Resolvent intertwining and spectral duality in Markov chains with geometric resetting

What the math gives to ML

The paper identifies spectral duality with an explicit operator symmetry: a weighted reflection commutes with the resolvent of a Markov transition operator. This is transferable to attention, graph neural networks, and state-space layers whose propagation matrix is stochastic or contractive: enforcing the same weighted intertwining makes every power and geometric multi-step propagation symmetry-compatible. The useful asset is not the resetting application itself, but the fact that a single commutator constraint controls an entire family of propagation scales through the resolvent. A practical first test is a paired-token or reflection-symmetric graph task where a weighted commutator regularizer is added to attention or message-passing propagation.