{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6WZJUPGWX66LX3YZ3QGLSPNGOG","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":"48c72ee80402e351af62e09702b04a4ee815eeb097a51ab1d9969352531cc394","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2017-12-15T15:02:12Z","title_canon_sha256":"36e997e8e3c74ae74ade5b19b93bd11e48712166df882ebaffaa2618f8df636e"},"schema_version":"1.0","source":{"id":"1801.01403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01403","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01403v1","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01403","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"pith_short_12","alias_value":"6WZJUPGWX66L","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6WZJUPGWX66LX3YZ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6WZJUPGW","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:7c0784964eb0616f15a5c0fde30a8bf6703dc6bea9d5155577d07cefb75ffae0","target":"graph","created_at":"2026-05-17T23:50:28Z","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":"The wave equation generalizing the Dirac operator to the Z3-graded case is introduced, whose diagonalization leads to a sixth-order equation. It intertwines not only quark and anti-quark state as well as the \"u\" and \"d\" quarks, but also the three colors, and is therefore invariant under the product group Z2 x Z2 x Z3. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry and of the SU(2) x U(1) that arise ","authors_text":"Richard Kerner","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2017-12-15T15:02:12Z","title":"Ternary Z2 x Z3 graded algebras and ternary Dirac equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01403","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":"sha256:2f8dac834488805be1444d3565db0330553ffc17e4939e9983c600a3e2bc4488","target":"record","created_at":"2026-05-17T23:50:28Z","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":"48c72ee80402e351af62e09702b04a4ee815eeb097a51ab1d9969352531cc394","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2017-12-15T15:02:12Z","title_canon_sha256":"36e997e8e3c74ae74ade5b19b93bd11e48712166df882ebaffaa2618f8df636e"},"schema_version":"1.0","source":{"id":"1801.01403","kind":"arxiv","version":1}},"canonical_sha256":"f5b29a3cd6bfbcbbef19dc0cb93da6718b68e564cabe436afb61a7a5b03d651e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5b29a3cd6bfbcbbef19dc0cb93da6718b68e564cabe436afb61a7a5b03d651e","first_computed_at":"2026-05-17T23:50:28.665818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:28.665818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zR0XkGmlO2/5gox1OpQJe0qp5AxuPJtkB5Bzq22jZHdDHzpvWARwxlfxTPWFGLidIOh4FaN1jC4nC07gUPsMBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:28.666449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.01403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f8dac834488805be1444d3565db0330553ffc17e4939e9983c600a3e2bc4488","sha256:7c0784964eb0616f15a5c0fde30a8bf6703dc6bea9d5155577d07cefb75ffae0"],"state_sha256":"f495c485aa24f77427a72f125164576641169a3b92f1f2fa0f423b21b5507429"}