{"paper":{"title":"A Ramanujan Pell Elliptic K3 Surface and Primitive Five-Cube Near Misses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"K. Srinivasa Raghava","submitted_at":"2026-07-09T19:53:47Z","abstract_excerpt":"We construct a trace-16 Ramanujan--Pell family of primitive positive five-cube near misses \\[ a_n^3+b_n^3+c_n^3+d_n^3+e_n^3=t_n^3+(-1)^{n+1}, \\] obtained from a six-cube identity of quadratic forms and the negative Pell orbit generated by \\(8+\\sqrt{65}\\). The six coefficient sequences have rational recurrence generating functions with common reciprocal denominator \\[ R(q)=1-257q-257q^2+q^3=(1+q)(1-258q+q^2). \\] The quadratic identity is derived from a conic source, explaining the constants, while the Pell mechanism accounts for both the alternating error term and the denominator.\n  The same co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11925","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.11925/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}