Topos Many-Node Theory: Roots, Foundations and Predictions

TL;DR

This work develops the many-node theory by mapping a space-time network to a topos-based discrete quantum manifold endowed with both discrete calculus and Alexandrov algebra. By assigning locales to network nodes, it argues that Lorentz invariance need not hold universally, and it derives a nonzero cosmological constant Λ that scales as Λ ∼ H^2 due to volume fluctuations in a causal-set/topos framework. Inflation emerges as a consequence of entropy growth in a population-like space-time network, with entropy quantization tied to network expansion via a Leslie-matrix model. The theory further predicts netons—vibrational quanta of the space-time network—and posits observable signatures in the cosmic background radiation, while rooting noncommutative geometry in the locale-centric description rather than point particles, forming a comprehensive quantum-relativistic framework called the many-node theory.

Abstract

Assuming that the first creatures of creation create a network, it is shown that how the network can be mapped to a topos discrete quantum manifold which is equipped with both the discrete calculus and the Alexandrov's algebra. We assign a locale to each nodes of the space-time network and show that in general, invariance under Lorentz transformations is no longer true. it is shown that the cosmological constant is non-zero and is proportional to the second power of the Hubble radius. By considering a population (set), it is shown that the entropy of the space-time network is quantized and increases as the network grows. In consequence the inflation of the world is expected phenomenon. Also, we show that how world inflation can be described based on the concept of truth object and truth value belong to the topos theory. It is shown that the quanta of vibrations, called netons, can be attributed to the vibration of space-time network, and it is expected that they will be observed in the future experiments related to cosmic background radiation. Finally, it is shown that the root of noncommutative geometry is in attributing the locale to the nodes of the space-time network instead of a point. This theory, which includes the roots, foundations and predictions, is called the many-node theory.