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### Undecidability of States and Epistemic Horizons as Quantum Gravity

#### Abstract

Quantum mechanics places limits on what can be observed. Further, while it is a deterministic wave theory, outcomes of specific measurements are purely stochastic. The geometry of quantum entanglements, or quantum phases in general, describes a topological obstruction to unitary transformations between GHZ and W states or bipartite and tripartite entanglements. The momentum map defined on Kirwan polytopes is in the framework of a fractal sets in state space has p-adic measure. Axiomatic incompleteness of any p-adic algorithm illustrates how these obstructions define these obstructions. This is similar to how the Euclid 5th axiom is undecidable, and geometry has different model systems. This is then argued to connect with quantum gravitation in how spacetime is an epiphenomenology from entanglement.