{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CBXOY3BYPFUHEJ35Y7H7ZDA5PG","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":"a780ca8320579b80adcbbedd682a7e01c3f96ba11a15df2202f9b39aa8001764","cross_cats_sorted":["cs.ET","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-10-25T03:52:05Z","title_canon_sha256":"5626fbf53e2f635795d191001648244833f27280d3315bb173473bb82d3067fb"},"schema_version":"1.0","source":{"id":"1310.6813","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6813","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6813v4","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6813","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"pith_short_12","alias_value":"CBXOY3BYPFUH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CBXOY3BYPFUHEJ35","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CBXOY3BY","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:3aa8e190d95650c938724023ed2ee65f8efd3041be746ddce1f1a1e3cebebd21","target":"graph","created_at":"2026-05-18T00:47:38Z","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":"We define a normal form for Clifford circuits, and we prove that every Clifford operator has a unique normal form. Moreover, we present a rewrite system by which any Clifford circuit can be reduced to normal form. This yields a presentation of Clifford operators in terms of generators and relations.","authors_text":"Canada), Peter Selinger (Dalhousie University","cross_cats":["cs.ET","cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-10-25T03:52:05Z","title":"Generators and relations for n-qubit Clifford operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6813","kind":"arxiv","version":4},"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":"sha256:6272e45cb03ce84269e7affba940acab4a819a51b15f47d58af03a5aa17b21c7","target":"record","created_at":"2026-05-18T00:47:38Z","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":"a780ca8320579b80adcbbedd682a7e01c3f96ba11a15df2202f9b39aa8001764","cross_cats_sorted":["cs.ET","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-10-25T03:52:05Z","title_canon_sha256":"5626fbf53e2f635795d191001648244833f27280d3315bb173473bb82d3067fb"},"schema_version":"1.0","source":{"id":"1310.6813","kind":"arxiv","version":4}},"canonical_sha256":"106eec6c38796872277dc7cffc8c1d79bf23149d9a2c7bd6f2608c4f8fb249e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"106eec6c38796872277dc7cffc8c1d79bf23149d9a2c7bd6f2608c4f8fb249e7","first_computed_at":"2026-05-18T00:47:38.473553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:38.473553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PMVIe1DGcMfsdWY7y94lK3WB+1HWYOQTTvSgFqj47qJywNBm361S0ZxmTDLnKZnkcr8BCqWjeOxHT0V9SDZaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:38.474078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6813","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6272e45cb03ce84269e7affba940acab4a819a51b15f47d58af03a5aa17b21c7","sha256:3aa8e190d95650c938724023ed2ee65f8efd3041be746ddce1f1a1e3cebebd21"],"state_sha256":"18a94be6a57bf5f9ed39b4fe82af4d556b68aeef17a412ee97e2df70b8c304dd"}