{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KRZ4D527YL6FUV3IXEHXREUFGC","short_pith_number":"pith:KRZ4D527","canonical_record":{"source":{"id":"1404.1401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-04T21:40:09Z","cross_cats_sorted":["hep-th","math.AP","math.MP"],"title_canon_sha256":"1f41e702cc0d033fd0ca101ffedd864d2ab20dd5e5012d076ee1a2342f572504","abstract_canon_sha256":"8e118c987e632c284065f1371d8c442846886f35c51fb155acbf2d37b23aae8e"},"schema_version":"1.0"},"canonical_sha256":"5473c1f75fc2fc5a5768b90f78928530bd6dc6990948efb03873c72ccf7b66ae","source":{"kind":"arxiv","id":"1404.1401","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1401","created_at":"2026-05-18T01:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1401v1","created_at":"2026-05-18T01:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1401","created_at":"2026-05-18T01:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"KRZ4D527YL6F","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KRZ4D527YL6FUV3I","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KRZ4D527","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KRZ4D527YL6FUV3IXEHXREUFGC","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-04T21:40:09Z","cross_cats_sorted":["hep-th","math.AP","math.MP"],"title_canon_sha256":"1f41e702cc0d033fd0ca101ffedd864d2ab20dd5e5012d076ee1a2342f572504","abstract_canon_sha256":"8e118c987e632c284065f1371d8c442846886f35c51fb155acbf2d37b23aae8e"},"schema_version":"1.0"},"canonical_sha256":"5473c1f75fc2fc5a5768b90f78928530bd6dc6990948efb03873c72ccf7b66ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:37.396305Z","signature_b64":"N0PtVxKab9Afz80RU0QgwmsyjVUvSdgoNlclx5Y3WptP4QjHAJnGuytHMs/Lpr9Q/x6UEWad12Ae95go31ThBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5473c1f75fc2fc5a5768b90f78928530bd6dc6990948efb03873c72ccf7b66ae","last_reissued_at":"2026-05-18T01:43:37.395650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:37.395650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1401","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":"2026-05-18T01:43:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z7862nNmuS1YFKnZBOfoA9IkDuIN+1Klogc9E7a/CEHGJ+mO1xiOheLcuZe81tV+Fd+S1ju5MTvFFwYs8QJNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T08:03:00.706002Z"},"content_sha256":"f1210c0f502dc9590e1fac20d8c2aa47a3085f007ccdc804535b578fa05904fa","schema_version":"1.0","event_id":"sha256:f1210c0f502dc9590e1fac20d8c2aa47a3085f007ccdc804535b578fa05904fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KRZ4D527YL6FUV3IXEHXREUFGC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac Equation with External Potential and Initial Data on Cauchy Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"D.-A. Deckert, F. Merkl","submitted_at":"2014-04-04T21:40:09Z","abstract_excerpt":"With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincar\\'e group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1401","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YIJyx6+2N3++OnLIV5Tra70NLMkx1pOEl83ze1T13pld3MHoFZGr53DGr9OouO73Q9W8A5SKYb52eofoJ4VcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T08:03:00.706709Z"},"content_sha256":"b4ecd866c14fada764172ffad1f135eb2c4f88e9e62394216cc49b879f6ce527","schema_version":"1.0","event_id":"sha256:b4ecd866c14fada764172ffad1f135eb2c4f88e9e62394216cc49b879f6ce527"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KRZ4D527YL6FUV3IXEHXREUFGC/bundle.json","state_url":"https://pith.science/pith/KRZ4D527YL6FUV3IXEHXREUFGC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KRZ4D527YL6FUV3IXEHXREUFGC/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":"2026-06-08T08:03:00Z","links":{"resolver":"https://pith.science/pith/KRZ4D527YL6FUV3IXEHXREUFGC","bundle":"https://pith.science/pith/KRZ4D527YL6FUV3IXEHXREUFGC/bundle.json","state":"https://pith.science/pith/KRZ4D527YL6FUV3IXEHXREUFGC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KRZ4D527YL6FUV3IXEHXREUFGC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KRZ4D527YL6FUV3IXEHXREUFGC","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":"8e118c987e632c284065f1371d8c442846886f35c51fb155acbf2d37b23aae8e","cross_cats_sorted":["hep-th","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-04T21:40:09Z","title_canon_sha256":"1f41e702cc0d033fd0ca101ffedd864d2ab20dd5e5012d076ee1a2342f572504"},"schema_version":"1.0","source":{"id":"1404.1401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1401","created_at":"2026-05-18T01:43:37Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1401v1","created_at":"2026-05-18T01:43:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1401","created_at":"2026-05-18T01:43:37Z"},{"alias_kind":"pith_short_12","alias_value":"KRZ4D527YL6F","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KRZ4D527YL6FUV3I","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KRZ4D527","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:b4ecd866c14fada764172ffad1f135eb2c4f88e9e62394216cc49b879f6ce527","target":"graph","created_at":"2026-05-18T01:43:37Z","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"},"paper":{"abstract_excerpt":"With this paper we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincar\\'e group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately a","authors_text":"D.-A. Deckert, F. Merkl","cross_cats":["hep-th","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-04T21:40:09Z","title":"Dirac Equation with External Potential and Initial Data on Cauchy Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1401","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:f1210c0f502dc9590e1fac20d8c2aa47a3085f007ccdc804535b578fa05904fa","target":"record","created_at":"2026-05-18T01:43:37Z","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":"8e118c987e632c284065f1371d8c442846886f35c51fb155acbf2d37b23aae8e","cross_cats_sorted":["hep-th","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-04T21:40:09Z","title_canon_sha256":"1f41e702cc0d033fd0ca101ffedd864d2ab20dd5e5012d076ee1a2342f572504"},"schema_version":"1.0","source":{"id":"1404.1401","kind":"arxiv","version":1}},"canonical_sha256":"5473c1f75fc2fc5a5768b90f78928530bd6dc6990948efb03873c72ccf7b66ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5473c1f75fc2fc5a5768b90f78928530bd6dc6990948efb03873c72ccf7b66ae","first_computed_at":"2026-05-18T01:43:37.395650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:37.395650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N0PtVxKab9Afz80RU0QgwmsyjVUvSdgoNlclx5Y3WptP4QjHAJnGuytHMs/Lpr9Q/x6UEWad12Ae95go31ThBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:37.396305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1210c0f502dc9590e1fac20d8c2aa47a3085f007ccdc804535b578fa05904fa","sha256:b4ecd866c14fada764172ffad1f135eb2c4f88e9e62394216cc49b879f6ce527"],"state_sha256":"1a76d03e9a4a2d99c18b8706b325404598cadf221ea8a4cc4438e4946c7cd4d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ciNb210V5KHPOlPJ3b3GWHvugOyYrAvw+oxZwN/UhHv5zcufSbDgxnKDaZQeBSmS/9n2KOZzwkMC7mgRRQWZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T08:03:00.710678Z","bundle_sha256":"844488115dfe33f598b23c1c4cbaebee624570cc02a0d53ac8d8db3d9ba8c2cb"}}