{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QT4TMPDUWD5KFW5OU7BVZ5CWLN","short_pith_number":"pith:QT4TMPDU","canonical_record":{"source":{"id":"1402.6807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T07:07:21Z","cross_cats_sorted":[],"title_canon_sha256":"1041c29f7383a951b4a9a1b0a3d1fe5d5f67f2b6ef509db8a5374e5e1f42ae1a","abstract_canon_sha256":"a47a4c1293c2d723891bfe46643eac80b77edb051ce902cb0473741ac54ffe8e"},"schema_version":"1.0"},"canonical_sha256":"84f9363c74b0faa2dbaea7c35cf4565b628f39580f5346349662d03b225bbf0e","source":{"kind":"arxiv","id":"1402.6807","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6807","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6807v1","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6807","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"QT4TMPDUWD5K","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QT4TMPDUWD5KFW5O","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QT4TMPDU","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QT4TMPDUWD5KFW5OU7BVZ5CWLN","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T07:07:21Z","cross_cats_sorted":[],"title_canon_sha256":"1041c29f7383a951b4a9a1b0a3d1fe5d5f67f2b6ef509db8a5374e5e1f42ae1a","abstract_canon_sha256":"a47a4c1293c2d723891bfe46643eac80b77edb051ce902cb0473741ac54ffe8e"},"schema_version":"1.0"},"canonical_sha256":"84f9363c74b0faa2dbaea7c35cf4565b628f39580f5346349662d03b225bbf0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:36.972042Z","signature_b64":"h7fdwckU5slAO2KMEv74SRVoJtG8v+2hWXpoluo8peqjWEdfan7S7859PTR48+mauyhFk4X0eRduU+Ae7lwRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84f9363c74b0faa2dbaea7c35cf4565b628f39580f5346349662d03b225bbf0e","last_reissued_at":"2026-05-18T02:57:36.971373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:36.971373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6807","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":"2026-05-18T02:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xh+GQdwCouRMF5wyCcLRi5vu9Gcg0fklxcEnBFQi5vLwFDDknlWyg9Y1o8Y7LffP00iKWwdtmp8DBhXAnhzLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:05:57.630964Z"},"content_sha256":"5dcd4dd3eba3cd5ccf99fc6feaddc246bcd0544339cfad99001d05c64b83ddb9","schema_version":"1.0","event_id":"sha256:5dcd4dd3eba3cd5ccf99fc6feaddc246bcd0544339cfad99001d05c64b83ddb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QT4TMPDUWD5KFW5OU7BVZ5CWLN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of Butson Hadamard matrices of small degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hirasaka Mitsugu, Kyoung-Tark Kim, Yoshihiro Mizoguchi","submitted_at":"2014-02-27T07:07:21Z","abstract_excerpt":"For positive integers $m$ and $n$, we denote by $\\mathrm{BH}(m,n)$ the set of all $H\\in M_{n\\times n}(\\mathbb{C})$ such that $HH^\\ast=nI_n$ and each entry of $H$ is an $m$-th root of unity where $H^\\ast$ is the adjoint matrix of $H$ and $I_n$ is the identity matrix.\n  For $H_1,H_2\\in \\mathrm{BH}(m,n)$ we say that $H_1$ is \\textit{equivalent} to $H_2$ if $H_1=PH_2 Q$ for some monomial matrices $P, Q$ whose nonzero entries are $m$-th roots of unity.\n  In this paper we classify $\\mathrm{BH}(17,17)$ up to equivalence by computer search."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6807","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":"2026-05-18T02:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fCYbicjWsyTdmK2pgSPlyd2wvJFs+oui3MJfp6Ny/+OoCMjuPhIOF+i0TwL/Fp+bJn05a9S78bJTWAHbsKcmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:05:57.631686Z"},"content_sha256":"d767eb82418183c88202bb685e35aaaa543f8c77f4c34663aecce9ea7a550d76","schema_version":"1.0","event_id":"sha256:d767eb82418183c88202bb685e35aaaa543f8c77f4c34663aecce9ea7a550d76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QT4TMPDUWD5KFW5OU7BVZ5CWLN/bundle.json","state_url":"https://pith.science/pith/QT4TMPDUWD5KFW5OU7BVZ5CWLN