MDC-X Theorem: Computational Verification and Ontological Hierarchy

The Mahapatra-Dalvi-Collatz X Theorem (MDC-X Theorem) is not a static mathematical description. It is a dynamic engine that generates topological control invariantsfrom the triadic coefficients (a, b, n)—where a is an odd positive integer (the algebraicmultiplier), b is an odd integer (the parity-sustaining shift), and n is a positive integer (the dissipating starting value). These three coefficients, with their necessary parityconditions (a odd, b odd), produce the generalized Collatz map Ca,b(n) as a necessaryconsequence, not as an external assumption. The map is not assumed; it is produced bythe triadic structure itself.This paper provides complete, deterministic, reproducible computational verificationof every step of the MDC-X Theorem using only standard Python libraries (NumPy,SciPy, Matplotlib). The code demonstrates the unidirectional deductive chain from thetriadic coefficients to number theory, to topology, to arithmetic, to geometry, and finallyto physics