{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:CVL32KMWMNEDXFWATLEDAVVVP3","short_pith_number":"pith:CVL32KMW","schema_version":"1.0","canonical_sha256":"1557bd299663483b96c09ac83056b57ec8f37780acee7645c4aed00541c48a4c","source":{"kind":"arxiv","id":"0712.4188","version":2},"attestation_state":"computed","paper":{"title":"The Lorentz Extension as Consequence of the Family Symmetry","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Hai-Jhun Wanng","submitted_at":"2007-12-27T05:50:14Z","abstract_excerpt":"In this paper we postulate an algebraic model to explain how the symmetry of three lepton species plays its role in the Lorentz extension. Inspired by the two-to-one mapping between the group SL (2, C) and the Lorentz group, we design a mapping between SL (3, C) group, which displays the family symmetry, and a generalized Lorentz group. Following the conventional method, we apply the mapping results to Dirac equation to discuss its transformation invariance, and it turns out that only when the vertex matrix is extended to the combination can the Dirac-equation-form be reserved. At the same tim"},"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":"0712.4188","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2007-12-27T05:50:14Z","cross_cats_sorted":[],"title_canon_sha256":"5a13bdd198f86e50338a28511c81cb9761b007167cdf23819d55b8b9131d72a6","abstract_canon_sha256":"004a63653c0098072849db86336cee4d557d603a928f5c4d4f0ed2e7493fa234"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:06.732963Z","signature_b64":"zC8vwFk8srP7r7PLpGYUYwIAEzYyKY41976meeKY56oo6/hVRPhCzV2DYfw3iH6E3QskalTTUwRDTjdTCN8mAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1557bd299663483b96c09ac83056b57ec8f37780acee7645c4aed00541c48a4c","last_reissued_at":"2026-05-18T03:28:06.732258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:06.732258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Lorentz Extension as Consequence of the Family Symmetry","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Hai-Jhun Wanng","submitted_at":"2007-12-27T05:50:14Z","abstract_excerpt":"In this paper we postulate an algebraic model to explain how the symmetry of three lepton species plays its role in the Lorentz extension. Inspired by the two-to-one mapping between the group SL (2, C) and the Lorentz group, we design a mapping between SL (3, C) group, which displays the family symmetry, and a generalized Lorentz group. Following the conventional method, we apply the mapping results to Dirac equation to discuss its transformation invariance, and it turns out that only when the vertex matrix is extended to the combination can the Dirac-equation-form be reserved. At the same tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4188","kind":"arxiv","version":2},"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":"0712.4188","created_at":"2026-05-18T03:28:06.732336+00:00"},{"alias_kind":"arxiv_version","alias_value":"0712.4188v2","created_at":"2026-05-18T03:28:06.732336+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4188","created_at":"2026-05-18T03:28:06.732336+00:00"},{"alias_kind":"pith_short_12","alias_value":"CVL32KMWMNED","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"CVL32KMWMNEDXFWA","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"CVL32KMW","created_at":"2026-05-18T12:25:55.427421+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/CVL32KMWMNEDXFWATLEDAVVVP3","json":"https://pith.science/pith/CVL32KMWMNEDXFWATLEDAVVVP3.json","graph_json":"https://pith.science/api/pith-number/CVL32KMWMNEDXFWATLEDAVVVP3/graph.json","events_json":"https://pith.science/api/pith-number/CVL32KMWMNEDXFWATLEDAVVVP3/events.json","paper":"https://pith.science/paper/CVL32KMW"},"agent_actions":{"view_html":"https://pith.science/pith/CVL32KMWMNEDXFWATLEDAVVVP3","download_json":"https://pith.science/pith/CVL32KMWMNEDXFWATLEDAVVVP3.json","view_paper":"https://pith.science/paper/CVL32KMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0712.4188&json=true","fetch_graph":"https://pith.science/api/pith-number/CVL32KMWMNEDXFWATLEDAVVVP3/graph.json","fetch_events":"https://pith.science/api/pith-number/CVL32KMWMNEDXFWATLEDAVVVP3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CVL32KMWMNEDXFWATLEDAVVVP3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CVL32KMWMNEDXFWATLEDAVVVP3/action/storage_attestation","attest_author":"https://pith.science/pith/CVL32KMWMNEDXFWATLEDAVVVP3/action/author_attestation","sign_citation":"https://pith.science/pith/CVL32KMWMNEDXFWATLEDAVVVP3/action/citation_signature","submit_replication":"https://pith.science/pith/CVL32KMWMNEDXFWATLEDAVVVP3/action/replication_record"}},"created_at":"2026-05-18T03:28:06.732336+00:00","updated_at":"2026-05-18T03:28:06.732336+00:00"}