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QT4TMPDUWD5KFW5OU7BVZ5CWLN/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":"2026-06-08T15:05:57Z","links":{"resolver":"https://pith.science/pith/QT4TMPDUWD5KFW5OU7BVZ5CWLN","bundle":"https://pith.science/pith/QT4TMPDUWD5KFW5OU7BVZ5CWLN/bundle.json","state":"https://pith.science/pith/QT4TMPDUWD5KFW5OU7BVZ5CWLN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QT4TMPDUWD5KFW5OU7BVZ5CWLN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QT4TMPDUWD5KFW5OU7BVZ5CWLN","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":"a47a4c1293c2d723891bfe46643eac80b77edb051ce902cb0473741ac54ffe8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T07:07:21Z","title_canon_sha256":"1041c29f7383a951b4a9a1b0a3d1fe5d5f67f2b6ef509db8a5374e5e1f42ae1a"},"schema_version":"1.0","source":{"id":"1402.6807","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6807","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6807v1","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6807","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"QT4TMPDUWD5K","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QT4TMPDUWD5KFW5O","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QT4TMPDU","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:d767eb82418183c88202bb685e35aaaa543f8c77f4c34663aecce9ea7a550d76","target":"graph","created_at":"2026-05-18T02:57:36Z","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":"For positive integers $m$ and $n$, we denote by $\\mathrm{BH}(m,n)$ the set of all $H\\in M_{n\\times n}(\\mathbb{C})$ such that $HH^\\ast=nI_n$ and each entry of $H$ is an $m$-th root of unity where $H^\\ast$ is the adjoint matrix of $H$ and $I_n$ is the identity matrix.\n  For $H_1,H_2\\in \\mathrm{BH}(m,n)$ we say that $H_1$ is \\textit{equivalent} to $H_2$ if $H_1=PH_2 Q$ for some monomial matrices $P, Q$ whose nonzero entries are $m$-th roots of unity.\n  In this paper we classify $\\mathrm{BH}(17,17)$ up to equivalence by computer search.","authors_text":"Hirasaka Mitsugu, Kyoung-Tark Kim, Yoshihiro Mizoguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T07:07:21Z","title":"Uniqueness of Butson Hadamard matrices of small degrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6807","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":"sha256:5dcd4dd3eba3cd5ccf99fc6feaddc246bcd0544339cfad99001d05c64b83ddb9","target":"record","created_at":"2026-05-18T02:57:36Z","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":"a47a4c1293c2d723891bfe46643eac80b77edb051ce902cb0473741ac54ffe8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-02-27T07:07:21Z","title_canon_sha256":"1041c29f7383a951b4a9a1b0a3d1fe5d5f67f2b6ef509db8a5374e5e1f42ae1a"},"schema_version":"1.0","source":{"id":"1402.6807","kind":"arxiv","version":1}},"canonical_sha256":"84f9363c74b0faa2dbaea7c35cf4565b628f39580f5346349662d03b225bbf0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84f9363c74b0faa2dbaea7c35cf4565b628f39580f5346349662d03b225bbf0e","first_computed_at":"2026-05-18T02:57:36.971373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:36.971373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h7fdwckU5slAO2KMEv74SRVoJtG8v+2hWXpoluo8peqjWEdfan7S7859PTR48+mauyhFk4X0eRduU+Ae7lwRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:36.972042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6807","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dcd4dd3eba3cd5ccf99fc6feaddc246bcd0544339cfad99001d05c64b83ddb9","sha256:d767eb82418183c88202bb685e35aaaa543f8c77f4c34663aecce9ea7a550d76"],"state_sha256":"d46e64c48a97045dfee9b33f780b13d7d87f2ca13b98ff16d24c36b961851b55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WoPg/uz2zBc5b8qxxFJzcvoGpi6EtFUci1ucwGiMVwZrJRgpcUl8peLfiA1gXZNOhGXNpO4MQAud+oPEx8fLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T15:05:57.635769Z","bundle_sha256":"592baeeb8b41b3fb0ff39e2a00411c3133873141655dd470881d7c7d706e4e50"}}