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Add fixed-point and stability diagnostic - #16

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fixed-point-stability-diagnostic
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fixed-point-stability-diagnostic

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Adds a NumPy-only scientific diagnostic for the current WaveLock evolution.

It measures:

  • normalized fixed-point residuals at multiple checkpoints;
  • denominator proximity to zero and one-step amplification;
  • exact small-grid Jacobian eigenvalues and spectral radius;
  • perturbation contraction against the unperturbed continuation;
  • classification as numerical fixed point, evolving transient, uniform damped transient, or non-finite state.

The smoke profile is pytest-compatible and uses only NumPy. Larger standard and deep profiles can be selected with WAVELOCK_FIXED_POINT_PROFILE.

Local validation of the fast profile produced:

  • terminal classification: uniform_damped_transient;
  • residual: 2.000003e-05;
  • relative spatial standard deviation: 2.822178e-05;
  • Jacobian spectral radius: 0.99998;
  • perturbation final gain after 500 steps: 0.163144.

This intentionally does not label the current 50-step terminal state as a fixed point unless the residual test is actually met.

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