{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QBRBAPPWWY55LFCFPUITJKBOKR","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":"7a4da6c7ef493946582f1f8d7a5be9228916a9128065e86fb43fc8e5991a281a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.HO","submitted_at":"2019-08-02T13:11:24Z","title_canon_sha256":"f55491114d8759778aecda79c2059d5b657e0f8ea945c71f65cd358dfaf88c17"},"schema_version":"1.0","source":{"id":"1908.00838","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00838","created_at":"2026-07-04T23:51:25Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00838v2","created_at":"2026-07-04T23:51:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00838","created_at":"2026-07-04T23:51:25Z"},{"alias_kind":"pith_short_12","alias_value":"QBRBAPPWWY55","created_at":"2026-07-04T23:51:25Z"},{"alias_kind":"pith_short_16","alias_value":"QBRBAPPWWY55LFCF","created_at":"2026-07-04T23:51:25Z"},{"alias_kind":"pith_short_8","alias_value":"QBRBAPPW","created_at":"2026-07-04T23:51:25Z"}],"graph_snapshots":[{"event_id":"sha256:65f84f445663bcef1ab7adabb1284b30356859b60b601c554d331e1f23c8dbb8","target":"graph","created_at":"2026-07-04T23:51:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.00838/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In an analogous construction as by Euler for 4x4 matrices, a parametrization of 8x8 magic squares of squares with orthogonal rows is shown to be obtainable by extending the quaternionic method, as shown by Hurwitz, to octonions, but not possible to be carried even further in the Cayley-Dickson construction series.","authors_text":"\\'Isabel Pirsic","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.HO","submitted_at":"2019-08-02T13:11:24Z","title":"A parametrization of 8x8 magic squares of squares through octonionic multiplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00838","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":"sha256:76bb51e8765b8a0713efd353114ba273f6016351f3a725175e877a2d7cebc2dd","target":"record","created_at":"2026-07-04T23:51:25Z","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":"7a4da6c7ef493946582f1f8d7a5be9228916a9128065e86fb43fc8e5991a281a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.HO","submitted_at":"2019-08-02T13:11:24Z","title_canon_sha256":"f55491114d8759778aecda79c2059d5b657e0f8ea945c71f65cd358dfaf88c17"},"schema_version":"1.0","source":{"id":"1908.00838","kind":"arxiv","version":2}},"canonical_sha256":"8062103df6b63bd594457d1134a82e54615ebda9639c673e60b53927151d7f6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8062103df6b63bd594457d1134a82e54615ebda9639c673e60b53927151d7f6a","first_computed_at":"2026-07-04T23:51:25.058450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:51:25.058450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+0yZqYcQbagkRRwaAUfPtqLVXsSVar80d+4sXjLXOy+X+414/JOck8KVGlJKGMLDcR2MJrZx97R+A+KotDCPCw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:51:25.058838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00838","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76bb51e8765b8a0713efd353114ba273f6016351f3a725175e877a2d7cebc2dd","sha256:65f84f445663bcef1ab7adabb1284b30356859b60b601c554d331e1f23c8dbb8"],"state_sha256":"3c88a2877f533ab47cd82a8f7df65a544945cfbd26a1ec2ea91be90128282194"}