{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:TJYHVYISE254EI24RCQZ7DY23F","short_pith_number":"pith:TJYHVYIS","schema_version":"1.0","canonical_sha256":"9a707ae11226bbc2235c88a19f8f1ad96c48d53b584524e36fa64726df778496","source":{"kind":"arxiv","id":"0901.1768","version":1},"attestation_state":"computed","paper":{"title":"Phenomenological Implications of the Generalized Uncertainty Principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-ph","quant-ph"],"primary_cat":"hep-th","authors_text":"Elias C. Vagenas, Saurya Das","submitted_at":"2009-01-13T11:48:52Z","abstract_excerpt":"Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to \\beta p^4 and \\beta^2 p^6 respectively, where \\beta \\sim 1/(M_{Pl}c)^2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these, and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and trans"},"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":"0901.1768","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-01-13T11:48:52Z","cross_cats_sorted":["gr-qc","hep-ph","quant-ph"],"title_canon_sha256":"b7a89d6d101b7a59124e441272af7a37be7da02aae6d5a3dc34f445d80742943","abstract_canon_sha256":"20b0dcdb05a88189003c955233e7859eb8d9c3dd319b263a8e9cfc596eff03f2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:22.829559Z","signature_b64":"nTjYsW+zR/zwDNO4sl0hq+du2ia8siR5LUUNV0F1CEaml9ix0LIAM2sTtTjPw5cHfkz1a6lRu5C97xkuxYrUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a707ae11226bbc2235c88a19f8f1ad96c48d53b584524e36fa64726df778496","last_reissued_at":"2026-05-18T04:37:22.829022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:22.829022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phenomenological Implications of the Generalized Uncertainty Principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-ph","quant-ph"],"primary_cat":"hep-th","authors_text":"Elias C. Vagenas, Saurya Das","submitted_at":"2009-01-13T11:48:52Z","abstract_excerpt":"Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to \\beta p^4 and \\beta^2 p^6 respectively, where \\beta \\sim 1/(M_{Pl}c)^2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these, and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and trans"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1768","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":""},"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":"0901.1768","created_at":"2026-05-18T04:37:22.829092+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.1768v1","created_at":"2026-05-18T04:37:22.829092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1768","created_at":"2026-05-18T04:37:22.829092+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJYHVYISE254","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJYHVYISE254EI24","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJYHVYIS","created_at":"2026-05-18T12:26:01.383474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2511.14869","citing_title":"From minimal-length quantum theory to modified gravity","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F","json":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F.json","graph_json":"https://pith.science/api/pith-number/TJYHVYISE254EI24RCQZ7DY23F/graph.json","events_json":"https://pith.science/api/pith-number/TJYHVYISE254EI24RCQZ7DY23F/events.json","paper":"https://pith.science/paper/TJYHVYIS"},"agent_actions":{"view_html":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F","download_json":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F.json","view_paper":"https://pith.science/paper/TJYHVYIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.1768&json=true","fetch_graph":"https://pith.science/api/pith-number/TJYHVYISE254EI24RCQZ7DY23F/graph.json","fetch_events":"https://pith.science/api/pith-number/TJYHVYISE254EI24RCQZ7DY23F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F/action/storage_attestation","attest_author":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F/action/author_attestation","sign_citation":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F/action/citation_signature","submit_replication":"https://pith.science/pith/TJYHVYISE254EI24RCQZ7DY23F/action/replication_record"}},"created_at":"2026-05-18T04:37:22.829092+00:00","updated_at":"2026-05-18T04:37:22.829092+00:00"}