{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HO6IW4SW4Z7JUPKF33UYVMJBCI","short_pith_number":"pith:HO6IW4SW","canonical_record":{"source":{"id":"1808.02853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T16:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"6ac98028532f308f3cf175d7c42d6700a46c85f18a06e7d332a84088b3a393c5","abstract_canon_sha256":"449dcb4e3b00e76f0c41f5d72def8c97c056dd577158a891cddeaa6c52af49aa"},"schema_version":"1.0"},"canonical_sha256":"3bbc8b7256e67e9a3d45dee98ab1211208ef42b5d04cf8a54a77829b3aec3e3c","source":{"kind":"arxiv","id":"1808.02853","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02853","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02853v1","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02853","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"HO6IW4SW4Z7J","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HO6IW4SW4Z7JUPKF","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HO6IW4SW","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HO6IW4SW4Z7JUPKF33UYVMJBCI","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T16:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"6ac98028532f308f3cf175d7c42d6700a46c85f18a06e7d332a84088b3a393c5","abstract_canon_sha256":"449dcb4e3b00e76f0c41f5d72def8c97c056dd577158a891cddeaa6c52af49aa"},"schema_version":"1.0"},"canonical_sha256":"3bbc8b7256e67e9a3d45dee98ab1211208ef42b5d04cf8a54a77829b3aec3e3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:31.974453Z","signature_b64":"ZeBNF12fhlQVruhqK+V1uZArR95IUvNCsscxfx+zPnGWuoW9tCR7b5iWXB2RxkLatH2z9bqlZzD9CsiFFvbLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bbc8b7256e67e9a3d45dee98ab1211208ef42b5d04cf8a54a77829b3aec3e3c","last_reissued_at":"2026-05-18T00:08:31.973801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:31.973801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02853","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NO64uYn+9PTwiJ10Hnoc1cUOT2NgAaashHNMTUR5qjYx04DgEhGKgzhHBIRBTDV56no8ct3jn1g9RH7S4I0QCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:15:53.542815Z"},"content_sha256":"5055595eb90782261e9f6762f1c52152b2673a76b1f0d4f6446cd097203088a6","schema_version":"1.0","event_id":"sha256:5055595eb90782261e9f6762f1c52152b2673a76b1f0d4f6446cd097203088a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HO6IW4SW4Z7JUPKF33UYVMJBCI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exotic matrix models: the Albert algebra and the spin factor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Paul E. Gunnells","submitted_at":"2018-08-08T16:41:59Z","abstract_excerpt":"The matrix models attached to real symmetric matrices and the complex/quaternionic Hermitian matrices have been studied by many authors. These models correspond to three of the simple formally real Jordan algebras over R. Such algebras were classified by Jordan, von Neumann, and Wigner in the 30s, and apart from these three there are two others: (i) the spin factor L_{1,n}, an algebra built on R^{n+1}, and (ii) the Albert algebra A of 3 by 3 Hermitian matrices over the octonions. In this paper we investigate the matrix models attached to these remaining cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02853","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oll1tRUB+1dzMsDmxJZHNPXmDwHMPjLMJzYYMmlnFKChsQMCVUz7AWCpBEISuF5kd5pNjXESx2XVkyxdLe9UAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:15:53.543214Z"},"content_sha256":"80e0f08f608b71b6e0d0815f724428aef58b694a79acccd40420ed7179d77c57","schema_version":"1.0","event_id":"sha256:80e0f08f608b71b6e0d0815f724428aef58b694a79acccd40420ed7179d77c57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HO6IW4SW4Z7JUPKF33UYVMJBCI/bundle.json","state_url":"https://pith.science/pith/HO6IW4SW4Z7JUPKF33UYVMJBCI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HO6IW4SW4Z7JUPKF33UYVMJBCI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T23:15:53Z","links":{"resolver":"https://pith.science/pith/HO6IW4SW4Z7JUPKF33UYVMJBCI","bundle":"https://pith.science/pith/HO6IW4SW4Z7JUPKF33UYVMJBCI/bundle.json","state":"https://pith.science/pith/HO6IW4SW4Z7JUPKF33UYVMJBCI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HO6IW4SW4Z7JUPKF33UYVMJBCI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HO6IW4SW4Z7JUPKF33UYVMJBCI","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":"449dcb4e3b00e76f0c41f5d72def8c97c056dd577158a891cddeaa6c52af49aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T16:41:59Z","title_canon_sha256":"6ac98028532f308f3cf175d7c42d6700a46c85f18a06e7d332a84088b3a393c5"},"schema_version":"1.0","source":{"id":"1808.02853","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02853","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02853v1","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02853","created_at":"2026-05-18T00:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"HO6IW4SW4Z7J","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HO6IW4SW4Z7JUPKF","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HO6IW4SW","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:80e0f08f608b71b6e0d0815f724428aef58b694a79acccd40420ed7179d77c57","target":"graph","created_at":"2026-05-18T00:08:31Z","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 matrix models attached to real symmetric matrices and the complex/quaternionic Hermitian matrices have been studied by many authors. These models correspond to three of the simple formally real Jordan algebras over R. Such algebras were classified by Jordan, von Neumann, and Wigner in the 30s, and apart from these three there are two others: (i) the spin factor L_{1,n}, an algebra built on R^{n+1}, and (ii) the Albert algebra A of 3 by 3 Hermitian matrices over the octonions. In this paper we investigate the matrix models attached to these remaining cases.","authors_text":"Paul E. Gunnells","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T16:41:59Z","title":"Exotic matrix models: the Albert algebra and the spin factor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02853","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":"sha256:5055595eb90782261e9f6762f1c52152b2673a76b1f0d4f6446cd097203088a6","target":"record","created_at":"2026-05-18T00:08:31Z","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":"449dcb4e3b00e76f0c41f5d72def8c97c056dd577158a891cddeaa6c52af49aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-08T16:41:59Z","title_canon_sha256":"6ac98028532f308f3cf175d7c42d6700a46c85f18a06e7d332a84088b3a393c5"},"schema_version":"1.0","source":{"id":"1808.02853","kind":"arxiv","version":1}},"canonical_sha256":"3bbc8b7256e67e9a3d45dee98ab1211208ef42b5d04cf8a54a77829b3aec3e3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bbc8b7256e67e9a3d45dee98ab1211208ef42b5d04cf8a54a77829b3aec3e3c","first_computed_at":"2026-05-18T00:08:31.973801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:31.973801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZeBNF12fhlQVruhqK+V1uZArR95IUvNCsscxfx+zPnGWuoW9tCR7b5iWXB2RxkLatH2z9bqlZzD9CsiFFvbLCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:31.974453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02853","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5055595eb90782261e9f6762f1c52152b2673a76b1f0d4f6446cd097203088a6","sha256:80e0f08f608b71b6e0d0815f724428aef58b694a79acccd40420ed7179d77c57"],"state_sha256":"954391fabdc09bf53a8f14c4121be126be341cfa5fc0cb8ccf04f1d4e8b4e8ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o8YQbTWu+Td2L0068B3uqI0fys4ChuLtsI9iy67CStWLcPA7uMFmZv3QQE+iQwlgXZf8f1+s9AXQuTPM7JE2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:15:53.545628Z","bundle_sha256":"8132e89b373c229c849530f296c2e432c9e37378b9f0afec577df8659db0594b"}}