{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZVGSMXTZWTIMDCS3GTEHP4V3AN","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":"e1109874cb19d581c95cc19e6a9cfb6df048cc18955f94c187d8fa6548cd79ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-17T18:33:48Z","title_canon_sha256":"2bec9bdc6b12dc8968d69c7bf3bb42e31149bae1c21d688cff455d10a9ce2798"},"schema_version":"1.0","source":{"id":"1207.4081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4081","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4081v1","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4081","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"ZVGSMXTZWTIM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZVGSMXTZWTIMDCS3","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZVGSMXTZ","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:c689befa79cbdf5109bf8a953c96a61caa4abe751c0a729e8eaf9e631d2ec6a0","target":"graph","created_at":"2026-05-18T03:50:49Z","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":"A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. Such cuboids are not yet discovered and their non-existence is also not proved. Perfect Euler cuboids are described by a system of four Diophantine equation possessing a natural $S_3$ symmetry. Recently these equations were factorized with respect to this $S_3$ symmetry and the factor equations were derived. In the present paper the factor equations are transformed to $E$-form and then reduced to a single biquadratic equation.","authors_text":"Ruslan Sharipov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-17T18:33:48Z","title":"A biquadratic Diophantine equation associated with perfect cuboids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4081","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:d8807f8fa59e301c3f108107204e71318bcf742dd1c4106cd8029ab8f0786d2c","target":"record","created_at":"2026-05-18T03:50:49Z","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":"e1109874cb19d581c95cc19e6a9cfb6df048cc18955f94c187d8fa6548cd79ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-17T18:33:48Z","title_canon_sha256":"2bec9bdc6b12dc8968d69c7bf3bb42e31149bae1c21d688cff455d10a9ce2798"},"schema_version":"1.0","source":{"id":"1207.4081","kind":"arxiv","version":1}},"canonical_sha256":"cd4d265e79b4d0c18a5b34c877f2bb037d0e55e6d2319c82fdd3bef80235b09f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd4d265e79b4d0c18a5b34c877f2bb037d0e55e6d2319c82fdd3bef80235b09f","first_computed_at":"2026-05-18T03:50:49.076074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:49.076074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CDxOOgTUdwhIth1Y2wpXewbpHov52g3fDfe5sd4B36702uyhylRVcFI8q84lEoULVfzqnBvFs2fvTO3gG5xdDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:49.076792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8807f8fa59e301c3f108107204e71318bcf742dd1c4106cd8029ab8f0786d2c","sha256:c689befa79cbdf5109bf8a953c96a61caa4abe751c0a729e8eaf9e631d2ec6a0"],"state_sha256":"cdece524a5be395c58160daa4a0c8c098fca5a0cfe05b4a18e2c795abca2b521"}