{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LL6NWACXBYKTOLGINBSA3MVQK4","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":"d59da0200b2bf17e1ed25064f523f01d0d5336e60106b66f7340e0473e4ae869","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-23T22:11:30Z","title_canon_sha256":"147bf1a1a6c4f7b4c8ac3e8d1b1902e851c0fb2313008b5953714a02dbb0ec83"},"schema_version":"1.0","source":{"id":"1411.6306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6306","created_at":"2026-05-18T02:33:00Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6306v1","created_at":"2026-05-18T02:33:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6306","created_at":"2026-05-18T02:33:00Z"},{"alias_kind":"pith_short_12","alias_value":"LL6NWACXBYKT","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LL6NWACXBYKTOLGI","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LL6NWACX","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:127885fda44c95dc4251cc22a4356dd638715a1aee165c5d9b3793ba9f4f0c5d","target":"graph","created_at":"2026-05-18T02:33:00Z","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":"In this paper we provide a new parametrization for the diophantine equation $A^2+B^2+C^2=3D^2$ and give a series of corollaries. We discuss some connections with Lagrange's four-square theorem. As applications, we find new parameterizations of equilateral triangles and regular tetrahedrons having integer coordinates in three dimensions.","authors_text":"Eugen J. Ionascu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-23T22:11:30Z","title":"New parametrization of $A^2+B^2+C^2=3D^2$ and Lagrange's four-square theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6306","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":"sha256:3c78ccfc3171c01f5fffc2eee4f84acfa1483c85489f58f2aaa2c419e6efdee6","target":"record","created_at":"2026-05-18T02:33:00Z","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":"d59da0200b2bf17e1ed25064f523f01d0d5336e60106b66f7340e0473e4ae869","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-23T22:11:30Z","title_canon_sha256":"147bf1a1a6c4f7b4c8ac3e8d1b1902e851c0fb2313008b5953714a02dbb0ec83"},"schema_version":"1.0","source":{"id":"1411.6306","kind":"arxiv","version":1}},"canonical_sha256":"5afcdb00570e15372cc868640db2b0570521109371fffbaf08955854b3414e39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5afcdb00570e15372cc868640db2b0570521109371fffbaf08955854b3414e39","first_computed_at":"2026-05-18T02:33:00.325137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:00.325137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ys/ntcvPXpMApSOADbFi2QADSAV8SNu2woCXPeKccU2cmH8v7HiWXr2UzEGDdY9JZwQNtWwB5QoXGqLzdBnCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:00.325534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c78ccfc3171c01f5fffc2eee4f84acfa1483c85489f58f2aaa2c419e6efdee6","sha256:127885fda44c95dc4251cc22a4356dd638715a1aee165c5d9b3793ba9f4f0c5d"],"state_sha256":"0e6648faab0633467f650c12d88e98d510663fe84e18bfb794f29fd0b78a445b"}