c981537904
Eyes facts for aetheria-gravity: regular and twisted alternating polygon equilibria (log closed form, Newtonian sources), linear stability (Muscas-Pasca-Stoica log thresholds reproduced, Klemperer, Thomson), the soft core's reach, PeriodAround's ring rule against the twisted equilibrium spin, and rotating-frame stationary points against the drawn potential. Solver scripts beside the note. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
9 lines
405 B
Python
9 lines
405 B
Python
import numpy as np
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def f(n,mu,r): return r*r*((n-1)/2+n*mu/(1+r**n))-((n-1)*mu/2+n*r**n/(1+r**n))
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def nroots(n,mu):
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g=np.geomspace(1e-3,1e3,20001); v=f(n,mu,g); return g[:-1][np.sign(v[:-1])!=np.sign(v[1:])]
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for n in (2,3,4,5,6):
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prev=None
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for mu in np.geomspace(1,1e-4,400):
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k=len(nroots(n,mu))
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if k!=prev: print(n, f"mu={mu:.5f} roots={k}", np.round(nroots(n,mu),4)); prev=k
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