{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IYSJJ4UPWJG4GCONJHB5KERIIZ","short_pith_number":"pith:IYSJJ4UP","schema_version":"1.0","canonical_sha256":"462494f28fb24dc309cd49c3d512284661af97dbc13f9d594abefda4e0454741","source":{"kind":"arxiv","id":"2603.04569","version":3},"attestation_state":"computed","paper":{"title":"Dirac Wave Functions of Positive Energy with Arbitrarily Small Position Uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ilmar B\\\"urck, Roderich Tumulka","submitted_at":"2026-03-04T19:56:07Z","abstract_excerpt":"We consider wave functions in the Hilbert space $\\mathcal{H}=L^2(\\mathbb{R}^3,\\mathbb{C}^4)$ of a single Dirac particle, specifically from the positive-energy subspace $\\mathcal{H}_+$ of the free Dirac Hamiltonian. Over the decades, various authors hypothesized that for wave functions from $\\mathcal{H}_+$, there is a positive lower bound to the position uncertainty $\\sigma_x$; in other words, that such states cannot be arbitrarily narrow in $x$. Using a sequence of wave functions introduced by Bracken and Melloy, we show that this hypothesis is false. (In fact, they already stated that it is f"},"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":"2603.04569","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-03-04T19:56:07Z","cross_cats_sorted":[],"title_canon_sha256":"6ff8ce32a407b623702291373942da6d49d952166fff1c3777b8b02998f983f5","abstract_canon_sha256":"926eb2dd3c059c09dc04919797df97afc64ef68432d84753e8019a58ee79e7c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T01:16:07.311833Z","signature_b64":"4u58GjtcaU8LW7kxopFVzUwBri9r700GBCvjLHJp+8Gxua0yUoh5K4gadqGWA98CusHKK4cgPzn5I9jdZ7jmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"462494f28fb24dc309cd49c3d512284661af97dbc13f9d594abefda4e0454741","last_reissued_at":"2026-07-07T01:16:07.310907Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T01:16:07.310907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirac Wave Functions of Positive Energy with Arbitrarily Small Position Uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ilmar B\\\"urck, Roderich Tumulka","submitted_at":"2026-03-04T19:56:07Z","abstract_excerpt":"We consider wave functions in the Hilbert space $\\mathcal{H}=L^2(\\mathbb{R}^3,\\mathbb{C}^4)$ of a single Dirac particle, specifically from the positive-energy subspace $\\mathcal{H}_+$ of the free Dirac Hamiltonian. Over the decades, various authors hypothesized that for wave functions from $\\mathcal{H}_+$, there is a positive lower bound to the position uncertainty $\\sigma_x$; in other words, that such states cannot be arbitrarily narrow in $x$. Using a sequence of wave functions introduced by Bracken and Melloy, we show that this hypothesis is false. (In fact, they already stated that it is f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.04569","kind":"arxiv","version":3},"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/2603.04569/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":"2603.04569","created_at":"2026-07-07T01:16:07.311001+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.04569v3","created_at":"2026-07-07T01:16:07.311001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.04569","created_at":"2026-07-07T01:16:07.311001+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYSJJ4UPWJG4","created_at":"2026-07-07T01:16:07.311001+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYSJJ4UPWJG4GCON","created_at":"2026-07-07T01:16:07.311001+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYSJJ4UP","created_at":"2026-07-07T01:16:07.311001+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.21266","citing_title":"Representation of the causal logic for the Dirac system and the electron","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ","json":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ.json","graph_json":"https://pith.science/api/pith-number/IYSJJ4UPWJG4GCONJHB5KERIIZ/graph.json","events_json":"https://pith.science/api/pith-number/IYSJJ4UPWJG4GCONJHB5KERIIZ/events.json","paper":"https://pith.science/paper/IYSJJ4UP"},"agent_actions":{"view_html":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ","download_json":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ.json","view_paper":"https://pith.science/paper/IYSJJ4UP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.04569&json=true","fetch_graph":"https://pith.science/api/pith-number/IYSJJ4UPWJG4GCONJHB5KERIIZ/graph.json","fetch_events":"https://pith.science/api/pith-number/IYSJJ4UPWJG4GCONJHB5KERIIZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ/action/storage_attestation","attest_author":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ/action/author_attestation","sign_citation":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ/action/citation_signature","submit_replication":"https://pith.science/pith/IYSJJ4UPWJG4GCONJHB5KERIIZ/action/replication_record"}},"created_at":"2026-07-07T01:16:07.311001+00:00","updated_at":"2026-07-07T01:16:07.311001+00:00"}