{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ZKQ5UUNIIGW2GGPCJ3VH5FRLEH","short_pith_number":"pith:ZKQ5UUNI","schema_version":"1.0","canonical_sha256":"caa1da51a841ada319e24eea7e962b21dd2736c9e94c601676913ce61cc492be","source":{"kind":"arxiv","id":"2606.17359","version":1},"attestation_state":"computed","paper":{"title":"Canonical regularization of the stationary Coulomb problem and an Aufbau-like spectral ordering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Anand Aruna Kumar","submitted_at":"2026-06-15T23:28:55Z","abstract_excerpt":"The stationary hydrogen atom has Coulomb degeneracy across orbital levels, whereas the Aufbau/Madelung ordering is an empirical, many-electron rule established in atomic physics. We examine the hydrogen atom through a regularized de Broglie--Bohm representation, in which stationary amplitude current constraints generate separable Sturm--Liouville branches. In this formulation, the radial, orbital, and magnetic sectors acquire canonical Langer-like inverse square corrections. The modified boundary value problems allow analytical solutions and produce a hydrogen-like spectrum with regularized ra"},"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":"2606.17359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-06-15T23:28:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a71fd102c4daf6b957494b109b89baea42b49e33f37fe554ec5d9df9a1ef34f0","abstract_canon_sha256":"f4bc57d5f0bd501de8451358cce5f049825dfccebdb71826df8f2c2f4586e2b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:10.095941Z","signature_b64":"INH9ocMFoDDkBzgeR3H/P7pwMG8G4M68YJ02Y//g7skLiJLn+zp5TojGdvt75lp6Rm3jj+6XXKOAr/bJZozoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caa1da51a841ada319e24eea7e962b21dd2736c9e94c601676913ce61cc492be","last_reissued_at":"2026-06-19T16:10:10.095570Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:10.095570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical regularization of the stationary Coulomb problem and an Aufbau-like spectral ordering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Anand Aruna Kumar","submitted_at":"2026-06-15T23:28:55Z","abstract_excerpt":"The stationary hydrogen atom has Coulomb degeneracy across orbital levels, whereas the Aufbau/Madelung ordering is an empirical, many-electron rule established in atomic physics. We examine the hydrogen atom through a regularized de Broglie--Bohm representation, in which stationary amplitude current constraints generate separable Sturm--Liouville branches. In this formulation, the radial, orbital, and magnetic sectors acquire canonical Langer-like inverse square corrections. The modified boundary value problems allow analytical solutions and produce a hydrogen-like spectrum with regularized ra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17359","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17359/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.17359","created_at":"2026-06-19T16:10:10.095638+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.17359v1","created_at":"2026-06-19T16:10:10.095638+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17359","created_at":"2026-06-19T16:10:10.095638+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKQ5UUNIIGW2","created_at":"2026-06-19T16:10:10.095638+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKQ5UUNIIGW2GGPC","created_at":"2026-06-19T16:10:10.095638+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKQ5UUNI","created_at":"2026-06-19T16:10:10.095638+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/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH","json":"https://pith.science/pith/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH.json","graph_json":"https://pith.science/api/pith-number/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/graph.json","events_json":"https://pith.science/api/pith-number/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/events.json","paper":"https://pith.science/paper/ZKQ5UUNI"},"agent_actions":{"view_html":"https://pith.science/pith/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH","download_json":"https://pith.science/pith/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH.json","view_paper":"https://pith.science/paper/ZKQ5UUNI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.17359&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/action/storage_attestation","attest_author":"https://pith.science/pith/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/action/author_attestation","sign_citation":"https://pith.science/pith/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/action/citation_signature","submit_replication":"https://pith.science/pith/ZKQ5UUNIIGW2GGPCJ3VH5FRLEH/action/replication_record"}},"created_at":"2026-06-19T16:10:10.095638+00:00","updated_at":"2026-06-19T16:10:10.095638+00:00"}