{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RTB6XXNVFGE3QFHRABY2PDJTZD","short_pith_number":"pith:RTB6XXNV","canonical_record":{"source":{"id":"2607.19197","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-21T15:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"1484ea72be27bd0705e88958d749097424a659434554c1d212c7b64f28fb151a","abstract_canon_sha256":"cbbe863a3a8a242d9a20fd27e4a8ea0fc33bb09e8134f220c503b258bf12f3aa"},"schema_version":"1.0"},"canonical_sha256":"8cc3ebddb52989b814f10071a78d33c8d3b87d2312db53dda06b3b5f50736d42","source":{"kind":"arxiv","id":"2607.19197","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19197","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19197v1","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19197","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"RTB6XXNVFGE3","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"pith_short_16","alias_value":"RTB6XXNVFGE3QFHR","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"pith_short_8","alias_value":"RTB6XXNV","created_at":"2026-07-22T01:24:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RTB6XXNVFGE3QFHRABY2PDJTZD","target":"record","payload":{"canonical_record":{"source":{"id":"2607.19197","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-21T15:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"1484ea72be27bd0705e88958d749097424a659434554c1d212c7b64f28fb151a","abstract_canon_sha256":"cbbe863a3a8a242d9a20fd27e4a8ea0fc33bb09e8134f220c503b258bf12f3aa"},"schema_version":"1.0"},"canonical_sha256":"8cc3ebddb52989b814f10071a78d33c8d3b87d2312db53dda06b3b5f50736d42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T01:24:13.727667Z","signature_b64":"wUdj7vNNFPvYb40wtSU3Vr3KEnVvHod/edUuMG6FyYHlEuFMlZC5S3C4NDpPrTVyVFjoFYvgYsezpvnljvD0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cc3ebddb52989b814f10071a78d33c8d3b87d2312db53dda06b3b5f50736d42","last_reissued_at":"2026-07-22T01:24:13.726717Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T01:24:13.726717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.19197","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-22T01:24:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDyXD2FOhl4LagPEkR3m8ToW/W4d3oh1QjEpanlGEsFB7B7ITO+KR5FHuq3SLqWp4RyN8VojkYb19vZV6csdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T04:38:16.845853Z"},"content_sha256":"6ddf8207912b730f1aea400ebb884d98a3674e13ae47a424cec554d454e11622","schema_version":"1.0","event_id":"sha256:6ddf8207912b730f1aea400ebb884d98a3674e13ae47a424cec554d454e11622"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RTB6XXNVFGE3QFHRABY2PDJTZD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bound state solutions of the Schr\\\"odinger equation for the atomic systems interacting with the radial screened Coulomb potential: analytical approximation methods","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Fatma Zohra Khaled, Mokhtar Falek, Mustafa Moumni","submitted_at":"2026-07-21T15:31:22Z","abstract_excerpt":"We investigate the bound state properties of the hydrogen-like atoms in the radial screened Coulomb potential (RSCP). using three complementary analytical approaches - expectation values with Coulomb and Kratzer reference states, variational optimization with a scaled Kratzer basis, and the Hellmann-Feynman theorem - we derive approximate energy eigenvalues as function of the screening parameter c. Benchmarked against high-precision generalized pseudospectral data, the expectation value-approach with the Kratzer basis achieves relative errors of 0.63% for the first ten s-states at $c=0.1$, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19197","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/2607.19197/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-22T01:24:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nubz8iWSkkUPK/2a2gL8MsHKVQ9PVU2ziYW3O5djtNWnrbp0/G6y7bXaIxIRiwe3gMQRhCM4nBfCPWVN+3DMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T04:38:16.846149Z"},"content_sha256":"10387457333e82c5b65336fd3d0696a4f622a2f02638229930363ea1f7847e8d","schema_version":"1.0","event_id":"sha256:10387457333e82c5b65336fd3d0696a4f622a2f02638229930363ea1f7847e8d"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:RTB6XXNVFGE3QFHRABY2PDJTZD","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1088/1402-4896/ad42e5) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Xu L, Fernandez F M, Jiao L G, Montgomery Jr H E, Ho Y K and Fritzsche S 2024 Revisiting the energy spectrum of the radial screened Coulomb potentialPhys. Scr.99065404 (doi:10.1088/1402- 4896/ad42e5) 20 IOP PublishingJournalvv(yyyy) aaaaaa ","arxiv_id":"2607.19197","detector":"doi_compliance","evidence":{"ref_index":34,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1088/1402-","reconstructed_doi":"10.1088/1402-4896/ad42e5"},"severity":"advisory","ref_index":34,"audited_at":"2026-08-01T13:28:51.688403Z","event_type":"pith.integrity.v1","detected_doi":"10.1088/1402-4896/ad42e5","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"769a85d777f09b16f0f39c73061fe8a07e54d960ee3c4dfb09d7e5b749fb1324","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":15865,"payload_sha256":"e1c5ef29f99b9ee345bfd7ccd82f218a9df2b0bcd617102b81438c7754308d5a","signature_b64":"LF1zgfAnmCOFAIy+5XkdICiUj7GiL/2czSDwGZoehFVYuYfSMrsHyqfCgbAxRQtJ5Lesa3QoouVo4JrAWOcKBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T13:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xUURRva3zJHAyUSGNaGBuDWRRStO4eloqkZ4sOuvWvwKyHY6eQ80NutWYNHcERHUj+ugC/wqkPu/kBqSAi9pDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T04:38:16.885888Z"},"content_sha256":"64cf5bea82991e8f74b22a4e143c63c037d6a0bff26ece15d01e4e10c21551a1","schema_version":"1.0","event_id":"sha256:64cf5bea82991e8f74b22a4e143c63c037d6a0bff26ece15d01e4e10c21551a1"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:RTB6XXNVFGE3QFHRABY2PDJTZD","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1088/0953-4075/42/17/175006) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Ghoshal A and Ho Y K 2009 Ground states and doubly excited resonance states of H − embedded in dense quantum plasmasJ. Phys. B: At. Mol. Opt. Phys.42175006 (doi:10.1088/0953- 4075/42/17/175006)","arxiv_id":"2607.19197","detector":"doi_compliance","evidence":{"ref_index":30,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1088/0953-","reconstructed_doi":"10.1088/0953-4075/42/17/175006"},"severity":"advisory","ref_index":30,"audited_at":"2026-08-01T13:28:51.688403Z","event_type":"pith.integrity.v1","detected_doi":"10.1088/0953-4075/42/17/175006","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"53f09b96824578c1bacf4e38173c6a2237d25641fe6ddbf19db7f5640bd813c9","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":15864,"payload_sha256":"375926ab159e703b0f2cf1f89180c98215b3d2909a7614a768b1ce722cbe8fc7","signature_b64":"dhXRyZ6hDCXjLLixlNJejyIvBkolAMkD1ht9phJrVt7lEqWXuuDGNqqaaPs632mBZv/KXux3bu6mOPhtN+XPAg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T13:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Vh+jVTnBDMaPKMO8BeZmBFcOXexyHCPirxTG8reQmian96P9thdKNNeRnIX9hdO/eYc7Atfg3lRJVH9i058Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T04:38:16.886129Z"},"content_sha256":"a4010ba89d94314f7490d2b08d238929b4ebe5e2f695de4ca132b93746aa1efc","schema_version":"1.0","event_id":"sha256:a4010ba89d94314f7490d2b08d238929b4ebe5e2f695de4ca132b93746aa1efc"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:RTB6XXNVFGE3QFHRABY2PDJTZD","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s40094-015-0173-9) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Falaye B J, Ikhdair S M and Hamzavi M 2015 Shifted Tietz-Wei oscillator for simulating the atomic interaction in diatomic moleculesJ Theor. Appl. Phys.9151–158 (doi:10.1007/s40094- 