{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M5LAYNNBY4IEAXXR66X3O3RHUC","short_pith_number":"pith:M5LAYNNB","canonical_record":{"source":{"id":"1504.01236","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-06T08:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"60291b1ed14f7dd958fb34b7750642172e9ef7ce4d3ddf82e941e621953ba9c0","abstract_canon_sha256":"ff108f1ec22a25829e68e3f036992968d3570bc346ae6b2d05d5a74c97d934e0"},"schema_version":"1.0"},"canonical_sha256":"67560c35a1c710405ef1f7afb76e27a0ab2b6ae5ef7cbdd14b17d2fe2bf09358","source":{"kind":"arxiv","id":"1504.01236","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01236","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01236v3","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01236","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"M5LAYNNBY4IE","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M5LAYNNBY4IEAXXR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M5LAYNNB","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M5LAYNNBY4IEAXXR66X3O3RHUC","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01236","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-06T08:39:22Z","cross_cats_sorted":[],"title_canon_sha256":"60291b1ed14f7dd958fb34b7750642172e9ef7ce4d3ddf82e941e621953ba9c0","abstract_canon_sha256":"ff108f1ec22a25829e68e3f036992968d3570bc346ae6b2d05d5a74c97d934e0"},"schema_version":"1.0"},"canonical_sha256":"67560c35a1c710405ef1f7afb76e27a0ab2b6ae5ef7cbdd14b17d2fe2bf09358","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:29.913963Z","signature_b64":"b4a8VePQeCu02R4rqdVtZ3lZ2T+CbbYISn+zoecKOXOS6WKYEjdTk+534ty06pZZcJiQ85OCZJMVsonxn4/gBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67560c35a1c710405ef1f7afb76e27a0ab2b6ae5ef7cbdd14b17d2fe2bf09358","last_reissued_at":"2026-05-18T01:31:29.913526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:29.913526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01236","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UVpRuVdavn5JNj7VP3/k5yp5jAFE1VCL9lZVeksgJdw41ku5OP4kdMcmfKZjxn4xTP+rtSxGY9TNHEZt0u3dBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:47:35.219902Z"},"content_sha256":"4a9e90fd937b62005ca413cabda7ac043e08934844627af938d2bb01947b72a8","schema_version":"1.0","event_id":"sha256:4a9e90fd937b62005ca413cabda7ac043e08934844627af938d2bb01947b72a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M5LAYNNBY4IEAXXR66X3O3RHUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: a coding-theoretic approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Makoto Araya, Masaaki Harada, Sho Suda","submitted_at":"2015-04-06T08:39:22Z","abstract_excerpt":"This paper is concerned with quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices, which are generalizations of unbiased Hadamard matrices, equivalently unbiased bases. These matrices are studied from the viewpoint of coding theory. As a consequence of a coding-theoretic approach, we provide upper bounds on the number of mutually quasi-unbiased Hadamard matrices. We give classifications of a certain class of self-complementary codes for modest lengths. These codes give quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices. Some modification of the notion of w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01236","kind":"arxiv","version":3},"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":"2026-05-18T01:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYzZhpXucdIVTngt+Xn0m7bU2YozIUIWJlvzs9227PUiTHwd2VmMEbeEzXmfDQrAz/8PFiiW89I188oGovU3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:47:35.220562Z"},"content_sha256":"455688802f720b3075aba78ae65b830de2ba90efd943dabed0b7cf08e62caad0","schema_version":"1.0","event_id":"sha256:455688802f720b3075aba78ae65b830de2ba90efd943dabed0b7cf08e62caad0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5LAYNNBY4IEAXXR66X3O3RHUC/bundle.json","state_url":"https://pith.science/pith/M5LAYNNBY4IEAXXR66X3O3RHUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5LAYNNBY4IEAXXR66X3O3RHUC/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":"2026-05-30T15:47:35Z","links":{"resolver":"https://pith.science/pith/M5LAYNNBY4IEAXXR66X3O3RHUC","bundle":"https://pith.science/pith/M5LAYNNBY4IEAXXR66X3O3RHUC/bundle.json","state":"https://pith.science/pith/M5LAYNNBY4IEAXXR66X3O3RHUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5LAYNNBY4IEAXXR66X3O3RHUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M5LAYNNBY4IEAXXR66X3O3RHUC","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":"ff108f1ec22a25829e68e3f036992968d3570bc346ae6b2d05d5a74c97d934e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-06T08:39:22Z","title_canon_sha256":"60291b1ed14f7dd958fb34b7750642172e9ef7ce4d3ddf82e941e621953ba9c0"},"schema_version":"1.0","source":{"id":"1504.01236","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01236","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01236v3","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01236","created_at":"2026-05-18T01:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"M5LAYNNBY4IE","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M5LAYNNBY4IEAXXR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M5LAYNNB","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:455688802f720b3075aba78ae65b830de2ba90efd943dabed0b7cf08e62caad0","target":"graph","created_at":"2026-05-18T01:31:29Z","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":"This paper is concerned with quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices, which are generalizations of unbiased Hadamard matrices, equivalently unbiased bases. These matrices are studied from the viewpoint of coding theory. As a consequence of a coding-theoretic approach, we provide upper bounds on the number of mutually quasi-unbiased Hadamard matrices. We give classifications of a certain class of self-complementary codes for modest lengths. These codes give quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices. Some modification of the notion of w","authors_text":"Makoto Araya, Masaaki Harada, Sho Suda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-06T08:39:22Z","title":"Quasi-unbiased Hadamard matrices and weakly unbiased Hadamard matrices: a coding-theoretic approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01236","kind":"arxiv","version":3},"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":"sha256:4a9e90fd937b62005ca413cabda7ac043e08934844627af938d2bb01947b72a8","target":"record","created_at":"2026-05-18T01:31:29Z","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":"ff108f1ec22a25829e68e3f036992968d3570bc346ae6b2d05d5a74c97d934e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-06T08:39:22Z","title_canon_sha256":"60291b1ed14f7dd958fb34b7750642172e9ef7ce4d3ddf82e941e621953ba9c0"},"schema_version":"1.0","source":{"id":"1504.01236","kind":"arxiv","version":3}},"canonical_sha256":"67560c35a1c710405ef1f7afb76e27a0ab2b6ae5ef7cbdd14b17d2fe2bf09358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67560c35a1c710405ef1f7afb76e27a0ab2b6ae5ef7cbdd14b17d2fe2bf09358","first_computed_at":"2026-05-18T01:31:29.913526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:29.913526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4a8VePQeCu02R4rqdVtZ3lZ2T+CbbYISn+zoecKOXOS6WKYEjdTk+534ty06pZZcJiQ85OCZJMVsonxn4/gBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:29.913963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01236","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a9e90fd937b62005ca413cabda7ac043e08934844627af938d2bb01947b72a8","sha256:455688802f720b3075aba78ae65b830de2ba90efd943dabed0b7cf08e62caad0"],"state_sha256":"5c64d4903e8faa87f381c68e5ea1e9a1ada0d1f75bb03112ae3162c989d706fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r49MQCehdfsYLhJ/kD2gbcDmpp8ubITgp9/csxJfkGTu7bWvShCpVywHEhc8jtOTR0M1mrjjpohs8rbOfxTkCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:47:35.224145Z","bundle_sha256":"ba053b8733236b72e4f10b4e14ba4d399e8ab0fb8ac09089e5ddcd39cc744688"}}