{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:C43OSIY3FYBS4OAHE4VZ46P6ZS","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":"60f7e3adafaec74302c99e853e3a0d32ed7dae943a72dd44c37bcdad34be2f20","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-07-05T17:18:38Z","title_canon_sha256":"ad94f475a85e58738e672f16a8fdf2f0e26cfa77ce4613792606c5d357320f92"},"schema_version":"1.0","source":{"id":"math-ph/0207010","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0207010","created_at":"2026-07-04T16:35:10Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0207010v2","created_at":"2026-07-04T16:35:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0207010","created_at":"2026-07-04T16:35:10Z"},{"alias_kind":"pith_short_12","alias_value":"C43OSIY3FYBS","created_at":"2026-07-04T16:35:10Z"},{"alias_kind":"pith_short_16","alias_value":"C43OSIY3FYBS4OAH","created_at":"2026-07-04T16:35:10Z"},{"alias_kind":"pith_short_8","alias_value":"C43OSIY3","created_at":"2026-07-04T16:35:10Z"}],"graph_snapshots":[{"event_id":"sha256:ca8f5caa9c2d0b25ee029fb662b1405f4be8b35a59b1a897141ada4d227fff95","target":"graph","created_at":"2026-07-04T16:35:10Z","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/math-ph/0207010/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the asymptotic evolution of a relativistic spin-1/2-particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector) surface converges to the probability, that the direction of the momentum of the particle lies within the solid angle defined by the (detector) surface, as the distance of the surface goes to infinity. This generalizes earlier non relativistic results, known as flux across surfaces theorems, to the relativistic regime.","authors_text":"D. Duerr, P. Pickl","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-07-05T17:18:38Z","title":"Flux-Across-Surfaces Theorem for a Dirac Particle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0207010","kind":"arxiv","version":2},"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":"sha256:16e7df1a16c56b7fdd671a185a86c1999dcd7f4343acd47b66823c042cc1d51e","target":"record","created_at":"2026-07-04T16:35:10Z","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":"60f7e3adafaec74302c99e853e3a0d32ed7dae943a72dd44c37bcdad34be2f20","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-07-05T17:18:38Z","title_canon_sha256":"ad94f475a85e58738e672f16a8fdf2f0e26cfa77ce4613792606c5d357320f92"},"schema_version":"1.0","source":{"id":"math-ph/0207010","kind":"arxiv","version":2}},"canonical_sha256":"1736e9231b2e032e3807272b9e79fecc901d336d599277f53cc5dcba38d2913b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1736e9231b2e032e3807272b9e79fecc901d336d599277f53cc5dcba38d2913b","first_computed_at":"2026-07-04T16:35:10.892184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:35:10.892184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CpLeOBMyf7jefIZnHrbzhJ/zvlO73SV9yw9H8csvguR5gXU/1z2nXpxF72kqBkCikaD7SjQieiqNb2vY5ck5DQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:35:10.892602Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0207010","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16e7df1a16c56b7fdd671a185a86c1999dcd7f4343acd47b66823c042cc1d51e","sha256:ca8f5caa9c2d0b25ee029fb662b1405f4be8b35a59b1a897141ada4d227fff95"],"state_sha256":"66d37599f1aa20e28891789c25d85abd9849ced58bfaadf3d69f0f8daac0e47b"}