":1}},"canonical_sha256":"6cba8b3f6e6a84d498f4d2e416648c770ab89fffc571d6d734421e0922187f57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cba8b3f6e6a84d498f4d2e416648c770ab89fffc571d6d734421e0922187f57","first_computed_at":"2026-05-18T01:59:59.696827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:59.696827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hyvzWiARvzFj8mDWEBOCWk6Ip22j31lkDQCvtf+sAqmSfwv7/sRVByjPPd3i/tu1AxesfiNLn95TmD1CmuOGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:59.697429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.08100","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:855250b9e2207338177665e80b8501ea97a789585dfcb15108dfb005ca29d072","sha256:c91a230b326c5f27bed0254d4abbcd3361efa41a0eb87228ac65b4561dac37dd"],"state_sha256":"aa5cdbc3f073f7ef7731970c8d2b877c5da75dfe5bc2722f6d5934f10aae7a42"}