{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7275PEHCJ3II577BEVEJOUFNYG","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":"99e7af421b0b4d3a303f85c25f03e5ee7547c48ca0559a2dcf789db807bcac26","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-25T23:55:10Z","title_canon_sha256":"1d95070206e0f43649ed20ca02d06c4c3e39974c416d7b7a3d27dc62ab31c3ed"},"schema_version":"1.0","source":{"id":"1705.09398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09398","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09398v1","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09398","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"7275PEHCJ3II","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"7275PEHCJ3II577B","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"7275PEHC","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:d9e7d40ea0864f3782882155382bf6180f9d86c20d55a935ef8b968f75c52ac9","target":"graph","created_at":"2026-05-18T00:43:38Z","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":"Operators acting on the discrete random chaos yield signed multiplicative systems, extending the notion of spin matrices and quaternions. We investigate signed groups through the associated sign matrices, focusing on generators and their replacements. Of particular interest are anticommutative generators leading to a complete classification of the generated groups. The classification of finite groups of mixed commutativity is also obtained.","authors_text":"Jerzy Szulga","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-25T23:55:10Z","title":"On signed generators of groups and algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09398","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:c1e371f7c210c5630f5dcd18064bf57c73bf52146c676e82b41e7517fee27070","target":"record","created_at":"2026-05-18T00:43:38Z","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":"99e7af421b0b4d3a303f85c25f03e5ee7547c48ca0559a2dcf789db807bcac26","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-25T23:55:10Z","title_canon_sha256":"1d95070206e0f43649ed20ca02d06c4c3e39974c416d7b7a3d27dc62ab31c3ed"},"schema_version":"1.0","source":{"id":"1705.09398","kind":"arxiv","version":1}},"canonical_sha256":"febfd790e24ed08effe125489750adc1990d384a9001a677bc33e60c28e548e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"febfd790e24ed08effe125489750adc1990d384a9001a677bc33e60c28e548e0","first_computed_at":"2026-05-18T00:43:38.811024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:38.811024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KZKGr48/rjFetCQVDhIve3Uz6E7MU9UYOTOQ85ow+Qg+atzCVJ5K8eHzEliV07K/q4XNGjUjhvlD6MsxbeYPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:38.811850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e371f7c210c5630f5dcd18064bf57c73bf52146c676e82b41e7517fee27070","sha256:d9e7d40ea0864f3782882155382bf6180f9d86c20d55a935ef8b968f75c52ac9"],"state_sha256":"0da548feb6daf86e5dfab9073676333ab41950228943e62417a5d9e2d950546b"}