{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:G25DDHFBQG7W7KSBDO7L6BB7IF","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":"fe36ad493b87921800ea4e4fcdf64a252c8bc4656166ad961145643e1ed117dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-28T07:50:38Z","title_canon_sha256":"c14c568b9758160cacb08dee7060c9e15e49b0f3f488aff8d4b66bbaf8c80e6c"},"schema_version":"1.0","source":{"id":"1501.07012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07012","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07012v1","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07012","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"G25DDHFBQG7W","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"G25DDHFBQG7W7KSB","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"G25DDHFB","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:21111f85cbb69cf6ca662b6f008c6206399412ad8b209a602ca987a8a932a63d","target":"graph","created_at":"2026-05-18T02:28:30Z","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 study orthogonal matrices whose elements have moduli $\\leq 1$. This paper shows that the existence of two such families of matrices is equivalent. Specifically we show that the existence of an Hadamard matrix of order $4t$ is equivalent to the existence of a Cretan$(4t-1,2)$-Mersenne matrix.","authors_text":"Jennifer Seberry, N. A. Balonin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-28T07:50:38Z","title":"Equivalence of the Existence of Hadamard Matrices and Cretan$(4t-1,2)$-Mersenne Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07012","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:fe19e8d4886a62395a91babefb65dcf2b44e4e4b1c22f3bde4c1f47a1f2f2f6a","target":"record","created_at":"2026-05-18T02:28:30Z","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":"fe36ad493b87921800ea4e4fcdf64a252c8bc4656166ad961145643e1ed117dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-28T07:50:38Z","title_canon_sha256":"c14c568b9758160cacb08dee7060c9e15e49b0f3f488aff8d4b66bbaf8c80e6c"},"schema_version":"1.0","source":{"id":"1501.07012","kind":"arxiv","version":1}},"canonical_sha256":"36ba319ca181bf6faa411bbebf043f414cb3d6a6b26d98ba7e0c43a55b0e5231","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36ba319ca181bf6faa411bbebf043f414cb3d6a6b26d98ba7e0c43a55b0e5231","first_computed_at":"2026-05-18T02:28:30.537025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:30.537025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M11BVn2oZYqgVnPx/r7hLQoYm/ZVj9AeRM8jBqo1zboMWPx1nfu8putStoi01MplgKm3j81w9XZgQCJqd8voBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:30.537653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe19e8d4886a62395a91babefb65dcf2b44e4e4b1c22f3bde4c1f47a1f2f2f6a","sha256:21111f85cbb69cf6ca662b6f008c6206399412ad8b209a602ca987a8a932a63d"],"state_sha256":"12de5a230d8d8acd06a83aa89326cd5a07c382e2e41d3f949f5cda4b951d4fc4"}