Measurement-induced entanglement Hamiltonian

What the math gives to ML

The paper provides a transferable construction for a measurement-conditioned effective Hamiltonian: a local inverse-temperature profile is fixed by geometry and vanishes with a square-root law at measurement-region endpoints, while a local chemical potential carries post-selection information through the induced charge density. This suggests an adaptive attention or message-passing layer with two separated channels: geometry controls interaction strength, while observed values enter through a distinct potential bias. The main falsifiable prediction is that the optimal boundary attenuation follows an exponent near one-half, and that outcome-dependent behavior is captured primarily by the potential channel rather than by the geometric temperature channel.