Algebraic Resolution of Divergent Topologies via Multilayered Discrete Fields and Contextual Zeros
Year: 2026
Type: preprint
Abstract: A central axiom of continuous real analysis is the strict structural equivalence of null states, asserting that a - a = b - b = 0, thereby reducing additive inverses to a featureless, absolute void. This paper formally challenges this paradigm by introducing the Multilayered Discrete Field, predicated on the Unitary Symmetry Series (USS). We propose that classical real numbers are approximations of discrete, base-anchored multiplicative layers governed by rational reciprocal operators (5/4 and 4/5). By formalizing the "Contextual Zero", we demonstrate that a null state natively retains the structural boundaries of its generating base. Evaluating singular limits via Discrete Boundary Normalization—the arithmetic mean of systemic tensions across exact fractional boundaries—resolves classical singularities into finite, base-dependent algebraic pressures. This framework provides a formally closed arithmetic mechanism to resolve topological divergence, exposing classical absolute infinity as an artifact of homomorphic information loss.
Author: Dagar, Nitin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7141346166
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