Koopman Deadline Controller

Integrate this at the controller around an iterative neural computation, not inside the base model initially. The first target should be a small multi-agent QA system or a recurrent transformer refinement loop in which each round produces agent belief embeddings $h_i^t$ and a final answer distribution. At each round form $z_t=[h_1^t;\ldots;h_N^t]$, and compute a fixed observable vector $\phi(z_t)$ containing the flattened mean embedding, pairwise disagreement statistics, answer logits, and squared versions of the first few PCA coordinates. Maintain a rolling buffer of transitions $(\phi(z_t),\phi(z_{t+1}))$. Once the buffer contains $M\ge 2d$ samples, compute the ridge-stabilized estimator $\widehat K=YX^{\mathsf T}(XX^{\mathsf T}+\alpha I)^{-1}$, where $\alpha$ is a small numerical regularizer. Compute the eigenvalues of $\widehat K$, identify the eigenvalue closest to one as the consensus mode, and set $|\lambda_2|$ to the largest remaining magnitude after rejecting modes with poor one-step prediction residual. Let $D_t$ be the norm of the disagreement observables relative to their consensus projection. Estimate the remaining rounds using the displayed logarithmic formula, clip it to a safe range, and stop early only when both the predicted residual is below $\varepsilon$ and the actual answer distribution changes by less than $\delta$ for two consecutive rounds. The paper supplies the Koopman construction and spectral certificate; the engineer must estimate $K$, eigenvalue uncertainty, and residuals empirically. Begin with 8 agents and 4 maximum rounds on GSM8K or a synthetic consensus task, comparing fixed-round debate and confidence-threshold stopping at equal answer accuracy. Success is lower mean rounds and FLOPs with no accuracy loss, while failure is systematic premature stopping, unstable eigenvalues, or worse calibration.