Geometry is Not the Trap: A Spectral‑Reopening Diagnostic for Protocol-Bounded Optimization Locking

While practice often equates the geometric collapse of deep representations with a loss of recoverability, and existing analyses frequently rely on proxies such as Neural Collapse, the relationship between whole-manifold rank-one geometric cliffs and persistent protocol lock under cross-entropy (CE)—the inability of CE to recover under a given protocol and budget—remains unclear. We show that what distinguishes recoverability under CE is not static forward geometry, but a dynamical object: whether the full-extractor Feature Neural Tangent Kernel (Feature-NTK) reopens. Across the convolutional networks we test, trained on standard image-classification benchmarks and covering residual networks, Visual Geometry Group (VGG) networks, and Group Normalization, standard CE recovers from the tested whole-manifold rank-one geometric cliffs. Among checkpoints with severe Feature-NTK spectral cut-offs induced by structured auxiliary regularizers, some checkpoints can still reopen the Feature-NTK and recover to approximately $80\%$ accuracy, so a spectral cut-off is not sufficient for persistent protocol lock. The critical bifurcation between persistent protocol lock and recoverable cut-off is whether the Feature-NTK reopens under a controlled $50$-minibatch CE spectral-reopening probe. Through controlled parameter interventions, we further show that maintaining the lock relies on a layer-structured batch normalization (BN) scale configuration. Finally, after freezing the rule, we prospectively evaluate unseen cut-off checkpoints across architectures. On the checkpoints we test, persistent protocol lock tracks whether the Feature-NTK reopens rather than static geometry.