015-0173-9)","arxiv_id":"2607.19197","detector":"doi_compliance","evidence":{"ref_index":23,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s40094-","reconstructed_doi":"10.1007/s40094-015-0173-9"},"severity":"advisory","ref_index":23,"audited_at":"2026-08-01T13:28:51.688403Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s40094-015-0173-9","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"4025d4d7d8f2971c5e09f15621d9c83897f79b9d2c487322f59a92e37b11eacc","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":15863,"payload_sha256":"cb1d47ec11e7706163346b507919c69c01f97f98b3fa8d0c1a8c76e50fec9b88","signature_b64":"Yj0XXhZgccvefnyiIl/BQvWH74eq/wgw0MtVpkQsNnHe/hzLeXtyYGmtHsIf6sfzoDCvV5gH0hP3XNUjr35BDg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T13:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0sYB2gY8GcACCJ00YKrGD4Nn4A/z5WXUA8bxOrXMtwkex+krO26gjLRbhLWGakDP4PhXNriPj0bWAWVI2usxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T04:38:16.886346Z"},"content_sha256":"e8b3a23c688b72200ef870736e8fa292a233444b5658e53ece31a09ff5ca0ab0","schema_version":"1.0","event_id":"sha256:e8b3a23c688b72200ef870736e8fa292a233444b5658e53ece31a09ff5ca0ab0"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:RTB6XXNVFGE3QFHRABY2PDJTZD","target":"integrity","payload":{"note":"Identifier '10.11429/ppmsj1919.17.0' is syntactically valid but the DOI registry (doi.org) returned 404, and Crossref / OpenAlex / internal corpus also have no record. The cited work could not be located through any authoritative source.","snippet":"Yukawa H 1935 On the interaction of elementary particles IProc. Phys. Math. Soc. Japan17 48–57 (doi:10.11429/ppmsj1919.17.0˙48)","arxiv_id":"2607.19197","detector":"doi_compliance","evidence":{"doi":"10.11429/ppmsj1919.17.0","arxiv_id":null,"ref_index":4,"raw_excerpt":"Yukawa H 1935 On the interaction of elementary particles IProc. Phys. Math. Soc. Japan17 48–57 (doi:10.11429/ppmsj1919.17.0˙48)","parse_status":"well_formed","verdict_class":"cross_source","checked_sources":["crossref_by_doi","openalex_by_doi","doi_org_head"],"resolution_status":"hard_miss"},"severity":"critical","ref_index":4,"audited_at":"2026-08-01T13:28:51.688403Z","event_type":"pith.integrity.v1","detected_doi":"10.11429/ppmsj1919.17.0","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"unresolvable_identifier","evidence_hash":"4318e1ee6cdd874d55c380e99341fbb85e08f5bce326617097984d83a1231236","paper_version":1,"verdict_class":"cross_source","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":15862,"payload_sha256":"f4f4a7fa670e7f759417c890ee7773b8f4189094c7289a24db5bf38b5c4efaf9","signature_b64":"PhkNcsPJh9VjPBcgO2yGEr/Y7kAEZH8fCD/E7owPVidNw2yRYJyH6zdC7vXCHtIE0fffDNITby9/udCzvQ13AQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T13:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4yxryKRnf/MWZKeUlSzwP8vDPuADpKRRTo4PA3MqjuR015FTSG0p7lPsJ88gxNnA7dDCBE8tjnLUi6zi4nhAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T04:38:16.886574Z"},"content_sha256":"766fb58ab841b719194d7cc362d232f85bfa7ec6bc64bd83c61460f8bda88cdd","schema_version":"1.0","event_id":"sha256:766fb58ab841b719194d7cc362d232f85bfa7ec6bc64bd83c61460f8bda88cdd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RTB6XXNVFGE3QFHRABY2PDJTZD/bundle.json","state_url":"https://pith.science/pith/RTB6XXNVFGE3QFHRABY2PDJTZD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RTB6XXNVFGE3QFHRABY2PDJTZD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-02T04:38:16Z","links":{"resolver":"https://pith.science/pith/RTB6XXNVFGE3QFHRABY2PDJTZD","bundle":"https://pith.science/pith/RTB6XXNVFGE3QFHRABY2PDJTZD/bundle.json","state":"https://pith.science/pith/RTB6XXNVFGE3QFHRABY2PDJTZD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RTB6XXNVFGE3QFHRABY2PDJTZD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RTB6XXNVFGE3QFHRABY2PDJTZD","merge_version":"pith-open-graph-merge-v1","event_count":6,"valid_event_count":6,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cbbe863a3a8a242d9a20fd27e4a8ea0fc33bb09e8134f220c503b258bf12f3aