{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZVGSMXTZWTIMDCS3GTEHP4V3AN","short_pith_number":"pith:ZVGSMXTZ","schema_version":"1.0","canonical_sha256":"cd4d265e79b4d0c18a5b34c877f2bb037d0e55e6d2319c82fdd3bef80235b09f","source":{"kind":"arxiv","id":"1207.4081","version":1},"attestation_state":"computed","paper":{"title":"A biquadratic Diophantine equation associated with perfect cuboids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ruslan Sharipov","submitted_at":"2012-07-17T18:33:48Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1207.4081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-17T18:33:48Z","cross_cats_sorted":[],"title_canon_sha256":"2bec9bdc6b12dc8968d69c7bf3bb42e31149bae1c21d688cff455d10a9ce2798","abstract_canon_sha256":"e1109874cb19d581c95cc19e6a9cfb6df048cc18955f94c187d8fa6548cd79ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:49.076792Z","signature_b64":"CDxOOgTUdwhIth1Y2wpXewbpHov52g3fDfe5sd4B36702uyhylRVcFI8q84lEoULVfzqnBvFs2fvTO3gG5xdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd4d265e79b4d0c18a5b34c877f2bb037d0e55e6d2319c82fdd3bef80235b09f","last_reissued_at":"2026-05-18T03:50:49.076074Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:49.076074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A biquadratic Diophantine equation associated with perfect cuboids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ruslan Sharipov","submitted_at":"2012-07-17T18:33:48Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4081","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.4081","created_at":"2026-05-18T03:50:49.076173+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.4081v1","created_at":"2026-05-18T03:50:49.076173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4081","created_at":"2026-05-18T03:50:49.076173+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZVGSMXTZWTIM","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZVGSMXTZWTIMDCS3","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZVGSMXTZ","created_at":"2026-05-18T12:27:30.460161+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN","json":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN.json","graph_json":"https://pith.science/api/pith-number/ZVGSMXTZWTIMDCS3GTEHP4V3AN/graph.json","events_json":"https://pith.science/api/pith-number/ZVGSMXTZWTIMDCS3GTEHP4V3AN/events.json","paper":"https://pith.science/paper/ZVGSMXTZ"},"agent_actions":{"view_html":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN","download_json":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN.json","view_paper":"https://pith.science/paper/ZVGSMXTZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.4081&json=true","fetch_graph":"https://pith.science/api/pith-number/ZVGSMXTZWTIMDCS3GTEHP4V3AN/graph.json","fetch_events":"https://pith.science/api/pith-number/ZVGSMXTZWTIMDCS3GTEHP4V3AN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN/action/storage_attestation","attest_author":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN/action/author_attestation","sign_citation":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN/action/citation_signature","submit_replication":"https://pith.science/pith/ZVGSMXTZWTIMDCS3GTEHP4V3AN/action/replication_record"}},"created_at":"2026-05-18T03:50:49.076173+00:00","updated_at":"2026-05-18T03:50:49.076173+00:00"}