{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CF3LX6QT4XLP4OJ5KA3RUNEAUZ","short_pith_number":"pith:CF3LX6QT","canonical_record":{"source":{"id":"1004.5086","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T17:26:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d4c317b247ddb6d568e6569876f389d9f334468e790bba7051b5292a73bd846a","abstract_canon_sha256":"8fa203ac33c4e402bd3010c0ef70303cfca3e8bbc09f42d3af127c93ddb6254f"},"schema_version":"1.0"},"canonical_sha256":"1176bbfa13e5d6fe393d50371a3480a6593dc92a010b8b9f60f97e9472fd2f60","source":{"kind":"arxiv","id":"1004.5086","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5086","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5086v2","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5086","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"CF3LX6QT4XLP","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CF3LX6QT4XLP4OJ5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CF3LX6QT","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CF3LX6QT4XLP4OJ5KA3RUNEAUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1004.5086","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T17:26:43Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d4c317b247ddb6d568e6569876f389d9f334468e790bba7051b5292a73bd846a","abstract_canon_sha256":"8fa203ac33c4e402bd3010c0ef70303cfca3e8bbc09f42d3af127c93ddb6254f"},"schema_version":"1.0"},"canonical_sha256":"1176bbfa13e5d6fe393d50371a3480a6593dc92a010b8b9f60f97e9472fd2f60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:11.724516Z","signature_b64":"2zivDuoqA6AzdvpTNQpquxCexqhSa8Ou0uXt0RIJWu/9V2MJztpweIVB0NS/qm/sR+/c5MYFvvR8qmOWgq2lDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1176bbfa13e5d6fe393d50371a3480a6593dc92a010b8b9f60f97e9472fd2f60","last_reissued_at":"2026-05-18T04:23:11.724123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:11.724123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.5086","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":"2026-05-18T04:23:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAiPDm5bkpzkCiyIKXXHZ6Kt9ereeN4T9oS8wJbZ9uP9BXq/2hD4dleqjVN5No7tiaGVwPhnSNbNR1fhEKD3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:26:43.384805Z"},"content_sha256":"675e071ebac6b16a48183495c859e7d1975fc870b4edc351560426bef0c2b778","schema_version":"1.0","event_id":"sha256:675e071ebac6b16a48183495c859e7d1975fc870b4edc351560426bef0c2b778"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CF3LX6QT4XLP4OJ5KA3RUNEAUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A transform of complementary aspects with applications to entropic uncertainty relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Niranjan Balachandran, Prabha Mandayam, Stephanie Wehner","submitted_at":"2010-04-28T17:26:43Z","abstract_excerpt":"Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in dimension d=2^n which have particularly beautiful symmetry properties derived from the Clifford algebra. More precisely, we show that there exists a unitary transformation that cyclically permutes such bases. This unitary can be understood as a generalization of the Fourier transform, which exchanges two MUBs, to multiple complementary aspects. We proceed to pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5086","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":"2026-05-18T04:23:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"itz2FE7cbZcnKut9sqTQsvPphCLVO80l2PVyVHufqux846hNWdTKvVlrYHnyAa5pyL5DDybkRQWOG4fjvUK/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:26:43.385151Z"},"content_sha256":"3be424514c7ec3c452ed59bc44a3ef64deaa757e0a7ba4f2df494e87cb4fe176","schema_version":"1.0","event_id":"sha256:3be424514c7ec3c452ed59bc44a3ef64deaa757e0a7ba4f2df494e87cb4fe176"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CF3LX6QT4XLP4OJ5KA3RUNEAUZ/bundle.json","state_url":"https://pith.science/pith/CF3LX6QT4XLP4OJ5KA3RUNEAUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CF3LX6QT4XLP4OJ5KA3RUNEAUZ/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":"2026-05-28T04:26:43Z","links":{"resolver":"https://pith.science/pith/CF3LX6QT4XLP4OJ5KA3RUNEAUZ","bundle":"https://pith.science/pith/CF3LX6QT4XLP4OJ5KA3RUNEAUZ/bundle.json","state":"https://pith.science/pith/CF3LX6QT4XLP4OJ5KA3RUNEAUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CF3LX6QT4XLP4OJ5KA3RUNEAUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CF3LX6QT4XLP4OJ5KA3RUNEAUZ","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":"8fa203ac33c4e402bd3010c0ef70303cfca3e8bbc09f42d3af127c93ddb6254f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T17:26:43Z","title_canon_sha256":"d4c317b247ddb6d568e6569876f389d9f334468e790bba7051b5292a73bd846a"},"schema_version":"1.0","source":{"id":"1004.5086","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5086","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5086v2","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5086","created_at":"2026-05-18T04:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"CF3LX6QT4XLP","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CF3LX6QT4XLP4OJ5","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CF3LX6QT","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:3be424514c7ec3c452ed59bc44a3ef64deaa757e0a7ba4f2df494e87cb4fe176","target":"graph","created_at":"2026-05-18T04:23:11Z","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":"Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in dimension d=2^n which have particularly beautiful symmetry properties derived from the Clifford algebra. More precisely, we show that there exists a unitary transformation that cyclically permutes such bases. This unitary can be understood as a generalization of the Fourier transform, which exchanges two MUBs, to multiple complementary aspects. We proceed to pr","authors_text":"Niranjan Balachandran, Prabha Mandayam, Stephanie Wehner","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T17:26:43Z","title":"A transform of complementary aspects with applications to entropic uncertainty relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5086","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":"sha256:675e071ebac6b16a48183495c859e7d1975fc870b4edc351560426bef0c2b778","target":"record","created_at":"2026-05-18T04:23:11Z","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":"8fa203ac33c4e402bd3010c0ef70303cfca3e8bbc09f42d3af127c93ddb6254f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-04-28T17:26:43Z","title_canon_sha256":"d4c317b247ddb6d568e6569876f389d9f334468e790bba7051b5292a73bd846a"},"schema_version":"1.0","source":{"id":"1004.5086","kind":"arxiv","version":2}},"canonical_sha256":"1176bbfa13e5d6fe393d50371a3480a6593dc92a010b8b9f60f97e9472fd2f60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1176bbfa13e5d6fe393d50371a3480a6593dc92a010b8b9f60f97e9472fd2f60","first_computed_at":"2026-05-18T04:23:11.724123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:11.724123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2zivDuoqA6AzdvpTNQpquxCexqhSa8Ou0uXt0RIJWu/9V2MJztpweIVB0NS/qm/sR+/c5MYFvvR8qmOWgq2lDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:11.724516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5086","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:675e071ebac6b16a48183495c859e7d1975fc870b4edc351560426bef0c2b778","sha256:3be424514c7ec3c452ed59bc44a3ef64deaa757e0a7ba4f2df494e87cb4fe176"],"state_sha256":"4ab4038ccd6d128cb3dcc797e1f7091c40a00352e65a2f6b632c8b583288aba0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rD0jBx1quFoWTBSqrVl3sD7/b3SCESjnJeUQG5V+w5BPCoOnyQKNb6oTduQnEbGLSTX4cr9V7epKWffvaXwbDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:26:43.387251Z","bundle_sha256":"f1659b68c8cb204420a555082a57635b683cf249bf8483438dd6cd04ab0b7fc3"}}