Number Theory Before Topology: Grounding Morishita's Arithmetic Topology in the MDC-X Invariant ∆ = 4 ln 99

Masanori Morishita’s arithmetic topology establishes a profound analogy between knotsand primes, embedding number-theoretic data into a 3-dimensional foliated dynamicalsystem (FDS³). The framework is brilliant and mathematically consistent. However, itpresupposes its foundational elements: the 3-manifold, the primes 3, 5, 7, the Legendresymbols, the Galois group, and the reciprocity law. These are taken as inputs, not derivedfrom first principles.This paper resolves this ontological presupposition. The Mahapatra-Dalvi-CollatzX (MDC-X) Theorem derives the primordial invariant ∆ = 4 ln 99 from the ergodicdissipation of the generalized Collatz map via the Dalvi Dictact — the principle of localto-global topological completion. From ∆ emerges: • The quadratic regulator Q(x) = (x − 99)(396 − x) and the geometric constant πvia R 39699 dx/pQ(x) = π• The 3-manifold S3 as spatial projection• The Hilbert space H = L2(H) as the functional arena• The primes 3, 5, 7 via the Swayambhu wave function ΨSN (p) = sin(∆ ln p)/(4 ln 2)≡0• The Milnor linking invariant µ(3, 5, 7) = 1• The vanishing curvature Ω3 = 0 and Morishita’s reciprocity law as a necessaryconsequence Nothing is presupposed. Everything is derived. Morishita’s brilliant edifice now standson ground, not on assumptions. Computational verification is provided in deterministicPython code