Iterative Dynamics and Sāṃkhya Principles: \\ A Structural Analysis of the Collatz Conjecture}}

This paper proposes an interdisciplinary analysis of the Collatz Conjecture through the principles of Sāṃkhya philosophy. It is observed that the digital roots of Collatz sequences show a strongly asymmetric yet harmonious distribution between a dominant sextet {1,2,4,5,7,8} and a minor triad {3,6,9}. Interpreting the sextet as the field of manifestation of Prakṛti and the triad as an intermittent expression of Avyakta, a clear harmonic complementarity emerges. The three guṇa (rajas, tamas, sattva) are used to precisely describe the dynamic equilibrium.