Construction and Properties of the Ground State of Natural Phenomena
Renaud Gauthier
TL;DR
The paper seeks a universal base—the ground state $ ext{G}$—from which higher algebraic structures modeling natural phenomena emerge. It builds $ ext{G}$ as the nerve of a dual IRV-based category $ ext{G}_0$ (via $ ext{G} = N( ext{G}_0)$), with IRVs encoding complete information-theoretic decompositions terminating at the elementary dichotomy $ ext{$ olinebreak$Z_2$}$. Its manifestations form the presentable $ ext{$ olinebreak$∞$}$-category $ ext{χ} = ext{Fun}( ext{G}, ext{Cat}_{ olinebreak ext{$ olinebreak$∞}})$, and its spectra $ ext{Sp}( ext{χ})$ are shown to be stable presentable, with a flexible presentation $ ext{Sp}( ext{χ}) olinebreak ext{≃} ext{Fun}( ext{$ olinebreak$E$, Sp})$ for some $ ext{$ olinebreak$E$}$. The work establishes that $ ext{χ}$ localizes to recover $ ext{G}$ and endows $ ext{Sp}( ext{χ})$ with a t-structure and a tangent-cotangent calculus, enabling algebraic derivations and triangulated-homotopical analysis. A spontaneous reconstruction viewpoint ties deconstruction and reconstruction via localization with respect to deconstruction maps, offering a coherent framework in which higher algebraic concepts arise from the ground-state information-theoretic basis. Overall, the paper provides a rigorous, information-theoretic foundation for the emergence of higher categories and spectra as realizations of natural phenomena.
Abstract
We construct an $\infty$-category $\mathcal{G}$ as a model for the Ground State of physical phenomena and we provide properties of its manifestations $χ= \text{Fun}(\mathcal{G}, \text{Cat}_{\infty})$ in $\text{Cat}_{\infty}$ as well as of its $\infty$-category of spectra $\text{Sp}(χ)$.