{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CBXOY3BYPFUHEJ35Y7H7ZDA5PG","short_pith_number":"pith:CBXOY3BY","canonical_record":{"source":{"id":"1310.6813","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-10-25T03:52:05Z","cross_cats_sorted":["cs.ET","cs.LO"],"title_canon_sha256":"5626fbf53e2f635795d191001648244833f27280d3315bb173473bb82d3067fb","abstract_canon_sha256":"a780ca8320579b80adcbbedd682a7e01c3f96ba11a15df2202f9b39aa8001764"},"schema_version":"1.0"},"canonical_sha256":"106eec6c38796872277dc7cffc8c1d79bf23149d9a2c7bd6f2608c4f8fb249e7","source":{"kind":"arxiv","id":"1310.6813","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CBXOY3BYPFUHEJ35Y7H7ZDA5PG","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6813","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-10-25T03:52:05Z","cross_cats_sorted":["cs.ET","cs.LO"],"title_canon_sha256":"5626fbf53e2f635795d191001648244833f27280d3315bb173473bb82d3067fb","abstract_canon_sha256":"a780ca8320579b80adcbbedd682a7e01c3f96ba11a15df2202f9b39aa8001764"},"schema_version":"1.0"},"canonical_sha256":"106eec6c38796872277dc7cffc8c1d79bf23149d9a2c7bd6f2608c4f8fb249e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:38.474078Z","signature_b64":"PMVIe1DGcMfsdWY7y94lK3WB+1HWYOQTTvSgFqj47qJywNBm361S0ZxmTDLnKZnkcr8BCqWjeOxHT0V9SDZaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"106eec6c38796872277dc7cffc8c1d79bf23149d9a2c7bd6f2608c4f8fb249e7","last_reissued_at":"2026-05-18T00:47:38.473553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:38.473553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6813","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bkKVZNnjtiXs3wHIdm8p3jBFBF6UeoYy8CurSAUmZXe7Pph9uT1DAlMZJ1TO6XLOgkO7BmIMRNsjpP0rQIBbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:43:18.355852Z"},"content_sha256":"6272e45cb03ce84269e7affba940acab4a819a51b15f47d58af03a5aa17b21c7","schema_version":"1.0","event_id":"sha256:6272e45cb03ce84269e7affba940acab4a819a51b15f47d58af03a5aa17b21c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CBXOY3BYPFUHEJ35Y7H7ZDA5PG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generators and relations for n-qubit Clifford operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.ET","cs.LO"],"primary_cat":"quant-ph","authors_text":"Canada), Peter Selinger (Dalhousie University","submitted_at":"2013-10-25T03:52:05Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6813","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y7Hqg6AZSLPIghEhOp+yuLdGzjU1eC/1TPdJ9i0jqgD0gdCyvbWPEWhGOyGu/IHmWr1FJhPf0CyKqNjcPyv+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:43:18.356471Z"},"content_sha256":"3aa8e190d95650c938724023ed2ee65f8efd3041be746ddce1f1a1e3cebebd21","schema_version":"1.0","event_id":"sha256:3aa8e190d95650c938724023ed2ee65f8efd3041be746ddce1f1a1e3cebebd21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBXOY3BYPFUHEJ35Y7H7ZDA5PG/bundle.json","state_url":"https://pith.science/pith/CBXOY3BYPFUHEJ35Y7H7ZDA5PG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBXOY3BYPFUHEJ35Y7H7ZDA5PG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T14:43:18Z","links":{"resolver":"https://pith.science/pith/CBXOY3BYPFUHEJ35Y7H7ZDA5PG","bundle":"https://pith.science/pith/CBXOY3BYPFUHEJ35Y7H7ZDA5PG/bundle.json","state":"https://pith.science/pith/CBXOY3BYPFUHEJ35Y7H7ZDA5PG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBXOY3BYPFUHEJ35Y7H7ZDA5PG/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"49INof9thQbnREPvsVKhz0jwoydo1cccPfmh1AgPx5fC33vbppQQusexpJu38MnwdwjBpbX4Ma3SIxagY7OpDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:43:18.360534Z","bundle_sha256":"14690083e1a7d738a55b8a7fc32ba08e78e83028e74b0c484375c923af86fe77"}}