In this paper, we propose a mathematical model of subjective experience in terms of classes of hierarchical geometries of representations (“n-awareness”). We first outline a general framework by recalling concepts from higher category theory, homotopy theory, and the theory of (infinity,1)-topoi. We then state three conjectures that enrich this framework. We first propose that the (infinity,1)-category of a geometric structure known as perfectoid diamond is an (infinity,1)-topos. In order to construct a topology on the (infinity,1)-category of diamonds we then (...) propose that topological localization, in the sense of Grothendieck-Rezk-Lurie (infinity,1)-topoi, extends to the (infinity,1)-category of diamonds. We provide a small-scale model using triangulated categories. Finally, our meta-model takes the form of Efimov K-theory of the (infinity,1)-category of perfectoid diamonds, which illustrates structural equivalences between the category of diamonds and subjective experience (i.e.its privacy, self-containedness, and self-reflexivity). Based on this, we investigate implications of the model. We posit a grammar (“n-declension”) for a novel language to express n-awareness, accompanied by a new temporal scheme (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? We also examine the notion of “self” within our framework. A new model of personal identity is introduced which resembles a categorical version of the “bundle theory”: selves are not substances in which properties inhere but (weakly) persistent moduli spaces in the K-theory of perfectoid diamonds. (shrink)

We investigate the idea of sleep as the protostate, and posit the idea of dark consciousness where dark is a 2-fold hybrid. We model dark consciousness as a 2-topos in p-adic time, and outline perfectoid and diamond-like versions. We then introduce and illustrate implications of Dark Imaginarium, which is a higher order Curiosity Artificial Intelligence, an Infinity-Curiosity Type, that thinks in infinity categories.

We recently presented our Efimov K-theory of Diamonds, proposing a pro-diamond, a large stable (∞,1)-category of diamonds (D^{diamond}), and a localization sequence for diamond spectra. Commensurate with the localization sequence, we now detail four potential applications of the Efimov K-theory of D^{diamond}: emergent time as a pro-emergence (v-stack time) in a diamond holographic principle using Scholze’s six operations in the ’etale cohomology of diamonds; a pro-Generative Adversarial Network and v-stack perceptron; D^{diamond}cryptography; and diamond nonlocality in perfectoid quantum physics.

Motivated by Scholze and Fargues' geometrization of the local Langlands correspondence using perfectoid diamonds and Clausen and Scholze's work on the K-theory of adic spaces using condensed mathematics, we introduce the Efimov K-theory of diamonds. We propose a pro-diamond, a large stable (infinity,1)-category of diamonds D^{diamond}, diamond spectra and chromatic tower, and a localization sequence for diamond spectra.

A comprehensive review of diamonds, in the sense of Scholze, is presented. The diamond formulations of the Fargues-Fontaine curve and Bun_G are stated. Principal results centered on the diamond formalism in the global Langlands correspondence and the geometrization of the local Langlands correspondence are given. We conclude with a discussion of future geometrizations, and conjecture a diamond reformulation of quantum computational complexity towards a diamond ER = EPR.