{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7R6326ALK5NZPCAGZBHU2Q4LQM","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":"c0dd67b2715c68ecb7ef1935249b5a36ab966180901db58aea942d2a049d9d5d","cross_cats_sorted":["math-ph","math.GR","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-09-22T23:21:55Z","title_canon_sha256":"8ec00a57d7520e7439bd4dec269659c72322d9f5316b3986c55076d96e4ef683"},"schema_version":"1.0","source":{"id":"2409.14624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.14624","created_at":"2026-07-05T09:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"2409.14624v1","created_at":"2026-07-05T09:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.14624","created_at":"2026-07-05T09:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"7R6326ALK5NZ","created_at":"2026-07-05T09:10:19Z"},{"alias_kind":"pith_short_16","alias_value":"7R6326ALK5NZPCAG","created_at":"2026-07-05T09:10:19Z"},{"alias_kind":"pith_short_8","alias_value":"7R6326AL","created_at":"2026-07-05T09:10:19Z"}],"graph_snapshots":[{"event_id":"sha256:841989b8ecaa200eb6678e72c2f6a28541e1889124a9613646f32db40931d80c","target":"graph","created_at":"2026-07-05T09:10:19Z","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/2409.14624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We perform a complete classification of all 56 subgroups of the two-qubit Clifford group containing the two-qubit Pauli group. We provide generators for these groups using gates familiar to the quantum information community and we reference these groups against the group libraries provided in GAP. We also list several families of groups in higher levels of the two-qubit Clifford hierarchy.","authors_text":"Eric Kubischta, Ian Teixeira","cross_cats":["math-ph","math.GR","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-09-22T23:21:55Z","title":"Classification of the Subgroups of the Two-Qubit Clifford Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14624","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":"sha256:8c46b76dc848206ee86a6541c80c40460d1bf373cf9d77aef0322ae4b95a6833","target":"record","created_at":"2026-07-05T09:10:19Z","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":"c0dd67b2715c68ecb7ef1935249b5a36ab966180901db58aea942d2a049d9d5d","cross_cats_sorted":["math-ph","math.GR","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-09-22T23:21:55Z","title_canon_sha256":"8ec00a57d7520e7439bd4dec269659c72322d9f5316b3986c55076d96e4ef683"},"schema_version":"1.0","source":{"id":"2409.14624","kind":"arxiv","version":1}},"canonical_sha256":"fc7dbd780b575b978806c84f4d438b830ed64ecc018107195bdc37d67424607a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc7dbd780b575b978806c84f4d438b830ed64ecc018107195bdc37d67424607a","first_computed_at":"2026-07-05T09:10:19.324077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:10:19.324077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o6ceMhq79WnnWCHts8KGn6SSkAqpII7qOm7VHShrEPgxKmHqwREpOmvZhZiXtLC6GsnxjjXjwGSLEuKN2wAeBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:10:19.324548Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.14624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c46b76dc848206ee86a6541c80c40460d1bf373cf9d77aef0322ae4b95a6833","sha256:841989b8ecaa200eb6678e72c2f6a28541e1889124a9613646f32db40931d80c"],"state_sha256":"03bd5e9f6abdcbe3e532900ac60625c12d5b9f4dea73286b8765df3ddb26c256"}