This paper establishes the axiomatic foundations of Non-Abelian Information Perception Theory (NIPT), completing the architectural synthesis of the pre-geometric qubit network paradigm. Instead of treating the observer as an external spectator, it endogenizes perception as an intrinsic algebraic restriction of a primordial, background-independent quantum substrate modeled by a hyperfinite type III1 von Neumann factor. By introducing the Spectral Cognitive Triplet (PO, DO, ΔO), the framework formalizes the core cognitive dimensions of Observation, Intelligence, and Vivacity. It demonstrates how Consensus, Plasticity (Memory), macroscopic spacetime geometry, and covariant quantum linearity naturally emerge from the homeostatic filtration of network entanglement loads. Finally, it maps the epistemic transition to Gödelian and Trans-Gödelian physical regimes, framing physical reality and observer phenomenology as dual emergent phases within a single, unified operator algebraic spectrum.
This paper bridges the gap between abstract operator algebras and high-energy physics by proposing a revolutionary paradigm: Non-Abelian Information Perception Theory (NIPT). Rather than treating elementary particles as independent blocks of mass-energy existing in a passive spacetime container, NIPT reveals the material universe to be an emergent, holographic user interface engineered by the observer's own finite cognitive constraints. Operating within a hyperfinite type III1 von Neumann substrate, the framework elegantly derives familiar physical entities—like photons, gauge bosons, and neutrinos—as localized hydrodynamic linearizations forced by a "Spectral Cognitive Triplet". Going beyond pure abstraction, this volume establishes explicit, testable cosmological and quantum phenomena: Dark Matter is unmasked as the gravitational footprint of heavy entanglement loads stored within the observer's unconscious Hilbert sector, resolving the astrophysical central cusp anomaly; standard quantum linearity emerges naturally from multi-observer lattice supremum phase transitions that generate novel "Consensus Bosons"; the black hole information paradox is resolved via non-local algebraic evacuation; and the relativistic arrow of time is derived directly from Tomita-Takesaki modular flows. Finally, the paper translates these non-local mechanisms into concrete, falsifiable experimental signatures—such as ultra-high-energy tau-neutrino deficits and Askaryan phase decoherence thresholds—detectable by next-generation polar observatories like IceCube-Gen2 and RNO-G. Ultimately, this work dismantles the artificial wall between mind and matter, framing the cosmos as a self-consistent computational feedback loop materializing itself through the structured horizons of consciousness.
This paper establishes a rigorous mathematical foundation for the Gauge/Fluid duality within Non-Abelian Information Theory. By bridging the microscopic dynamics of a finite qubit network with the macroscopic continuum, we demonstrate how the covariant Schrödinger-Klein-Gordon equation naturally emerges from the Chamseddine-Connes spectral action using an almost-commutative spectral triple. Using the Takabayasi-Fabbri geometric formalism, we extract the hydrodynamic equations of state and prove that the network’s non-linear self-interactions asymptotically converge to the Euler-Bohm quantum stress tensor. Finally, we derive the fluid's irrotationality from the ergodicity of the modular flow on type III1 Von Neumann factors, providing an unassailable geometric link between microscopic quantum entanglement and macroscopic phenomena without relying on free parameters.
Higher-form symmetries generalize conventional global symmetries and act on lower-dimensional submanifolds of a quantum system. While Abelian topological phases can be organized by 1-form symmetries that form a group, non-Abelian topological phases based on finite groups require 1-form symmetry operators governed by non-invertible fusion algebras. In this work, we make this statement precise in quantum double lattice models
D(G) for finite non-Abelian groups
G. We construct the electric, magnetic, and dyonic 1-form operators directly at the lattice fixed point and show that together they form a complete nonlocal diagnostic algebra for the topological Hilbert space. Using these operators, we explicitly determine the cylinder and torus ground-state subspaces for arbitrary finite
G. Furthermore, we calculate the microscopic fusion and gluing of the 1-form symmetries and show that their topological deformation properties emerge after projection to the defect-free topological subspace. Our results establish ground states of non-Abelian quantum double models as a concrete microscopic realization of spontaneous non-invertible 1-form symmetry breaking and provide an operator language that may be useful for characterizing such states in quantum processors.