Annihilation Cosmology Mathematics Version 2.4: Noumenal Foundations in Three Axioms Superabundant Irreducibility Eternal

Abstract

This document presents version 2.4 of the mathematical architecture for Annihilation Cosmology (AC). It extends the epistemological critique of Kant’s thing-in-itself directly into the foundations of arithmetic and discrete geometry. Classical mathematics presumes an unconditioned, objective universalism—a shared noumenal substrate underlying synthetic a priori propositions (such as 7+5=12). However, if the transcendental unity of apperception requires no unknowable ground, these purportedly sharp mathematical universals lose their dogmatic standing, revealing themselves as bounded, dynamic syntheses of private apperception.

Recognizing this epistemological limit opens the door to regulated speculation regarding the true nature of geometry. AC Math V2.4 introduces an alternative mathematical candidate. Rather than relying on actual infinities, continuous symmetries, or unconditioned probabilities, this architecture proposes a rigorously discrete, geometric lattice.

The compelling nature of this alternative framework lies in its phenomenal application. When this purely discrete geometry is allowed to organically generate a phenomenal realm, the resulting structure remarkably mirrors our observed physical universe. It derives the parameters of the standard model entirely through geometric necessity, without ad-hoc mass tuning or free parameters.

Ultimately, this regulated speculation proves ontologically superior at handling empirical reality, seamlessly mapping standard model anomalies directly onto its geometric struts. Tested against the internal fracture mechanics of conventional phenomenology, this framework steps into the public arena not merely as an epistemological exercise, but as a serious structural contender for the foundational mechanics of the universe.

This document emerges from A Fifth Paralogism: The Superfluity of the Thing-in-Itself in Kant's Transcendental Unity of Apperception 10.5281/zenodo.20837896 and serves as the foundational preamble to the Annihilation Cosmology framework. It establishes the mathematical and geometric grounding for the subsequent phenomenological derivations found at 10.5281/zenodo.19636883 and 10.5281/zenodo.19748671.

This paper and AC Math V2.4 are foundational for the two derivations papers. The bridge between the two is the AC Particle Table here: https://zenodo.org/records/20975973

Contact the Author regarding the Annihilation Cosmology framework at: [DavidMcClean@protonmail.com] or David McClean - Splat Cosmology