{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CNI2UCTNKR2NHZVZHL6CAIZLQE","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":"6f86621a857632b0cc1ccd906d1c374a36d8b11f57733bb6d975956e9bd8a2cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-17T17:18:38Z","title_canon_sha256":"643ad78e50e81355f5449452eddbd972e64dc861865548ef0707946885f2ed71"},"schema_version":"1.0","source":{"id":"1202.3972","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3972","created_at":"2026-05-18T02:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3972v2","created_at":"2026-05-18T02:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3972","created_at":"2026-05-18T02:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"CNI2UCTNKR2N","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CNI2UCTNKR2NHZVZ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CNI2UCTN","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:c92e1c4de78003e5dc722894f78528a6da3ded127427662b416774026b9bb9c1","target":"graph","created_at":"2026-05-18T02:49:30Z","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":"We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with Semi-Dihedral groups $SD_{8n}$. The dimensions of these symmetry classes of tensors are also computed.","authors_text":"Kijti Rodtes, Mahdi Hormozi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-17T17:18:38Z","title":"Symmetry classes of tensors associated with the Semi-Dihedral groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3972","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":"sha256:353ce6ee58dd24107bd1d4384630683a4c3d9e644eb1e5c422a7e46745aaa880","target":"record","created_at":"2026-05-18T02:49:30Z","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":"6f86621a857632b0cc1ccd906d1c374a36d8b11f57733bb6d975956e9bd8a2cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-17T17:18:38Z","title_canon_sha256":"643ad78e50e81355f5449452eddbd972e64dc861865548ef0707946885f2ed71"},"schema_version":"1.0","source":{"id":"1202.3972","kind":"arxiv","version":2}},"canonical_sha256":"1351aa0a6d5474d3e6b93afc20232b813dffbf6f4a914dded2a7647c76341d43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1351aa0a6d5474d3e6b93afc20232b813dffbf6f4a914dded2a7647c76341d43","first_computed_at":"2026-05-18T02:49:30.127994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:30.127994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XXFPvhX/qNKJgme6C0/GDp5AS3N1/ZaU4j2sqp5XpQgBunMCYBThwPaos6eOweLa0OKqmMKRQs7KZ/pKip7eAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:30.128443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3972","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:353ce6ee58dd24107bd1d4384630683a4c3d9e644eb1e5c422a7e46745aaa880","sha256:c92e1c4de78003e5dc722894f78528a6da3ded127427662b416774026b9bb9c1"],"state_sha256":"a16f3ad8cb8b7a04d025626346f7acf7746f6e48367d1354cdfd37de34e86ad5"}