{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OD5ZCHFPUAZKHGCD4SBF2FNAES","short_pith_number":"pith:OD5ZCHFP","canonical_record":{"source":{"id":"1201.0631","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T13:53:26Z","cross_cats_sorted":[],"title_canon_sha256":"001514ccf3375aa3016b9ab9cab75c3cd34168466c162b465134ff6fc8986f65","abstract_canon_sha256":"d6418325c164e3f634082b564d44c6f6c7ae58d4d2f3d7380cb5bb25d340f98a"},"schema_version":"1.0"},"canonical_sha256":"70fb911cafa032a39843e4825d15a024ac7cd2dad724594d7f1ac1af2c5fd3ea","source":{"kind":"arxiv","id":"1201.0631","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0631","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0631v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0631","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"OD5ZCHFPUAZK","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OD5ZCHFPUAZKHGCD","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OD5ZCHFP","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OD5ZCHFPUAZKHGCD4SBF2FNAES","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0631","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T13:53:26Z","cross_cats_sorted":[],"title_canon_sha256":"001514ccf3375aa3016b9ab9cab75c3cd34168466c162b465134ff6fc8986f65","abstract_canon_sha256":"d6418325c164e3f634082b564d44c6f6c7ae58d4d2f3d7380cb5bb25d340f98a"},"schema_version":"1.0"},"canonical_sha256":"70fb911cafa032a39843e4825d15a024ac7cd2dad724594d7f1ac1af2c5fd3ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:17.038490Z","signature_b64":"IFNbq64TXtjGoxsoSuCdPKmmTKLi3pQI2N9KuY4dKBinzO/zyRCRalbXjRehxWAYJPREMBjNRRSxr2RcZ0T/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70fb911cafa032a39843e4825d15a024ac7cd2dad724594d7f1ac1af2c5fd3ea","last_reissued_at":"2026-05-18T04:05:17.037702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:17.037702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0631","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":"2026-05-18T04:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"txKlNsjs1ktRU2ScnJRSy2z9nNYFicz97ReWyv3FpANPbu7kHiiDoGs31smP2lqzxgl79P7JMDDvWs23TdGsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T01:24:13.869419Z"},"content_sha256":"541629c006703db4f351fc461aff8c52e1b93c9fde8c80473dd79eed72a3fb09","schema_version":"1.0","event_id":"sha256:541629c006703db4f351fc461aff8c52e1b93c9fde8c80473dd79eed72a3fb09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OD5ZCHFPUAZKHGCD4SBF2FNAES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Real and complex unbiased Hadamard matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Imre Z. Ruzsa, Mate Matolcsi, Mihaly Weiner","submitted_at":"2012-01-03T13:53:26Z","abstract_excerpt":"We use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and complex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard matrices (MUHs) in any dimension $d$ cannot contain more than one real Hadamard matrix. We also give new proofs of several known structural results in low dimensions, for $d\\le 6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0631","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":"2026-05-18T04:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lIln7jcJ8q5Rqc/xIBhjLlrRZOuZQWbLOchNqWmyx0XIT7O/ChgJGOTyUv4FwA9O3oQvI5crZhqXSuFYoQwkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T01:24:13.870094Z"},"content_sha256":"390bcca144a3bfd86bce137f4d5b6c8a356a32e228154463871eb9b4663d2967","schema_version":"1.0","event_id":"sha256:390bcca144a3bfd86bce137f4d5b6c8a356a32e228154463871eb9b4663d2967"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OD5ZCHFPUAZKHGCD4SBF2FNAES/bundle.json","state_url":"https://pith.science/pith/OD5ZCHFPUAZKHGCD4SBF2FNAES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OD5ZCHFPUAZKHGCD4SBF2FNAES/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":"2026-05-23T01:24:13Z","links":{"resolver":"https://pith.science/pith/OD5ZCHFPUAZKHGCD4SBF2FNAES","bundle":"https://pith.science/pith/OD5ZCHFPUAZKHGCD4SBF2FNAES/bundle.json","state":"https://pith.science/pith/OD5ZCHFPUAZKHGCD4SBF2FNAES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OD5ZCHFPUAZKHGCD4SBF2FNAES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OD5ZCHFPUAZKHGCD4SBF2FNAES","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":"d6418325c164e3f634082b564d44c6f6c7ae58d4d2f3d7380cb5bb25d340f98a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T13:53:26Z","title_canon_sha256":"001514ccf3375aa3016b9ab9cab75c3cd34168466c162b465134ff6fc8986f65"},"schema_version":"1.0","source":{"id":"1201.0631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0631","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0631v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0631","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"OD5ZCHFPUAZK","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OD5ZCHFPUAZKHGCD","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OD5ZCHFP","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:390bcca144a3bfd86bce137f4d5b6c8a356a32e228154463871eb9b4663d2967","target":"graph","created_at":"2026-05-18T04:05:17Z","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 use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and complex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard matrices (MUHs) in any dimension $d$ cannot contain more than one real Hadamard matrix. We also give new proofs of several known structural results in low dimensions, for $d\\le 6$.","authors_text":"Imre Z. Ruzsa, Mate Matolcsi, Mihaly Weiner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T13:53:26Z","title":"Real and complex unbiased Hadamard matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0631","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":"sha256:541629c006703db4f351fc461aff8c52e1b93c9fde8c80473dd79eed72a3fb09","target":"record","created_at":"2026-05-18T04:05:17Z","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":"d6418325c164e3f634082b564d44c6f6c7ae58d4d2f3d7380cb5bb25d340f98a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T13:53:26Z","title_canon_sha256":"001514ccf3375aa3016b9ab9cab75c3cd34168466c162b465134ff6fc8986f65"},"schema_version":"1.0","source":{"id":"1201.0631","kind":"arxiv","version":1}},"canonical_sha256":"70fb911cafa032a39843e4825d15a024ac7cd2dad724594d7f1ac1af2c5fd3ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70fb911cafa032a39843e4825d15a024ac7cd2dad724594d7f1ac1af2c5fd3ea","first_computed_at":"2026-05-18T04:05:17.037702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:17.037702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IFNbq64TXtjGoxsoSuCdPKmmTKLi3pQI2N9KuY4dKBinzO/zyRCRalbXjRehxWAYJPREMBjNRRSxr2RcZ0T/Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:17.038490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:541629c006703db4f351fc461aff8c52e1b93c9fde8c80473dd79eed72a3fb09","sha256:390bcca144a3bfd86bce137f4d5b6c8a356a32e228154463871eb9b4663d2967"],"state_sha256":"4db23cc1df0918e8331165a7a261e706857b372621f4f411aa1f9adc4ce66693"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1B+mkvSBLIHu436/OQF3okRjGkCMm8Bzq/sb5X/i7Oi0Q3PT3zoO9NFSyOd/zGJ7qkykBWhxfkiLhCs8XdOgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T01:24:13.874798Z","bundle_sha256":"fcff7021fc48213493ee25c9099a303be2b1856ac7b238c45624b943f4d23d7c"}}