Add quotient state and RG flow analysis

[charlesmartin14]

Summary

• materialize FC1/FC2 quotient representatives and run WeightWatcher raw plus fix_fingers=clip_xmax
• scan nonlinear Gram diagonal subtraction at three counterterm strengths and add anchor-frozen Feshbach downfolding
• add finite between-checkpoint radial, transfer, Grassmann, and polar-flow spectra
• compare observed centered-log-singular flow to the actual local map-Jacobian prediction
• add gap-aware, log-Gram, ridge-resolvent, and Feshbach single-checkpoint Jacobians
• generalize right-singular ECS geometry to square FC2
• generate separate AdamW and MuonClip figures and extensive shareable HTML documentation

Scientific labeling

• state maps are declared quotient hypotheses, not a uniquely identified unknown Muon quotient
• two-checkpoint objects are finite secants/transfers, not D beta(W)
• single-checkpoint objects are exact Jacobians of declared weight-only maps, not optimizer Jacobians
• the same-checkpoint Feshbach first-order shell collapse is retained as an explicit control

Validation

• Python compilation passed
• shell syntax passed
• dependency-light square-FC2 algebra checks passed
• complete synthetic report generation passed, including eight optimizer-specific figures
• Git diff checks passed
• full PyTorch/pytest suite unavailable in the validation sandbox because PyTorch and pytest are not installed