Mathematical Formalization of Ayurvedic Principles: A Qualitative Framework Without Quantification

This document presents a rigorous mathematical formalization of Ayurvedic principles using qualitative mathematics — specifically set theory, order theory, formal logic, combinatorics, and graph theory. Critically, this formalization avoids quantification: we do not assign numerical values to doshas, gunas, or elements. Instead, we capture the logical structure, hierarchical relationships, and systematic reasoning that form the foundation of Ayurvedic medicine. The framework formalizes: Panchamahabhuta as property clusters via set-theoretic mappings; the 41 Gunas classification with its 10 opposition pairs; Shad Rasa elemental composition; hierarchical dominance and Taratamya (relative gradation); Prakriti (7 types) and Vikruti (15 types) via combinatorics; the Sapta Dhatu sequential transformation chain; Rasa-Veerya-Vipaka pharmacological hierarchy; the 49 Maruts as a rooted tree; and clinical diagnostic algorithms as multi-variable decision functions. The paper includes corrections to classical element-property attributions (Chala, Shlakshna, Sara) based on dosha-composition verification, a first-principles derivation of the Tikta Ksheer Basti formulation, Drava Guna mechanics of Vamana Karma, and two predictive test cases — Nipah virus (10/11 confirmed) and Chronic Kidney Disease (17/17 confirmed) — demonstrating the framework's generative power. Based on independent study of 40+ classical Ayurvedic texts. Inspired by the clinical practice of Dr. Arun Mishra (@mishraveda). All textual study, analysis, and mathematical formalization by the author.