{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6UJGG6OA7XOU2DQE3PQSWGUUCC","short_pith_number":"pith:6UJGG6OA","canonical_record":{"source":{"id":"1704.02106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-07T06:53:42Z","cross_cats_sorted":["math.GR","math.SP"],"title_canon_sha256":"f091e6674da69d7af12199f623a389e9b7994960975f511a8b15828c945df590","abstract_canon_sha256":"ad0c5eeb9696e3b4c32465c278871503281aba13f83d6883d1a54e4568e826f8"},"schema_version":"1.0"},"canonical_sha256":"f5126379c0fddd4d0e04dbe12b1a9410bffa1464b177632cb285c101ac68a9e6","source":{"kind":"arxiv","id":"1704.02106","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02106","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02106v1","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02106","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"6UJGG6OA7XOU","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6UJGG6OA7XOU2DQE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6UJGG6OA","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6UJGG6OA7XOU2DQE3PQSWGUUCC","target":"record","payload":{"canonical_record":{"source":{"id":"1704.02106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-07T06:53:42Z","cross_cats_sorted":["math.GR","math.SP"],"title_canon_sha256":"f091e6674da69d7af12199f623a389e9b7994960975f511a8b15828c945df590","abstract_canon_sha256":"ad0c5eeb9696e3b4c32465c278871503281aba13f83d6883d1a54e4568e826f8"},"schema_version":"1.0"},"canonical_sha256":"f5126379c0fddd4d0e04dbe12b1a9410bffa1464b177632cb285c101ac68a9e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:53.864854Z","signature_b64":"qdmMtLSvYg03bssSemmlmRqEARotIXHF5Q33uiGcEsoSoiBF1+keTx9jwcgxvEzG60BPE9nhrMS40tmROVWLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5126379c0fddd4d0e04dbe12b1a9410bffa1464b177632cb285c101ac68a9e6","last_reissued_at":"2026-05-18T00:18:53.863555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:53.863555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.02106","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":"2026-05-18T00:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHt/U1k+/uWxijPx76VytW9Ina91YCn29cRDYNoU6kVivNX4O428qBH9DashD3J8hMZDy0l/TIQM7I8Oim5zAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:51:41.026337Z"},"content_sha256":"028a807675a646747d2e1e47209b2049a57206d66cfed0b4b329305c19effd53","schema_version":"1.0","event_id":"sha256:028a807675a646747d2e1e47209b2049a57206d66cfed0b4b329305c19effd53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6UJGG6OA7XOU2DQE3PQSWGUUCC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Super-Golden-Gates for PU(2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.SP"],"primary_cat":"math.NT","authors_text":"Ori Parzanchevski, Peter Sarnak","submitted_at":"2017-04-07T06:53:42Z","abstract_excerpt":"To each of the symmetry groups of the Platonic solids we adjoin a carefully designed involution yielding topological generators of PU(2) which have optimal covering properties as well as efficient navigation. These are a consequence of optimal strong approximation for integral quadratic forms associated with certain special quaternion algebras and their arithmetic groups. The generators give super efficient 1-qubit quantum gates and are natural building blocks for the design of universal quantum gates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02106","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":"2026-05-18T00:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FwSerRRkI7/yXr7s4DqMgjRHfWjf/RMv2Toi4T8rWbRWo2UGXsn9NXsNI69QjFwhd5T59wdb4dpKJFO/m/WuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:51:41.027042Z"},"content_sha256":"0785b9388d22421872e92a882a6dd276a58b6452a0f2fb8de7a0abdcec1850b3","schema_version":"1.0","event_id":"sha256:0785b9388d22421872e92a882a6dd276a58b6452a0f2fb8de7a0abdcec1850b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UJGG6OA7XOU2DQE3PQSWGUUCC/bundle.json","state_url":"https://pith.science/pith/6UJGG6OA7XOU2DQE3PQSWGUUCC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UJGG6OA7XOU2DQE3PQSWGUUCC/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":"2026-06-11T16:51:41Z","links":{"resolver":"https://pith.science/pith/6UJGG6OA7XOU2DQE3PQSWGUUCC","bundle":"https://pith.science/pith/6UJGG6OA7XOU2DQE3PQSWGUUCC/bundle.json","state":"https://pith.science/pith/6UJGG6OA7XOU2DQE3PQSWGUUCC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UJGG6OA7XOU2DQE3PQSWGUUCC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6UJGG6OA7XOU2DQE3PQSWGUUCC","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":"ad0c5eeb9696e3b4c32465c278871503281aba13f83d6883d1a54e4568e826f8","cross_cats_sorted":["math.GR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-07T06:53:42Z","title_canon_sha256":"f091e6674da69d7af12199f623a389e9b7994960975f511a8b15828c945df590"},"schema_version":"1.0","source":{"id":"1704.02106","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02106","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02106v1","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02106","created_at":"2026-05-18T00:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"6UJGG6OA7XOU","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6UJGG6OA7XOU2DQE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6UJGG6OA","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:0785b9388d22421872e92a882a6dd276a58b6452a0f2fb8de7a0abdcec1850b3","target":"graph","created_at":"2026-05-18T00:18:53Z","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":"To each of the symmetry groups of the Platonic solids we adjoin a carefully designed involution yielding topological generators of PU(2) which have optimal covering properties as well as efficient navigation. These are a consequence of optimal strong approximation for integral quadratic forms associated with certain special quaternion algebras and their arithmetic groups. The generators give super efficient 1-qubit quantum gates and are natural building blocks for the design of universal quantum gates.","authors_text":"Ori Parzanchevski, Peter Sarnak","cross_cats":["math.GR","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-07T06:53:42Z","title":"Super-Golden-Gates for PU(2)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02106","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":"sha256:028a807675a646747d2e1e47209b2049a57206d66cfed0b4b329305c19effd53","target":"record","created_at":"2026-05-18T00:18:53Z","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":"ad0c5eeb9696e3b4c32465c278871503281aba13f83d6883d1a54e4568e826f8","cross_cats_sorted":["math.GR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-07T06:53:42Z","title_canon_sha256":"f091e6674da69d7af12199f623a389e9b7994960975f511a8b15828c945df590"},"schema_version":"1.0","source":{"id":"1704.02106","kind":"arxiv","version":1}},"canonical_sha256":"f5126379c0fddd4d0e04dbe12b1a9410bffa1464b177632cb285c101ac68a9e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5126379c0fddd4d0e04dbe12b1a9410bffa1464b177632cb285c101ac68a9e6","first_computed_at":"2026-05-18T00:18:53.863555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:53.863555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qdmMtLSvYg03bssSemmlmRqEARotIXHF5Q33uiGcEsoSoiBF1+keTx9jwcgxvEzG60BPE9nhrMS40tmROVWLAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:53.864854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02106","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:028a807675a646747d2e1e47209b2049a57206d66cfed0b4b329305c19effd53","sha256:0785b9388d22421872e92a882a6dd276a58b6452a0f2fb8de7a0abdcec1850b3"],"state_sha256":"e3dd779853956fe54bea03c29630278aa9d2bd1d418c537d6c1caf7a48e7f37f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4tzK1AHpnv8rdG9kK3CIv04C31fggCS4YVdrLE3bBr6nlqdk0OW8uSmcb8VdPamESJELllf5l8el0EqaPpYXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:51:41.030664Z","bundle_sha256":"8e245226ad65d2811530884fe8df8fafbf29cc89f9bdf5505c1e16febcbe6aec"}}