Nasanjargal Mathematics: A Unified Kinematic and Non-Scalar Framework for Cosmological and Cognitive Computation

The trajectory of computational mathematics has been defined by a deep divergence from the
tangible physical properties of the natural universe. Contemporary computer science,
numerical simulation pipelines, and machine learning architectures rely heavily on Cartesian
abstractions and linear scalar fields. This legacy framework introduces a fundamental
mismatch between the physical laws governing the universe and the mathematical structures
utilized to model them.
At the core of this mismatch is the unphysical construct of negative numbers. In the
observable physical universe, fundamental properties such as energy density, absolute
distance, mass, and time operate strictly within the positive domain; physical bodies do not
possess negative mass, and thermodynamic systems do not experience negative entropy.
Despite this, contemporary algorithmic environments rely on Cartesian coordinate systems
that divide space into arbitrary positive and negative dimensions, requiring substantial
computational correction layers to prevent non-physical predictions, such as negative mass,
inverted volumes, or impossible probability distributions.
To bridge this gap, Nasanjargal Mathematics (NM) replaces static scalar coordinates with
dynamic, vector-based spatial trajectories operating within a native Base-6 (Senary) positional
radix. By representing numerical states as kinematic trajectories tracked via fractional
Hex-Turns and governed by binary thermodynamic phases, NM eliminates the translation
losses and logical paradoxes introduced by legacy scalar frameworks.