{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QUUL5LQNM52DIAST7QJ42FMMBY","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":"ff5a7a5a297692845cee55cf601235ee9cc613f7f3c5d1965c7286a7bd9f15f6","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-07T07:29:25Z","title_canon_sha256":"b0acb0f33a34e667fb28ba4a8a4ec5903eecf120c3ef63dbb7ec18d81743cb44"},"schema_version":"1.0","source":{"id":"1708.02015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02015","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02015v1","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02015","created_at":"2026-05-18T00:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"QUUL5LQNM52D","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QUUL5LQNM52DIAST","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QUUL5LQN","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:fd04f3c40c40f19553265775d36092f20b6290722141a0b224177ded958f1eb3","target":"graph","created_at":"2026-05-18T00:38:32Z","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 Matsuo algebra associated with a connected Fischer space is shown to be a Jordan algebra over a field of characteristic 3 if and only if the Fischer space is isomorphic to either the affine space of order 3 or the Fischer space associated with the symmetric group. The proof uses a characterization of the affine spaces of order 3 and equivalence of Jordan and linearized Jordan identities over a field of characteristic 3 in case the algebra is spanned by idempotents.","authors_text":"Takahiro Yabe","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-07T07:29:25Z","title":"Jordan Matsuo algebras over fields of characteristic 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02015","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":"sha256:8a150c8f299f174feca3c7e751018b549679729925e537c059aaeb483de3b0e5","target":"record","created_at":"2026-05-18T00:38:32Z","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":"ff5a7a5a297692845cee55cf601235ee9cc613f7f3c5d1965c7286a7bd9f15f6","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-07T07:29:25Z","title_canon_sha256":"b0acb0f33a34e667fb28ba4a8a4ec5903eecf120c3ef63dbb7ec18d81743cb44"},"schema_version":"1.0","source":{"id":"1708.02015","kind":"arxiv","version":1}},"canonical_sha256":"8528beae0d6774340253fc13cd158c0e0bb4f5da2cff894cfdfb37cd6aac91e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8528beae0d6774340253fc13cd158c0e0bb4f5da2cff894cfdfb37cd6aac91e0","first_computed_at":"2026-05-18T00:38:32.545958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:32.545958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YUOkxpgkZ120oX2O1qzEl1YMkQLXATUNCEWOH9n739gauPZQKyz8MJEyuCKzEKV0Un1Oyq4APfPB/OU5l3NICg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:32.546515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a150c8f299f174feca3c7e751018b549679729925e537c059aaeb483de3b0e5","sha256:fd04f3c40c40f19553265775d36092f20b6290722141a0b224177ded958f1eb3"],"state_sha256":"f4126c28e938c2b4faccad5c3b1603d228f51fdcd729942091c86500da4add26"}