Integer root detection data set

We introduce the Generalized Triangular Method of Quadratics (GTMQ), a figuratenumber based framework that unifies quadratic, cubic, and quartic equations under combinatorial structures. GTMQ connects integer roots to triangular, tetrahedral, and pentatope indices, offering a new lens for detecting and interpreting integer solutions. We validate GTMQ with billion-scale computations: over 1.085 billion cubic equations were scanned in 25 minutes on a consumer Intel i7 processor, confirming that integer roots are exceedingly rare (< 0.5%) and strongly clustered around small integers (±1, ±2, ±3). Smaller confirmatory scans reproduce the same distribution. These findings highlight both the theoretical novelty of GTMQ and its computational viability, contributing to number theory, Diophantine analysis, and experimental mathematics