{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WUOUUX5IKDH6PK7FCKB5XOFXTG","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":"bc1620af67cc519fe8b493d534be7dfd10c53b69baa967d8da853a2403ce61b6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-30T21:22:42Z","title_canon_sha256":"3f865ccd6b5a2de7226acddd38c258d2e701f305f5deeb5a672906c8150f08c9"},"schema_version":"1.0","source":{"id":"1210.8173","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.8173","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1210.8173v2","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8173","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"WUOUUX5IKDH6","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"WUOUUX5IKDH6PK7F","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"WUOUUX5I","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:cfb73a89038ced6de6e4cfb912403426d5034b3d6fe75aeb7e741d07531886cb","target":"graph","created_at":"2026-05-18T03:26:32Z","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 show how to transform the problem of finding d+1 mutually unbiased bases in the d-dimensional Hilbert space into the one of finding d(d+1) vectors in the N-dimensional Hilbert space with N=d**2. The transformation formulas admit a solution when d is a prime number.","authors_text":"Maurice Robert Kibler (IPNL)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-30T21:22:42Z","title":"On mutually unbiased bases: Passing from d to d**2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8173","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:fcbe829a2551c55ef1602f3d5a2211887610c4560af15236771c8084b00affa3","target":"record","created_at":"2026-05-18T03:26:32Z","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":"bc1620af67cc519fe8b493d534be7dfd10c53b69baa967d8da853a2403ce61b6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-30T21:22:42Z","title_canon_sha256":"3f865ccd6b5a2de7226acddd38c258d2e701f305f5deeb5a672906c8150f08c9"},"schema_version":"1.0","source":{"id":"1210.8173","kind":"arxiv","version":2}},"canonical_sha256":"b51d4a5fa850cfe7abe51283dbb8b799b3a2ef5ee5e166291428b00b5eef27f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b51d4a5fa850cfe7abe51283dbb8b799b3a2ef5ee5e166291428b00b5eef27f4","first_computed_at":"2026-05-18T03:26:32.277208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:32.277208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"klDuSFgtImX8YuyMa3k/OjzvhlMGOPCqa5fqO2JnvqkZsSKeQ0+KKNVd8znzOkvtLu+XrYWLJhCFZIzidkMXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:32.277621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.8173","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcbe829a2551c55ef1602f3d5a2211887610c4560af15236771c8084b00affa3","sha256:cfb73a89038ced6de6e4cfb912403426d5034b3d6fe75aeb7e741d07531886cb"],"state_sha256":"e11710f54506c3e88a348888ea06a3eafea7e3be2018e036a24472bb63597497"}