{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DEBW7ZRGZCZAI77JJZFBD6OR24","short_pith_number":"pith:DEBW7ZRG","canonical_record":{"source":{"id":"2410.11965","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-10-15T18:11:03Z","cross_cats_sorted":["hep-ph","hep-th"],"title_canon_sha256":"cb2e776c06cce629ab114e6d998028e397b8f743e503a8c3ff2f3f9d1a074461","abstract_canon_sha256":"f8191d8ccb7498a3db1a34af005e48582352695a3608da993ee811b04e677963"},"schema_version":"1.0"},"canonical_sha256":"19036fe626c8b2047fe94e4a11f9d1d704d713f1254d22dd7158cfd30d00526f","source":{"kind":"arxiv","id":"2410.11965","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.11965","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"2410.11965v1","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.11965","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"DEBW7ZRGZCZA","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"pith_short_16","alias_value":"DEBW7ZRGZCZAI77J","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"pith_short_8","alias_value":"DEBW7ZRG","created_at":"2026-07-05T09:21:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DEBW7ZRGZCZAI77JJZFBD6OR24","target":"record","payload":{"canonical_record":{"source":{"id":"2410.11965","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-10-15T18:11:03Z","cross_cats_sorted":["hep-ph","hep-th"],"title_canon_sha256":"cb2e776c06cce629ab114e6d998028e397b8f743e503a8c3ff2f3f9d1a074461","abstract_canon_sha256":"f8191d8ccb7498a3db1a34af005e48582352695a3608da993ee811b04e677963"},"schema_version":"1.0"},"canonical_sha256":"19036fe626c8b2047fe94e4a11f9d1d704d713f1254d22dd7158cfd30d00526f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:21:10.987735Z","signature_b64":"iEFHJtIsoPjpCpaJca2KU0Ik6X+CTkxmqVaq97ib0sdRqNCVME7VRTum2WlM9REm2O+0ZjGevQWrzxEmMLd1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19036fe626c8b2047fe94e4a11f9d1d704d713f1254d22dd7158cfd30d00526f","last_reissued_at":"2026-07-05T09:21:10.987265Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:21:10.987265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.11965","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":"2026-07-05T09:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LLJf+J9CPuf2e0btkF5EY8FP61UmVJ/mhxn3FF71fXFLgba7673ylfGZZDt9VazkUaFHGH+448NMuBex6ltgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:37:17.512600Z"},"content_sha256":"c436e7a5df1ed682d1fa02ce8a69a4db2c2c8e029d1c7ea513a369d1fcc752dc","schema_version":"1.0","event_id":"sha256:c436e7a5df1ed682d1fa02ce8a69a4db2c2c8e029d1c7ea513a369d1fcc752dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DEBW7ZRGZCZAI77JJZFBD6OR24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Uncertainty Principle and the Zeeman Effect: Relativistic Corrections Unveiled","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"quant-ph","authors_text":"Gaurav Bhandari, Manabendra Sharma, S. D. Pathak","submitted_at":"2024-10-15T18:11:03Z","abstract_excerpt":"In this paper, we calculate the relativistic corrections to the Zeeman effect for hydrogen-like atoms based on the Generalized Uncertainty Principle (GUP). We propose a relativistic GUP algebra using the Stetsko and Tkachuk approximation and incorporate these corrections into the Zeeman effect. In the relativistic limit, our results recover previously derived GUP corrections as well as the standard Lande energy shift expression when GUP effects are absent. This work presents a generalized expression that accounts for both relativistic and GUP corrections to the Zeeman effect."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.11965","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/2410.11965/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":"2026-07-05T09:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t2UH/p/LcvMhHimxN1PT1CONmt+RhVpiYAxyq8XcM2GfYbPaVZVxmQSgT5NJJH/dXTs2G4nlIWhlohivTMa8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:37:17.513099Z"},"content_sha256":"07eac5497222b7748655eefa46433fbc41b811cb2a4f02d371ba35db141c5bc9","schema_version":"1.0","event_id":"sha256:07eac5497222b7748655eefa46433fbc41b811cb2a4f02d371ba35db141c5bc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DEBW7ZRGZCZAI77JJZFBD6OR24/bundle.json","state_url":"https://pith.science/pith/DEBW7ZRGZCZAI77JJZFBD6OR24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DEBW7ZRGZCZAI77JJZFBD6OR24/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":"2026-08-15T08:37:17Z","links":{"resolver":"https://pith.science/pith/DEBW7ZRGZCZAI77JJZFBD6OR24","bundle":"https://pith.science/pith/DEBW7ZRGZCZAI77JJZFBD6OR24/bundle.json","state":"https://pith.science/pith/DEBW7ZRGZCZAI77JJZFBD6OR24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DEBW7ZRGZCZAI77JJZFBD6OR24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DEBW7ZRGZCZAI77JJZFBD6OR24","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":"f8191d8ccb7498a3db1a34af005e48582352695a3608da993ee811b04e677963","cross_cats_sorted":["hep-ph","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-10-15T18:11:03Z","title_canon_sha256":"cb2e776c06cce629ab114e6d998028e397b8f743e503a8c3ff2f3f9d1a074461"},"schema_version":"1.0","source":{"id":"2410.11965","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.11965","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"2410.11965v1","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.11965","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"DEBW7ZRGZCZA","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"pith_short_16","alias_value":"DEBW7ZRGZCZAI77J","created_at":"2026-07-05T09:21:10Z"},{"alias_kind":"pith_short_8","alias_value":"DEBW7ZRG","created_at":"2026-07-05T09:21:10Z"}],"graph_snapshots":[{"event_id":"sha256:07eac5497222b7748655eefa46433fbc41b811cb2a4f02d371ba35db141c5bc9","target":"graph","created_at":"2026-07-05T09:21:10Z","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/2410.11965/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we calculate the relativistic corrections to the Zeeman effect for hydrogen-like atoms based on the Generalized Uncertainty Principle (GUP). We propose a relativistic GUP algebra using the Stetsko and Tkachuk approximation and incorporate these corrections into the Zeeman effect. In the relativistic limit, our results recover previously derived GUP corrections as well as the standard Lande energy shift expression when GUP effects are absent. This work presents a generalized expression that accounts for both relativistic and GUP corrections to the Zeeman effect.","authors_text":"Gaurav Bhandari, Manabendra Sharma, S. D. Pathak","cross_cats":["hep-ph","hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-10-15T18:11:03Z","title":"Generalized Uncertainty Principle and the Zeeman Effect: Relativistic Corrections Unveiled"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.11965","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:c436e7a5df1ed682d1fa02ce8a69a4db2c2c8e029d1c7ea513a369d1fcc752dc","target":"record","created_at":"2026-07-05T09:21:10Z","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":"f8191d8ccb7498a3db1a34af005e48582352695a3608da993ee811b04e677963","cross_cats_sorted":["hep-ph","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-10-15T18:11:03Z","title_canon_sha256":"cb2e776c06cce629ab114e6d998028e397b8f743e503a8c3ff2f3f9d1a074461"},"schema_version":"1.0","source":{"id":"2410.11965","kind":"arxiv","version":1}},"canonical_sha256":"19036fe626c8b2047fe94e4a11f9d1d704d713f1254d22dd7158cfd30d00526f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19036fe626c8b2047fe94e4a11f9d1d704d713f1254d22dd7158cfd30d00526f","first_computed_at":"2026-07-05T09:21:10.987265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:21:10.987265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iEFHJtIsoPjpCpaJca2KU0Ik6X+CTkxmqVaq97ib0sdRqNCVME7VRTum2WlM9REm2O+0ZjGevQWrzxEmMLd1DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:21:10.987735Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.11965","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c436e7a5df1ed682d1fa02ce8a69a4db2c2c8e029d1c7ea513a369d1fcc752dc","sha256:07eac5497222b7748655eefa46433fbc41b811cb2a4f02d371ba35db141c5bc9"],"state_sha256":"c5e0cde03f77702a40efc034a1ee9e5cf1aa344e445d67f222bcfebc80eccff8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+t/cyjnOVeEFcPO8bjd4rztdVoOx1lGca/v4Qd94VdBbI8a0ZWk0VbtPTaz6mxe6HYC6/1Pu6aQF8Jg22zfvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T08:37:17.516869Z","bundle_sha256":"b9e8033dcefea163faff8256e9ec85c64c90c1a605b4ab2df979436f1daefeb4"}}