The K3 Theorem: Mathematical Awareness and Global State Inference in a Unitarily Evolving Multiverse

Abstract

The quantum measurement problem is resolved through the Everett interpretation, with de-
coherence explaining the subjective appearance of collapse. However, a fundamental tension
remains: how can a physically localized observer, confined to a single decoherent branch,
have knowledge of the global, unitarily evolving universal wavefunction? This paper presents
a formal theorem—the K3 Theorem—demonstrating that an observer modeled as a compu-
tational subsystem (a Universal Turing Machine) can, through axiomatic derivation alone,
infer the complete structure of the multiverse. We prove that by strictly adhering to the prin-
ciple of unitarity, such an observer can construct an internal mathematical model isomorphic
to the universal state vector |ΨU i. This model enables the ”measurement” of properties in
other, physically inaccessible branches via calculation, not physical interaction. This result
unifies the physics of decoherence, the ontology of many-worlds, and a computational theory
of mind, establishing that while experience is branch-local, understanding can be multiverse-
global.

Keywords: Quantum Foundations, Many-Worlds Interpretation, Decoherence, Quantum Mea-
surement Problem, Mathematical Logic, Universal Turing Machine, Unitarity, Consciousness,
K3 Theorem.