{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:4HTUC4EM5E6UW3LMCAM4XGWLNX","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":"bd50653cc1c940ee0a4191a863bda61d84ea1f50db02618720f1a5b4566f2d05","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-12-01T21:37:15Z","title_canon_sha256":"a5a6005543a9ce810569d823bb83df4ecb43cc49d2317855ee540eadcafe9216"},"schema_version":"1.0","source":{"id":"2112.00840","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.00840","created_at":"2026-07-05T05:55:07Z"},{"alias_kind":"arxiv_version","alias_value":"2112.00840v3","created_at":"2026-07-05T05:55:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.00840","created_at":"2026-07-05T05:55:07Z"},{"alias_kind":"pith_short_12","alias_value":"4HTUC4EM5E6U","created_at":"2026-07-05T05:55:07Z"},{"alias_kind":"pith_short_16","alias_value":"4HTUC4EM5E6UW3LM","created_at":"2026-07-05T05:55:07Z"},{"alias_kind":"pith_short_8","alias_value":"4HTUC4EM","created_at":"2026-07-05T05:55:07Z"}],"graph_snapshots":[{"event_id":"sha256:2af0ce3cf2ff920d3ae2521ffcf1e674df2991050932a72a213f7a4df5775e04","target":"graph","created_at":"2026-07-05T05:55:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.00840/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The \"$10$-fold way\" refers to the combined classification of the $3$ associative division algebras (of real, complex and quaternionic numbers) and of the $7$, ${\\mathbb Z}_2$-graded, superdivision algebras (in a superdivision algebra each homogeneous element is invertible). The connection of the $10$-fold way with the periodic table of topological insulators and superconductors is well known. Motivated by the recent interest in ${\\mathbb Z}_2\\times{\\mathbb Z}_2$-graded physics (classical and quantum invariant models, parastatistics) we classify the associative ${\\mathbb Z}_2\\times {\\mathbb Z}_","authors_text":"Francesco Toppan, Zhanna Kuznetsova","cross_cats":["cond-mat.mes-hall","hep-th","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-12-01T21:37:15Z","title":"Beyond the $10$-fold way: $13$ associative $Z_2\\times Z_2$-graded superdivision algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.00840","kind":"arxiv","version":3},"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:a91d02cd5e79042f8fa40119a133d5818f1b6e76670e7ed86059318212cf7886","target":"record","created_at":"2026-07-05T05:55:07Z","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":"bd50653cc1c940ee0a4191a863bda61d84ea1f50db02618720f1a5b4566f2d05","cross_cats_sorted":["cond-mat.mes-hall","hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-12-01T21:37:15Z","title_canon_sha256":"a5a6005543a9ce810569d823bb83df4ecb43cc49d2317855ee540eadcafe9216"},"schema_version":"1.0","source":{"id":"2112.00840","kind":"arxiv","version":3}},"canonical_sha256":"e1e741708ce93d4b6d6c1019cb9acb6dcf2c1b81739cf45689f050123352a36a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1e741708ce93d4b6d6c1019cb9acb6dcf2c1b81739cf45689f050123352a36a","first_computed_at":"2026-07-05T05:55:07.092967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:55:07.092967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lR9JidUwFLOoz7JKa4I1zoazEeaPrkhyNN8BBxQyLleMtrQrJGp6NYwhAvCPpx+Ey67X9488Pk5e71cP0cNTDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:55:07.093492Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.00840","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a91d02cd5e79042f8fa40119a133d5818f1b6e76670e7ed86059318212cf7886","sha256:2af0ce3cf2ff920d3ae2521ffcf1e674df2991050932a72a213f7a4df5775e04"],"state_sha256":"615ed1ee1675fe0eb4602e498bc652be3830ffbc722a68c9b407e399c7c4eaab"}