{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZOFCTS67QQDDB22HBLYVKLNMTM","short_pith_number":"pith:ZOFCTS67","canonical_record":{"source":{"id":"1609.08172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-26T20:08:43Z","cross_cats_sorted":[],"title_canon_sha256":"06c4507522b81bddfaa735c8ffdfbf075ba29e795bd280634562ee9cfe2b9fb1","abstract_canon_sha256":"aab6bb0027c40d8594ff3b23c446f2cf8d0dd3541a575a11e2abc5cb16b00c6d"},"schema_version":"1.0"},"canonical_sha256":"cb8a29cbdf840630eb470af1552dac9b340e950aa8ff9a6e2ca8036e80a24c0c","source":{"kind":"arxiv","id":"1609.08172","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08172","created_at":"2026-05-18T01:03:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08172v1","created_at":"2026-05-18T01:03:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08172","created_at":"2026-05-18T01:03:47Z"},{"alias_kind":"pith_short_12","alias_value":"ZOFCTS67QQDD","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZOFCTS67QQDDB22H","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZOFCTS67","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZOFCTS67QQDDB22HBLYVKLNMTM","target":"record","payload":{"canonical_record":{"source":{"id":"1609.08172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-26T20:08:43Z","cross_cats_sorted":[],"title_canon_sha256":"06c4507522b81bddfaa735c8ffdfbf075ba29e795bd280634562ee9cfe2b9fb1","abstract_canon_sha256":"aab6bb0027c40d8594ff3b23c446f2cf8d0dd3541a575a11e2abc5cb16b00c6d"},"schema_version":"1.0"},"canonical_sha256":"cb8a29cbdf840630eb470af1552dac9b340e950aa8ff9a6e2ca8036e80a24c0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:47.978874Z","signature_b64":"uHrvZa9jzZJJdSDTN10JBfcQST011Cw1PhwQ8m2pMZQJhkwkCHS2VQBkx/IeD0VSGsWJ2ijNsMw0GMIcAED1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb8a29cbdf840630eb470af1552dac9b340e950aa8ff9a6e2ca8036e80a24c0c","last_reissued_at":"2026-05-18T01:03:47.978377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:47.978377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.08172","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fBoKkBBZNoEDgJGWSpW5cz5dcBTMrR9i0hNnMuCsfkf9eGauHlsRt5Giw6KICoDGdGaWEs0PyO7Qewwy4q7GCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:46:59.150466Z"},"content_sha256":"04b29afd9befa1bba8c31593b258f4b8f40f603feeab588a9552c0c1bec7eaf4","schema_version":"1.0","event_id":"sha256:04b29afd9befa1bba8c31593b258f4b8f40f603feeab588a9552c0c1bec7eaf4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZOFCTS67QQDDB22HBLYVKLNMTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Clifford group fails gracefully to be a unitary 4-design","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David Gross, Huangjun Zhu, Markus Grassl, Richard Kueng","submitted_at":"2016-09-26T20:08:43Z","abstract_excerpt":"A unitary t-design is a set of unitaries that is \"evenly distributed\" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information theory -- one frequently encounters constructions that rely on matrices drawn uniformly at random from the unitary group. Often, it suffices to sample these matrices from a unitary t-design, for sufficiently high t. This results in more explicit, derandomized constructions. The most prominent unitary t-design considered in quantum information is the multi-q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08172","kind":"arxiv","version":1},"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":"2026-05-18T01:03:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9CHTVdmiMhw6LUyiEdMUje72Q0U0YwtgsheEQOxZoVW0upQfk4Xu721TFNUNa8AMCv1/8X6ssroj5dZ7DeMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T17:46:59.150825Z"},"content_sha256":"e2953cd14090d29908976ca39fddf0050ae4395a848b339bb4f767b78685eb01","schema_version":"1.0","event_id":"sha256:e2953cd14090d29908976ca39fddf0050ae4395a848b339bb4f767b78685eb01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOFCTS67QQDDB22HBLYVKLNMTM/bundle.json","state_url":"https://pith.science/pith/ZOFCTS67QQDDB22HBLYVKLNMTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOFCTS67QQDDB22HBLYVKLNMTM/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":"2026-05-30T17:46:59Z","links":{"resolver":"https://pith.science/pith/ZOFCTS67QQDDB22HBLYVKLNMTM","bundle":"https://pith.science/pith/ZOFCTS67QQDDB22HBLYVKLNMTM/bundle.json","state":"https://pith.science/pith/ZOFCTS67QQDDB22HBLYVKLNMTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOFCTS67QQDDB22HBLYVKLNMTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZOFCTS67QQDDB22HBLYVKLNMTM","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":"aab6bb0027c40d8594ff3b23c446f2cf8d0dd3541a575a11e2abc5cb16b00c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-26T20:08:43Z","title_canon_sha256":"06c4507522b81bddfaa735c8ffdfbf075ba29e795bd280634562ee9cfe2b9fb1"},"schema_version":"1.0","source":{"id":"1609.08172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08172","created_at":"2026-05-18T01:03:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08172v1","created_at":"2026-05-18T01:03:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08172","created_at":"2026-05-18T01:03:47Z"},{"alias_kind":"pith_short_12","alias_value":"ZOFCTS67QQDD","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZOFCTS67QQDDB22H","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZOFCTS67","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:e2953cd14090d29908976ca39fddf0050ae4395a848b339bb4f767b78685eb01","target":"graph","created_at":"2026-05-18T01:03:47Z","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":"A unitary t-design is a set of unitaries that is \"evenly distributed\" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information theory -- one frequently encounters constructions that rely on matrices drawn uniformly at random from the unitary group. Often, it suffices to sample these matrices from a unitary t-design, for sufficiently high t. This results in more explicit, derandomized constructions. The most prominent unitary t-design considered in quantum information is the multi-q","authors_text":"David Gross, Huangjun Zhu, Markus Grassl, Richard Kueng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-26T20:08:43Z","title":"The Clifford group fails gracefully to be a unitary 4-design"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08172","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":"sha256:04b29afd9befa1bba8c31593b258f4b8f40f603feeab588a9552c0c1bec7eaf4","target":"record","created_at":"2026-05-18T01:03:47Z","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":"aab6bb0027c40d8594ff3b23c446f2cf8d0dd3541a575a11e2abc5cb16b00c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-26T20:08:43Z","title_canon_sha256":"06c4507522b81bddfaa735c8ffdfbf075ba29e795bd280634562ee9cfe2b9fb1"},"schema_version":"1.0","source":{"id":"1609.08172","kind":"arxiv","version":1}},"canonical_sha256":"cb8a29cbdf840630eb470af1552dac9b340e950aa8ff9a6e2ca8036e80a24c0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb8a29cbdf840630eb470af1552dac9b340e950aa8ff9a6e2ca8036e80a24c0c","first_computed_at":"2026-05-18T01:03:47.978377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:47.978377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uHrvZa9jzZJJdSDTN10JBfcQST011Cw1PhwQ8m2pMZQJhkwkCHS2VQBkx/IeD0VSGsWJ2ijNsMw0GMIcAED1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:47.978874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04b29afd9befa1bba8c31593b258f4b8f40f603feeab588a9552c0c1bec7eaf4","sha256:e2953cd14090d29908976ca39fddf0050ae4395a848b339bb4f767b78685eb01"],"state_sha256":"75c5c4a7a52217f8242533c3622046f9a87c9c3a42cfaaf9d41efcdea67c37ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mNQX7G3cZYfm1cM79WTv2P7i8DQ/HwVo0UChXOutefIWgktDeTpfCu4ocbTZA9TIs4cNLrNUPktN7vFVHLo2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T17:46:59.152838Z","bundle_sha256":"850f81c8a6f016ee382ab7cd69a03523ccf0fbe17311c8c4dfed7f6915dbd546"}}