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-21T15:31:22Z","title_canon_sha256":"1484ea72be27bd0705e88958d749097424a659434554c1d212c7b64f28fb151a"},"schema_version":"1.0","source":{"id":"2607.19197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19197","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19197v1","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19197","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"RTB6XXNVFGE3","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"pith_short_16","alias_value":"RTB6XXNVFGE3QFHR","created_at":"2026-07-22T01:24:13Z"},{"alias_kind":"pith_short_8","alias_value":"RTB6XXNV","created_at":"2026-07-22T01:24:13Z"}],"graph_snapshots":[{"event_id":"sha256:10387457333e82c5b65336fd3d0696a4f622a2f02638229930363ea1f7847e8d","target":"graph","created_at":"2026-07-22T01:24:13Z","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/2607.19197/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the bound state properties of the hydrogen-like atoms in the radial screened Coulomb potential (RSCP). using three complementary analytical approaches - expectation values with Coulomb and Kratzer reference states, variational optimization with a scaled Kratzer basis, and the Hellmann-Feynman theorem - we derive approximate energy eigenvalues as function of the screening parameter c. Benchmarked against high-precision generalized pseudospectral data, the expectation value-approach with the Kratzer basis achieves relative errors of 0.63% for the first ten s-states at $c=0.1$, whi","authors_text":"Fatma Zohra Khaled, Mokhtar Falek, Mustafa Moumni","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-21T15:31:22Z","title":"Bound state solutions of the Schr\\\"odinger equation for the atomic systems interacting with the radial screened Coulomb potential: analytical approximation methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19197","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":"sha256:6ddf8207912b730f1aea400ebb884d98a3674e13ae47a424cec554d454e11622","target":"record","created_at":"2026-07-22T01:24:13Z","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":"cbbe863a3a8a242d9a20fd27e4a8ea0fc33bb09e8134f220c503b258bf12f3aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-21T15:31:22Z","title_canon_sha256":"1484ea72be27bd0705e88958d749097424a659434554c1d212c7b64f28fb151a"},"schema_version":"1.0","source":{"id":"2607.19197","kind":"arxiv","version":1}},"canonical_sha256":"8cc3ebddb52989b814f10071a78d33c8d3b87d2312db53dda06b3b5f50736d42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cc3ebddb52989b814f10071a78d33c8d3b87d2312db53dda06b3b5f50736d42","first_computed_at":"2026-07-22T01:24:13.726717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T01:24:13.726717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wUdj7vNNFPvYb40wtSU3Vr3KEnVvHod/edUuMG6FyYHlEuFMlZC5S3C4NDpPrTVyVFjoFYvgYsezpvnljvD0Cg==","signature_status":"signed_v1","signed_at":"2026-07-22T01:24:13.727667Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.19197","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:64cf5bea82991e8f74b22a4e143c63c037d6a0bff26ece15d01e4e10c21551a1","sha256:766fb58ab841b719194d7cc362d232f85bfa7ec6bc64bd83c61460f8bda88cdd","sha256:a4010ba89d94314f7490d2b08d238929b4ebe5e2f695de4ca132b93746aa1efc","sha256:e8b3a23c688b72200ef870736e8fa292a233444b5658e53ece31a09ff5ca0ab0"]}],"invalid_events":[],"applied_event_ids":["sha256:6ddf8207912b730f1aea400ebb884d98a3674e13ae47a424cec554d454e11622","sha256:10387457333e82c5b65336fd3d0696a4f622a2f02638229930363ea1f7847e8d"],"state_sha256":"c326b268679afbb0a0c27a8e75c120fe08a3d1e92191010e3f3347e266b31fbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5wpc2x8hOrIIV4GeC6FtQwYU45iazPhoqY/TchjdV10Z2bDIBwMG7C7n3bPYc14kdXnpCwT1TutriKybUW9WAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T04:38:16.888638Z","bundle_sha256":"eae7654761784171300333faa44bde8f12f4e01dda76e60d27cc838c2e70c010"}}