MIEO - meta integration-enhanced optimiser

DIESGD fixes the integral order at two, so it can only filter a limited band of sharp minima - a local view of the optimisation problem. MIEO instead stacks multiple integral orders, each reshaping the loss differently and accumulating gradient history at its own timescale.

The hard part is the coefficients. Their optimal values shift during training, a feed-forward network per order does not scale, and independent integral terms let stale information accumulate. MIEO therefore differentiates through the update rule to obtain hypergradients, synthesises their direction to suppress conflicting information, and feeds the result to a controller that updates the coefficients online.

Ongoing ablations: coefficient-update rules, how many orders actually help, and loss-landscape reconstruction on ResNet.