MDC-X Theorem: Computational Verification and Ontological Hierarchy
Year: 2026
Type: preprint
Abstract: 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
Author: Mahapatra, Dillip Kumar
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161731900
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