{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ISGEEF4QBNC7LJG2U5HBAJQUZB","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":"3c6c352be58fb2adcb41bc929998857fda1737a9732fa0d5d9e1a040a8c58e77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-27T21:00:21Z","title_canon_sha256":"08ed1e5e697bc700bb3fc6d6db3e9213a5b8c2d89da36045dff6bbc5e3662b40"},"schema_version":"1.0","source":{"id":"2505.21766","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21766","created_at":"2026-07-05T12:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21766v3","created_at":"2026-07-05T12:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21766","created_at":"2026-07-05T12:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"ISGEEF4QBNC7","created_at":"2026-07-05T12:04:35Z"},{"alias_kind":"pith_short_16","alias_value":"ISGEEF4QBNC7LJG2","created_at":"2026-07-05T12:04:35Z"},{"alias_kind":"pith_short_8","alias_value":"ISGEEF4Q","created_at":"2026-07-05T12:04:35Z"}],"graph_snapshots":[{"event_id":"sha256:adee9d54aa030a54f2bbe6c434367a694a2124b9c67b645a4822e4c31013595f","target":"graph","created_at":"2026-07-05T12:04:35Z","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/2505.21766/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using elementary algebraic arguments, it is shown that $SU(2)^{m}:=SU(2)\\times \\cdots \\times SU(2)$ ($m$ times) admits no left-invariant hypercomplex structures for all $m\\ge 1$. This result answers (in a clear and easily accessible way) the question of whether every compact Lie group of dimension $4n$ admits a left-invariant hypercomplex structure. The aforementioned question has apparently been the source of some confusion in the recent literature.","authors_text":"David N. Pham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-27T21:00:21Z","title":"On the non-existence of left-invariant hypercomplex structures on $SU(2)^{4n}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21766","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":"sha256:7f275c7e886e5892768d0671af2225f1e818f79cacb6a80fca1114b806c8e2fb","target":"record","created_at":"2026-07-05T12:04:35Z","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":"3c6c352be58fb2adcb41bc929998857fda1737a9732fa0d5d9e1a040a8c58e77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-05-27T21:00:21Z","title_canon_sha256":"08ed1e5e697bc700bb3fc6d6db3e9213a5b8c2d89da36045dff6bbc5e3662b40"},"schema_version":"1.0","source":{"id":"2505.21766","kind":"arxiv","version":3}},"canonical_sha256":"448c4217900b45f5a4daa74e102614c86cae0c69f371613b08f1c8f5fcc1a398","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"448c4217900b45f5a4daa74e102614c86cae0c69f371613b08f1c8f5fcc1a398","first_computed_at":"2026-07-05T12:04:35.269599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:35.269599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aiMAiY2tTZx7bPzukV6Nh8OuuCtTrRdNFQDroJGceazeWOUBOIxyl1z/Le5gw28aaWZp19mxBz1Ai9BZb8qoBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:35.270119Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21766","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f275c7e886e5892768d0671af2225f1e818f79cacb6a80fca1114b806c8e2fb","sha256:adee9d54aa030a54f2bbe6c434367a694a2124b9c67b645a4822e4c31013595f"],"state_sha256":"68b788bc3cb954ebafba1476e2e8fab2401e1b11018600062420e3ccc97a7303"}