{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KIEBOOFFDYWGRVWQTOZJXSGM5S","short_pith_number":"pith:KIEBOOFF","canonical_record":{"source":{"id":"1808.06831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-21T10:12:55Z","cross_cats_sorted":["math-ph","math.GR","math.MP","math.NT","quant-ph"],"title_canon_sha256":"ac0a3e6965ad93b7d7ab1f18911a7be61ae09ef0e5440fc94f1f39a358346d62","abstract_canon_sha256":"fe1838ac9b01638d5174ada6b6c75fb661d021781a0b5ee55810ae159edcb672"},"schema_version":"1.0"},"canonical_sha256":"52081738a51e2c68d6d09bb29bc8ccec9f02d2c2aeb552504198d7e29264ea23","source":{"kind":"arxiv","id":"1808.06831","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.06831","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.06831v2","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06831","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"KIEBOOFFDYWG","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KIEBOOFFDYWGRVWQ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KIEBOOFF","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KIEBOOFFDYWGRVWQTOZJXSGM5S","target":"record","payload":{"canonical_record":{"source":{"id":"1808.06831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-21T10:12:55Z","cross_cats_sorted":["math-ph","math.GR","math.MP","math.NT","quant-ph"],"title_canon_sha256":"ac0a3e6965ad93b7d7ab1f18911a7be61ae09ef0e5440fc94f1f39a358346d62","abstract_canon_sha256":"fe1838ac9b01638d5174ada6b6c75fb661d021781a0b5ee55810ae159edcb672"},"schema_version":"1.0"},"canonical_sha256":"52081738a51e2c68d6d09bb29bc8ccec9f02d2c2aeb552504198d7e29264ea23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:29.281352Z","signature_b64":"5srisZ1HbQlvOeyRcEk3zKgQSyVtZUN3f/FhjqpXg6Rmduu5Fcbseqx72L73RFulZ68KDLnckC4pRZnKGlMSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52081738a51e2c68d6d09bb29bc8ccec9f02d2c2aeb552504198d7e29264ea23","last_reissued_at":"2026-05-17T23:53:29.280740Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:29.280740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.06831","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LVx2vJvnEy06sE1LHJbVZbmoDFDi0vUT94etqnWr5pknvSnxqpXGtmeIBezsWiaISbuJwyiJlf076cNOh8/OBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:41:31.946861Z"},"content_sha256":"39726ee85d261d3ade53b261bc85cea4bf7398d34fd4752c49f69a2972025dbc","schema_version":"1.0","event_id":"sha256:39726ee85d261d3ade53b261bc85cea4bf7398d34fd4752c49f69a2972025dbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KIEBOOFFDYWGRVWQTOZJXSGM5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum computing with Bianchi groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.GR","math.MP","math.NT","quant-ph"],"primary_cat":"math.GT","authors_text":"Klee Irwin, Marcelo M. Amaral, Michel Planat, Raymond Aschheim","submitted_at":"2018-08-21T10:12:55Z","abstract_excerpt":"It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing $d$-dimensional universal quantum computing (uqc) based on minimal informationally complete POVMs. The relevant quantum gates may be built from subgroups of finite index of the modular group $\\Gamma=PSL(2,\\mathbb{Z})$ [M. Planat, Entropy 20, 16 (2018)] or more generally from subgroups of fundamental groups of $3$-manifolds [M. Planat, R. Aschheim, M.~M. Amaral and K. Irwin, arXiv 1802.04196(quant-ph)]. In this paper, previous work is encompassed by the use of torsion-free subgroups of Bianchi gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06831","kind":"arxiv","version":2},"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":"2026-05-17T23:53:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xsvkztrtII3SP1u5nTIcMKMumOZPW7qcUL3Jh/tssUJxStB5Vh6qqNQRPfJDxKYa8U/R+FpZG7TunqFSHPEbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:41:31.947505Z"},"content_sha256":"c10ca9c12871748779c46efdb6a6fcd2004cea398d83300766863bc6ef3c4090","schema_version":"1.0","event_id":"sha256:c10ca9c12871748779c46efdb6a6fcd2004cea398d83300766863bc6ef3c4090"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIEBOOFFDYWGRVWQTOZJXSGM5S/bundle.json","state_url":"https://pith.science/pith/KIEBOOFFDYWGRVWQTOZJXSGM5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIEBOOFFDYWGRVWQTOZJXSGM5S/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":"2026-05-27T12:41:31Z","links":{"resolver":"https://pith.science/pith/KIEBOOFFDYWGRVWQTOZJXSGM5S","bundle":"https://pith.science/pith/KIEBOOFFDYWGRVWQTOZJXSGM5S/bundle.json","state":"https://pith.science/pith/KIEBOOFFDYWGRVWQTOZJXSGM5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIEBOOFFDYWGRVWQTOZJXSGM5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KIEBOOFFDYWGRVWQTOZJXSGM5S","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":"fe1838ac9b01638d5174ada6b6c75fb661d021781a0b5ee55810ae159edcb672","cross_cats_sorted":["math-ph","math.GR","math.MP","math.NT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-21T10:12:55Z","title_canon_sha256":"ac0a3e6965ad93b7d7ab1f18911a7be61ae09ef0e5440fc94f1f39a358346d62"},"schema_version":"1.0","source":{"id":"1808.06831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.06831","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.06831v2","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06831","created_at":"2026-05-17T23:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"KIEBOOFFDYWG","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KIEBOOFFDYWGRVWQ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KIEBOOFF","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:c10ca9c12871748779c46efdb6a6fcd2004cea398d83300766863bc6ef3c4090","target":"graph","created_at":"2026-05-17T23:53:29Z","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":"It has been shown that non-stabilizer eigenstates of permutation gates are appropriate for allowing $d$-dimensional universal quantum computing (uqc) based on minimal informationally complete POVMs. The relevant quantum gates may be built from subgroups of finite index of the modular group $\\Gamma=PSL(2,\\mathbb{Z})$ [M. Planat, Entropy 20, 16 (2018)] or more generally from subgroups of fundamental groups of $3$-manifolds [M. Planat, R. Aschheim, M.~M. Amaral and K. Irwin, arXiv 1802.04196(quant-ph)]. In this paper, previous work is encompassed by the use of torsion-free subgroups of Bianchi gr","authors_text":"Klee Irwin, Marcelo M. Amaral, Michel Planat, Raymond Aschheim","cross_cats":["math-ph","math.GR","math.MP","math.NT","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-21T10:12:55Z","title":"Quantum computing with Bianchi groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06831","kind":"arxiv","version":2},"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":"sha256:39726ee85d261d3ade53b261bc85cea4bf7398d34fd4752c49f69a2972025dbc","target":"record","created_at":"2026-05-17T23:53:29Z","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":"fe1838ac9b01638d5174ada6b6c75fb661d021781a0b5ee55810ae159edcb672","cross_cats_sorted":["math-ph","math.GR","math.MP","math.NT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-08-21T10:12:55Z","title_canon_sha256":"ac0a3e6965ad93b7d7ab1f18911a7be61ae09ef0e5440fc94f1f39a358346d62"},"schema_version":"1.0","source":{"id":"1808.06831","kind":"arxiv","version":2}},"canonical_sha256":"52081738a51e2c68d6d09bb29bc8ccec9f02d2c2aeb552504198d7e29264ea23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52081738a51e2c68d6d09bb29bc8ccec9f02d2c2aeb552504198d7e29264ea23","first_computed_at":"2026-05-17T23:53:29.280740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:29.280740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5srisZ1HbQlvOeyRcEk3zKgQSyVtZUN3f/FhjqpXg6Rmduu5Fcbseqx72L73RFulZ68KDLnckC4pRZnKGlMSCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:29.281352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.06831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39726ee85d261d3ade53b261bc85cea4bf7398d34fd4752c49f69a2972025dbc","sha256:c10ca9c12871748779c46efdb6a6fcd2004cea398d83300766863bc6ef3c4090"],"state_sha256":"c43d1fb01a3f1bb2eef06c6302b52653e07b41ac9f13a65a6a4c19dee96963e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TcRT+TZDAhc8XhfEoKhoZlsT7SlvFeb+DcbeTM7KVEnqVnCqk1ZHGrdCoKHn3aj7u/ApiAYobRuPRfuXpufmDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:41:31.951029Z","bundle_sha256":"25c93489806f35259465e597aab10fab866b3e5ae2adc8ed6ba934cd31f57221"}}