{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QOXQFCRUJKWE3D3E2AOTWBP36Y","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":"fb31e67d60afabfbaf29abec89bf61b718ee4d6202dd034d5e537a5ad42cee3e","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-07-18T12:58:45Z","title_canon_sha256":"02ac510ca98f01163f4df8a3e81663842eebf6cb523d84bc19d268ca592e512c"},"schema_version":"1.0","source":{"id":"1907.08024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08024","created_at":"2026-07-05T01:24:27Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08024v1","created_at":"2026-07-05T01:24:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08024","created_at":"2026-07-05T01:24:27Z"},{"alias_kind":"pith_short_12","alias_value":"QOXQFCRUJKWE","created_at":"2026-07-05T01:24:27Z"},{"alias_kind":"pith_short_16","alias_value":"QOXQFCRUJKWE3D3E","created_at":"2026-07-05T01:24:27Z"},{"alias_kind":"pith_short_8","alias_value":"QOXQFCRU","created_at":"2026-07-05T01:24:27Z"}],"graph_snapshots":[{"event_id":"sha256:f1ed484d53099683037d493dc97a0947986bc6afe5846def2b52900543cb3cd0","target":"graph","created_at":"2026-07-05T01:24:27Z","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/1907.08024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are equivalent up to single-qubit Clifford operations is known to be decidable in polynomial time and have been studied both in the context of producing certain required states in a quantum network but also in relation to stabilizer codes. The reason for the latter this is that single-qubit Clifford equivalent graph states exactly corresponds to equivalent stabilizer c","authors_text":"Axel Dahlberg, Jonas Helsen, Stephanie Wehner","cross_cats":["cs.CC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-07-18T12:58:45Z","title":"Counting single-qubit Clifford equivalent graph states is #P-Complete"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08024","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":"sha256:85dbdbb605ff9fc86c5a8758a2975c12618ee15a52b77aa84933ea4c8c5836fa","target":"record","created_at":"2026-07-05T01:24:27Z","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":"fb31e67d60afabfbaf29abec89bf61b718ee4d6202dd034d5e537a5ad42cee3e","cross_cats_sorted":["cs.CC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-07-18T12:58:45Z","title_canon_sha256":"02ac510ca98f01163f4df8a3e81663842eebf6cb523d84bc19d268ca592e512c"},"schema_version":"1.0","source":{"id":"1907.08024","kind":"arxiv","version":1}},"canonical_sha256":"83af028a344aac4d8f64d01d3b05fbf60b172f7fc7040cf336bfb7ba9ca4e432","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83af028a344aac4d8f64d01d3b05fbf60b172f7fc7040cf336bfb7ba9ca4e432","first_computed_at":"2026-07-05T01:24:27.449144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:24:27.449144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ctT+s6AML7NFOlJ4SmxRVVzuwNNp456uHLEUmEx9BN0HaQ+oxOcp7s+u4Q5SJHQuGvkhPuraSU6MgnYXMXKDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:24:27.449528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85dbdbb605ff9fc86c5a8758a2975c12618ee15a52b77aa84933ea4c8c5836fa","sha256:f1ed484d53099683037d493dc97a0947986bc6afe5846def2b52900543cb3cd0"],"state_sha256":"0411d410f99ac1de72b56cab46d1504674c8ca9f8b3837d69021a5d9038f8a84"}