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The research establishes a theorem asserting all measurable quantities are doubly bounded within Srinivas Bounded Mathematics.

March 24, 2026Open Access

The Non-Zero Measurability Theorem: Quantization of Observable Existence in Srinivas Bounded Mathematics

Key Points

The research establishes a theorem asserting all measurable quantities are doubly bounded within Srinivas Bounded Mathematics.
Developed a theorem based on the Prohibition of Infinite Subdivision axiom.
Proved bounds for measurable quantities |Q| using Peano arithmetic relationships.
Derived consequences including Yang–Mills mass gap and modified Wightman axioms.
Confirmed that for any measurable quantity Q, ε_AR(Π) ≤ |Q| ≤ ð(Π).
Eliminated true zeros and infinities from measurable physics, ensuring m ≥ ε_AR > 0 for massless particles.
Established that empirical input is required for any formal system describing reality.

Abstract

We establish a fundamental theorem within Srinivas Bounded Mathematics (SBM): all measurable quantities are doubly bounded. For any measurable quantity Q in context Π, we prove εAR (Π) ≤ |Q| ≤ ð (Π), where εAR > 0 is the lower (AR) bound and ð 0 for photons, gluons, gravitons), no singularities (r ≥ εAR > 0), no UV divergences (momentum bounded), and the Yang–Mills mass gap Δ > 0 follows as a one-line corollary. We establish the mass gap as independent of subdivision axioms—analogous to the Continuum Hypothesis being independent of ZFC. The Physical Incompleteness Theorem proves that empirical input is logically necessary for any formal system describing reality. We further derive the Bekenstein bound, the Principle of Least Action, and modified Wightman axioms as natural consequences of the doubly bounded framework.

The Non-Zero Measurability Theorem: Quantization of Observable Existence in Srinivas Bounded Mathematics

Key Points

Abstract

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