{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZWPTU4V65HPRCOQ3UCZMTWQOKC","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":"aeb7810a218ebd173dca1ff5b3c36b03d95ca55420e51a7e44aef56f51afe05a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-04-05T07:39:24Z","title_canon_sha256":"bd8eeaf41aede5cc7efe0d97a337be234812b7d66e8d74e4b5366ee0a5ba36d5"},"schema_version":"1.0","source":{"id":"1904.03186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03186","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03186v1","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03186","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"ZWPTU4V65HPR","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZWPTU4V65HPRCOQ3","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZWPTU4V6","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:1ca325f2fe59ed00452dc17c0036f7aa6b866dd077aa26fc9afc04fbdc5538fe","target":"graph","created_at":"2026-05-17T23:44:42Z","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":"We show that three generations of leptons and quarks with unbroken Standard Model gauge symmetry $SU(3)_c\\times U(1)_{em}$ can be described using the algebra of complexified sedenions $\\mathbb{C}\\otimes\\mathbb{S}$. A primitive idempotent is constructed by selecting a special direction, and the action of this projector on the basis of $\\mathbb{C}\\otimes\\mathbb{S}$ can be used to uniquely split the algebra into three complex octonion subalgebras $\\mathbb{C}\\otimes \\mathbb{O}$. These subalgebras all share a common quaternionic subalgebra. The left adjoint actions of the 8 $\\mathbb{C}$-dimensional","authors_text":"Adam B. Gillard, Niels G. Gresnigt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-04-05T07:39:24Z","title":"Three fermion generations with two unbroken gauge symmetries from the complex sedenions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03186","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":"sha256:3cce86d09761bec638d36c1a5f1651fbb2be4f6e7d06c90a8fd68c0e79d05630","target":"record","created_at":"2026-05-17T23:44:42Z","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":"aeb7810a218ebd173dca1ff5b3c36b03d95ca55420e51a7e44aef56f51afe05a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-04-05T07:39:24Z","title_canon_sha256":"bd8eeaf41aede5cc7efe0d97a337be234812b7d66e8d74e4b5366ee0a5ba36d5"},"schema_version":"1.0","source":{"id":"1904.03186","kind":"arxiv","version":1}},"canonical_sha256":"cd9f3a72bee9df113a1ba0b2c9da0e508f1994c78c4688d33b800a683e514c5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd9f3a72bee9df113a1ba0b2c9da0e508f1994c78c4688d33b800a683e514c5f","first_computed_at":"2026-05-17T23:44:42.329866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:42.329866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gv5Z6L+MtcqKQZzgfgqyyVTa7lNjMDVD5C6LevHykwg9HrdejKrMhYxHV5oJ0Raih4ESEagRdXmI3SonAjIQAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:42.330755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cce86d09761bec638d36c1a5f1651fbb2be4f6e7d06c90a8fd68c0e79d05630","sha256:1ca325f2fe59ed00452dc17c0036f7aa6b866dd077aa26fc9afc04fbdc5538fe"],"state_sha256":"4f7c4641313f7b7ceeda924710d51704d5fe2c70e38328308c88079c45c3a94b"}