Theorem on the Absence of Asymptotic Chaos

Ontic chaos is impossible; observable chaos is an artefact of coarse-graining. <br><span>Within Quantumograph theory - where the universe is modelled as a finite directed quantum graph with unitary evolution - asymptotic chaos is impossible in three rigorous senses:<br> (1) spectral quasiperiodicity: the Hilbert-space trajectory is an almost-periodic function of time;<br> (2) Poincaré recurrence: the system returns arbitrarily close to any initial state in finite time;<br> (3) saturation of the quantum Lyapunov exponent: the OTOC function is bounded above and saturates at t* ~ ln N /lambda_{max}</span><span>, after which there is no further exponential divergence. We present here is an explicit separation of ontic chaos (a property of the exact microdynamics) from epistemic/coarse-grained chaos (an artefact of incomplete information), together with a rigorous proof that coarse-graining at scale ℓ &gt;&gt; a generates observable stochasticity from deterministic unitary dynamics.</span>