Establish uniform conditional bounds for QART asymptotic reliability

Establish uniform positive lower bounds, as the reasoning horizon grows under a specified resource schedule, for QART’s conditional probabilities of semantic coverage and fidelity, spectral certification, dynamical reachability, and faithful readout, thereby supporting its claimed non-vanishing global optimal-path recovery guarantee.

Background

The paper derives a conditional lower bound for QART’s probability of recovering a globally optimal reasoning path. The bound is expressed as the product of four conditional factors: the probability that the semantic representation satisfies the coverage and fidelity requirements, the probability that the encoded Ising instance satisfies the spectral certificate, the probability that the physical dynamics reaches and retains a certified sign pattern within the execution budget, and the probability that measurement and decoding faithfully preserve that solution.

The asymptotic reliability claim requires each of these factors to remain bounded below by a positive constant as the reasoning horizon increases. The paper explicitly notes that QART’s architecture alone does not imply such uniformity. Establishing these bounds is therefore an unresolved technical and empirical problem involving representation coverage, encoding quality, hardware dynamics, noise, readout, and the resource schedule used as task size grows.