{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:K253S3R7S6WD6R7NNJEZAM3RCK","short_pith_number":"pith:K253S3R7","schema_version":"1.0","canonical_sha256":"56bbb96e3f97ac3f47ed6a499033711284be5fbbc9978735f28c2bbae3ef6c51","source":{"kind":"arxiv","id":"quant-ph/0304167","version":1},"attestation_state":"computed","paper":{"title":"Nonlinear Dirac equations and nonlinear gauge transformations","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"H.-D. Doebner, R. Zhdanov","submitted_at":"2003-04-25T15:36:00Z","abstract_excerpt":"Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schr\\\"odinger equations. To relate N^2 with physically motivated principles we assume: locality (i.e. it contains no explicit derivative and no derivatives of the wave function), separability (i.e. it acts on product states componentwise) and Poincar\\'e invariance. Furthermore we want that a positional density is invariant under N^2. Such nonlinear transformations yield NLDE which describe physica"},"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":"quant-ph/0304167","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2003-04-25T15:36:00Z","cross_cats_sorted":[],"title_canon_sha256":"55b5a64ed152ee40c0a63bb84face54282f456e26175740366474d7e45d38748","abstract_canon_sha256":"c56ccca7a03411c5037058dcd466c09676bd4f97c096acff61ba928a016da65b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:46:10.338209Z","signature_b64":"qKVlpegGf4wb/9cvPKhXoQ4W6Han4Lq+xEARWb3zrYwI6pkYnLngX4Z7zwNiO/lvQhytkXp55Jkxg5MzNRS5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56bbb96e3f97ac3f47ed6a499033711284be5fbbc9978735f28c2bbae3ef6c51","last_reissued_at":"2026-07-04T14:46:10.337810Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:46:10.337810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear Dirac equations and nonlinear gauge transformations","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"H.-D. Doebner, R. Zhdanov","submitted_at":"2003-04-25T15:36:00Z","abstract_excerpt":"Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schr\\\"odinger equations. To relate N^2 with physically motivated principles we assume: locality (i.e. it contains no explicit derivative and no derivatives of the wave function), separability (i.e. it acts on product states componentwise) and Poincar\\'e invariance. Furthermore we want that a positional density is invariant under N^2. Such nonlinear transformations yield NLDE which describe physica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0304167","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/quant-ph/0304167/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":"quant-ph/0304167","created_at":"2026-07-04T14:46:10.337866+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0304167v1","created_at":"2026-07-04T14:46:10.337866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0304167","created_at":"2026-07-04T14:46:10.337866+00:00"},{"alias_kind":"pith_short_12","alias_value":"K253S3R7S6WD","created_at":"2026-07-04T14:46:10.337866+00:00"},{"alias_kind":"pith_short_16","alias_value":"K253S3R7S6WD6R7N","created_at":"2026-07-04T14:46:10.337866+00:00"},{"alias_kind":"pith_short_8","alias_value":"K253S3R7","created_at":"2026-07-04T14:46:10.337866+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK","json":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK.json","graph_json":"https://pith.science/api/pith-number/K253S3R7S6WD6R7NNJEZAM3RCK/graph.json","events_json":"https://pith.science/api/pith-number/K253S3R7S6WD6R7NNJEZAM3RCK/events.json","paper":"https://pith.science/paper/K253S3R7"},"agent_actions":{"view_html":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK","download_json":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK.json","view_paper":"https://pith.science/paper/K253S3R7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0304167&json=true","fetch_graph":"https://pith.science/api/pith-number/K253S3R7S6WD6R7NNJEZAM3RCK/graph.json","fetch_events":"https://pith.science/api/pith-number/K253S3R7S6WD6R7NNJEZAM3RCK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK/action/storage_attestation","attest_author":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK/action/author_attestation","sign_citation":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK/action/citation_signature","submit_replication":"https://pith.science/pith/K253S3R7S6WD6R7NNJEZAM3RCK/action/replication_record"}},"created_at":"2026-07-04T14:46:10.337866+00:00","updated_at":"2026-07-04T14:46:10.337866+00:00"}