Mathematical Semiotics: The Parabolic Centroid Model of Human Karyotype: Numerical Correspondence of 22, 22.5, 45, 506, 15, 30 and 15,000 in Turner Syndrome (45,X) and the X-Linked miR-506 Cluster at Xq27.3

This paper presents a mathematical semiotic reading of the parabolic centroid model f(x) = -x^2 + 45x + 1/4, applied to Turner syndrome (45,X) and the X-linked miR-506 cluster at Xq27.3. It is not a causal biological model and does not claim that the parabola causes, predicts, or explains any clinical phenotype. The numbers 22, 22.5, 45, 506, 15, 30, and 15,000 are read as signs within an interpretive code: 22 as the sign of autosomal stability, 23 as the sign of totality, 22.5 as the centroid of tension between them, 45 as the sign of lack in 45,X, 506 as the numerical echo pointing to the miR-506 cluster, 15 and 30 as symmetric threshold signs in clinical discourse, and 15,000 as the sign of genomic scale. The symmetric evaluations f(22) = f(23) = 506.25, f(15) = f(30) = 450.25, and f(45) = 0.25 are treated as diagrammatic correspondences, not as biological measurements or therapeutic predictions. The value of this reading is didactic and interpretive: it offers a memorable semiotic diagram for recalling karyotype structure, ISCN counting rules, and the location of the miR-506 cluster, while preserving a clear distinction between semiotic correspondence and biological causation.