A First-Principles Theory of the Human Body: Order from the Chaos of Indices

Body mass index (BMI) remains the most widely used anthropometric scale, but its formula relates body mass only to the square of height and does not include an independent transverse body dimension. This paper introduces the anthropometric coordinate k=m/(w^2h), where m is body mass, h is height, and w is waist circumference. The expression w^2h is treated as a simple body-volume proxy that allows a transition from planar BMI normalization to a description in which body mass is related to both height and waist circumference. Values of k were calculated from unweighted NHANES 2017–2023 data for a working sample of 20,699 observations with complete anthropometric records. The analysis compares k with BMI, constructs a scatter plot and histograms, and calculates approximate BMI-aligned reference ranges for k. The results show that k is not a correction to BMI and is not derived from it: the same BMI score may correspond to different estimates of k because of differences in waist circumference and body geometry. The k scale has an inverse numerical direction with respect to transverse body size: at fixed body mass and height, greater waist circumference decreases the value of k. The distribution along the k axis differs from the BMI distribution and shows lower asymmetry and a less pronounced right tail. This study does not introduce a new clinical norm or propose a medical classification. Its aim is to establish the geometric meaning of k and substantiate its use as an independent population-level anthropometric axis for further analysis. This work is part of the research series A First-Principles Theory of the Human Body. Series repository: Open Science Framework, DOI: https://doi.org/10.17605/OSF.IO/ENAUQ.