Runtime Optim

NN.Runtime.Optim is the small umbrella for TorchLean's reusable optimizer math.

This subsystem contains pure, tensor-level pieces:

• NN.Runtime.Optim.Optimizers defines per-parameter update equations such as SGD, Adam, AdamW, AdaGrad, RMSProp, Adadelta, GaLore-style projected SGD, and Muon-style updates.
• NN.Runtime.Optim.Schedulers defines deterministic learning-rate schedule state machines.

What this file does not contain:

• heterogeneous parameter-list handling, bound optimizer state, or training-loop mutation;
• the public optim.sgd / optim.adam API; or
• CUDA / PyTorch fused optimizer kernels.

Those are separate on purpose. The high-level runtime bridge in NN.Runtime.Autograd.Model.Optim lifts these pure single-tensor equations to parameter lists, and NN.API.Runtime exposes user-facing optimizer configs. Proofs, tests, and runtime code all use these pure update formulas.