{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UKZ2H7CAQRRHNIOSPNOJSBQHDU","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":"c862c5ca0ee4d6b8e6f3bc3cbaf99cc5f7ba83dae410aa866b0bf55b2c3ec679","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-08-08T18:41:15Z","title_canon_sha256":"1a0dd6cfdbe43f87287867265d7387b0573c1ac0138ec5747b154d17d7d78612"},"schema_version":"1.0","source":{"id":"1908.03236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03236","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03236v2","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03236","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"UKZ2H7CAQRRH","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_16","alias_value":"UKZ2H7CAQRRHNIOS","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_8","alias_value":"UKZ2H7CA","created_at":"2026-07-04T23:55:13Z"}],"graph_snapshots":[{"event_id":"sha256:39c2c439f98d913dd59378d75ae3aeb4be6add9c283f27f1bc2e3c349365857f","target":"graph","created_at":"2026-07-04T23:55:13Z","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/1908.03236/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show the 3 by 3 magic square of squares problem equivalent to solving quartic polynomials with certain factorization constraints over an abelian extension of the rationals. We analyze a particular case in which said extension is assumed to be the Gaussian integers resulting a new search method. Additionally, the magic square of squares is analyzed over finite fields and rings of the form Z/nZ resulting in some conjectures enumerating the rings and finite fields in which a magic square of squares can be constructed. Code is made available.","authors_text":"Onno Cain","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-08-08T18:41:15Z","title":"Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03236","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":"sha256:29432ea1f51923946a69de05f7b900b028fd388b6f3e541656760e9a0700433a","target":"record","created_at":"2026-07-04T23:55:13Z","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":"c862c5ca0ee4d6b8e6f3bc3cbaf99cc5f7ba83dae410aa866b0bf55b2c3ec679","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-08-08T18:41:15Z","title_canon_sha256":"1a0dd6cfdbe43f87287867265d7387b0573c1ac0138ec5747b154d17d7d78612"},"schema_version":"1.0","source":{"id":"1908.03236","kind":"arxiv","version":2}},"canonical_sha256":"a2b3a3fc40846276a1d27b5c9906071d22f37b48bd12ad38ed9b59cd136ac823","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2b3a3fc40846276a1d27b5c9906071d22f37b48bd12ad38ed9b59cd136ac823","first_computed_at":"2026-07-04T23:55:13.234503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:55:13.234503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fBdHpCfu4TBO2Lgw96JVCNs4FH5jJkiSrTKibHHSKFhkxG/3rzduIR1ot7hEoipcL3r+tM9kdl7Az8ftcdXWBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:55:13.234891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29432ea1f51923946a69de05f7b900b028fd388b6f3e541656760e9a0700433a","sha256:39c2c439f98d913dd59378d75ae3aeb4be6add9c283f27f1bc2e3c349365857f"],"state_sha256":"811280a9c8f321a1b7030c8d8287ce39fed877b90647dc7de8a8aa9d7a30da0b"}