Discrete Hilbert space, the Born Rule, and quantum gravity

Quantum gravitational effects suggest a minimal length, or spacetime interval, of order the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is quantum states with norm below some very small threshold do not exist. The exclusion what Everett referred to as maverick branches necessary for emergence Born Rule no collapse mechanics. We discuss this context gravity, showing models (such simplicial lattice gravity) indeed minimum norm. These considerations are related ultimate level fine-graining found decoherent histories (of geometry plus matter fields) produced by gravity.