The Numerical Yantra: Digital Roots, Tesla's Triad, and the Trimūrti

This paper studies the behaviour of digital roots under repeated doubling and asks what, if anything, that behaviour reveals about the relationship between mathematics and metaphysics. Three families emerge. The Loopers (1, 2, 4, 8, 7, 5) trace a closed six-step cycle; the Flippers (3, 6) oscillate between two states; the Invariant (9) is a fixed point. The central mathematical claim of the paper is that this trichotomy is not an observed curiosity but an algebraic necessity: working modulo nine, the three families are exactly the residue classes sorted by their greatest common divisor with nine, and the six-step cycle is forced because two is a primitive root modulo nine. The paper then confronts the most serious objection to any mystical reading — that the whole structure is an artefact of base ten — and argues that the particular numerals are indeed base-relative, while the form of the result (a units-orbit, an intermediate oscillation, and an invariant zero-class) is not. With that honesty established, the three behaviours are read as a contemplative correspondence: first with the triad of dynamic abstractions popularly associated with Nikola Tesla — energy, frequency, and vibration — and then with the Trimūrti of Brahmā, Viṣṇu, and Śhiva. These mappings are presented explicitly as a hermeneutic bridge, not a doctrine: a way of using simple arithmetic as a yantra for contemplating creation, preservation, and dissolution. The paper concludes that mathematics and metaphysics are not identical, but that number can carry — without proving — the cosmological intuitions of the Indic tradition.