Quantum Steenrod powers and Hamiltonian maps

What the math gives to ML

The paper develops equivariant power maps relating a complex to its p-fold tensor power, together with strict action or energy filtration inequalities and a bar-length spectrum preserved under passage to the p-th iterate. The transferable asset is not Floer theory itself, but the combination of cyclic-group quotienting, replica-to-power consistency, and a provable non-decrease of a scalar filtration under a power map. A neural analogue is a p-replica module that aggregates cyclically permuted views or token groups and is trained to match a separately computed p-fold representation while enforcing a filtration margin on nontrivial transformations. This creates a concrete architecture and regularizer that can be compared against ordinary pairwise augmentation consistency.