Gradient descent reaches equal-weight superposition on Erdős-Rényi reachability via a Möbius attractor under S_n symmetry and Cascade Supervision, with a parameter-free decay law matching experimental cosines within 0.02.
DefiningA:= 1 +ηaandB:=ηb ′ 1, αeff,c = α A+m (c) f B A+ √kc B
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Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision
Gradient descent reaches equal-weight superposition on Erdős-Rényi reachability via a Möbius attractor under S_n symmetry and Cascade Supervision, with a parameter-free decay law matching experimental cosines within 0.02.