{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:AXULFGUZ3GDI56FOHP3EKXQ5OQ","short_pith_number":"pith:AXULFGUZ","schema_version":"1.0","canonical_sha256":"05e8b29a99d9868ef8ae3bf6455e1d741e839821fce85e543348592041e780eb","source":{"kind":"arxiv","id":"2607.04132","version":1},"attestation_state":"computed","paper":{"title":"Left-right symmetry breaking in $E_6^L\\times E_6^R$ occurs only in spacetime -- with possible implications for strong $CP$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Tejinder P. Singh","submitted_at":"2026-07-05T06:18:51Z","abstract_excerpt":"Two-sided octonionic $E_6^L\\times E_6^R$ unification carries a nominal second colour $SU(3)_{c'}$ which, gauged, would colour the charged lepton and must be suppressed by hand. We argue no such device is needed: the left-right symmetry acts in spacetime, not internally -- in the gravi-weak reading $SU(2)_R$ is the gravitational frame group and the exchange is ordinary parity on the Dirac field; a spacetime operation cannot double the internal colour, so $SU(3)_{c'}=SU(3)_c$, one vector-like colour with a colour-singlet electron. The right sector contributes one colour-blind datum, $\\sqrt m$ (v"},"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":"2607.04132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2026-07-05T06:18:51Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"9ab722ef6d2e7f3d2f988e278abffdf1a7c7facd9c125901fc62682e034e8481","abstract_canon_sha256":"a59313460b109de8f7b2feef766cbd668cd6c26c4a2d0f9e32025e1c6c9ec2b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:18:58.988211Z","signature_b64":"A5F4zBYC+j5FGTami2aitumUNmw8nwCXkJGGQ/RPBg2raMm5jlZjaR4MngUZa1usvfeq1uh+ejlMcXh9JAfdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05e8b29a99d9868ef8ae3bf6455e1d741e839821fce85e543348592041e780eb","last_reissued_at":"2026-07-07T02:18:58.987472Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:18:58.987472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Left-right symmetry breaking in $E_6^L\\times E_6^R$ occurs only in spacetime -- with possible implications for strong $CP$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Tejinder P. Singh","submitted_at":"2026-07-05T06:18:51Z","abstract_excerpt":"Two-sided octonionic $E_6^L\\times E_6^R$ unification carries a nominal second colour $SU(3)_{c'}$ which, gauged, would colour the charged lepton and must be suppressed by hand. We argue no such device is needed: the left-right symmetry acts in spacetime, not internally -- in the gravi-weak reading $SU(2)_R$ is the gravitational frame group and the exchange is ordinary parity on the Dirac field; a spacetime operation cannot double the internal colour, so $SU(3)_{c'}=SU(3)_c$, one vector-like colour with a colour-singlet electron. The right sector contributes one colour-blind datum, $\\sqrt m$ (v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04132","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/2607.04132/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":"2607.04132","created_at":"2026-07-07T02:18:58.987581+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.04132v1","created_at":"2026-07-07T02:18:58.987581+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04132","created_at":"2026-07-07T02:18:58.987581+00:00"},{"alias_kind":"pith_short_12","alias_value":"AXULFGUZ3GDI","created_at":"2026-07-07T02:18:58.987581+00:00"},{"alias_kind":"pith_short_16","alias_value":"AXULFGUZ3GDI56FO","created_at":"2026-07-07T02:18:58.987581+00:00"},{"alias_kind":"pith_short_8","alias_value":"AXULFGUZ","created_at":"2026-07-07T02:18:58.987581+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/AXULFGUZ3GDI56FOHP3EKXQ5OQ","json":"https://pith.science/pith/AXULFGUZ3GDI56FOHP3EKXQ5OQ.json","graph_json":"https://pith.science/api/pith-number/AXULFGUZ3GDI56FOHP3EKXQ5OQ/graph.json","events_json":"https://pith.science/api/pith-number/AXULFGUZ3GDI56FOHP3EKXQ5OQ/events.json","paper":"https://pith.science/paper/AXULFGUZ"},"agent_actions":{"view_html":"https://pith.science/pith/AXULFGUZ3GDI56FOHP3EKXQ5OQ","download_json":"https://pith.science/pith/AXULFGUZ3GDI56FOHP3EKXQ5OQ.json","view_paper":"https://pith.science/paper/AXULFGUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.04132&json=true","fetch_graph":"https://pith.science/api/pith-number/AXULFGUZ3GDI56FOHP3EKXQ5OQ/graph.json","fetch_events":"https://pith.science/api/pith-number/AXULFGUZ3GDI56FOHP3EKXQ5OQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AXULFGUZ3GDI56FOHP3EKXQ5OQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AXULFGUZ3GDI56FOHP3EKXQ5OQ/action/storage_attestation","attest_author":"https://pith.science/pith/AXULFGUZ3GDI56FOHP3EKXQ5OQ/action/author_attestation","sign_citation":"https://pith.science/pith/AXULFGUZ3GDI56FOHP3EKXQ5OQ/action/citation_signature","submit_replication":"https://pith.science/pith/AXULFGUZ3GDI56FOHP3EKXQ5OQ/action/replication_record"}},"created_at":"2026-07-07T02:18:58.987581+00:00","updated_at":"2026-07-07T02:18:58.987581+00:00"}