{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:NEC5LBYKZ3MUZ7BX6CF3QXE4W5","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":"79624eb2ec88a9e5b45c77bbdec664e3c14c4c5d3a1c6b63e89d1c194276325e","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-06-15T06:53:40Z","title_canon_sha256":"0a686200372dd4427e9e0343565de60c228940f5c7dec6b829e841f02494535f"},"schema_version":"1.0","source":{"id":"2006.08169","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.08169","created_at":"2026-07-05T01:49:17Z"},{"alias_kind":"arxiv_version","alias_value":"2006.08169v2","created_at":"2026-07-05T01:49:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08169","created_at":"2026-07-05T01:49:17Z"},{"alias_kind":"pith_short_12","alias_value":"NEC5LBYKZ3MU","created_at":"2026-07-05T01:49:17Z"},{"alias_kind":"pith_short_16","alias_value":"NEC5LBYKZ3MUZ7BX","created_at":"2026-07-05T01:49:17Z"},{"alias_kind":"pith_short_8","alias_value":"NEC5LBYK","created_at":"2026-07-05T01:49:17Z"}],"graph_snapshots":[{"event_id":"sha256:86aefd6f1db02ad584ed2edca789b9b901da8e2fae68482a4efd6b861d2b5687","target":"graph","created_at":"2026-07-05T01:49:17Z","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/2006.08169/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a natural $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$-graded generalisation of $d=2$, $\\mathcal{N}=(1,1)$ supersymmetry and construct a $\\mathbb{Z}_2^2$-space realisation thereof. Due to the grading, the supercharges close with respect to, in the classical language, a commutator rather than an anticommutator. This is then used to build classical (linear and non-linear) sigma models that exhibit this novel supersymmetry via mimicking standard superspace methods. The fields in our models are bosons, right-handed and left-handed Majorana-Weyl spinors, and exotic bosons. The bosons commute with ","authors_text":"Andrew James Bruce","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-06-15T06:53:40Z","title":"$\\mathbb{Z}_2\\times \\mathbb{Z}_2$-graded supersymmetry: $2$-d sigma models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08169","kind":"arxiv","version":2},"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":"sha256:40bfc0d974eb09e75e012b86ded3b63b7efdaea49b41c0724f6d3d18dfcf418c","target":"record","created_at":"2026-07-05T01:49:17Z","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":"79624eb2ec88a9e5b45c77bbdec664e3c14c4c5d3a1c6b63e89d1c194276325e","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-06-15T06:53:40Z","title_canon_sha256":"0a686200372dd4427e9e0343565de60c228940f5c7dec6b829e841f02494535f"},"schema_version":"1.0","source":{"id":"2006.08169","kind":"arxiv","version":2}},"canonical_sha256":"6905d5870aced94cfc37f08bb85c9cb7663bb5d8436f212198ebde8101de87b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6905d5870aced94cfc37f08bb85c9cb7663bb5d8436f212198ebde8101de87b2","first_computed_at":"2026-07-05T01:49:17.408008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:49:17.408008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZfjyvxZsq1Cs4D/xiPS8lNYatir4oDQ4ODkjFPQ2OST89KsG5C8WSP9/rXglR2YjKcd5oOy1fqKQAGXNsgjFCw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:49:17.408486Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.08169","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40bfc0d974eb09e75e012b86ded3b63b7efdaea49b41c0724f6d3d18dfcf418c","sha256:86aefd6f1db02ad584ed2edca789b9b901da8e2fae68482a4efd6b861d2b5687"],"state_sha256":"aaba10880a65a53dc5caa1c41cde8c1224aa727942ff6b4d767417cc0104a123"}