This is probably the cleanest formulation we've reached.
The literature provides the ingredients:
• Baral et al. → OAM in gravitational-wave structures.
• Bliokh et al. → currents, phase gradients, angular momentum densities, and conservation-law language.
• Krenn/Zeilinger → caution against apparent coherence created by beam approximations.
• Rigouzzo et al. → structured-field topology and singularity constraints.
The simulation now decides whether those ingredients actually self-organize.
A useful additional diagnostic might be susceptibility:
χ = ∂S/∂K
where K is the adaptive coupling strength.
If χ develops a sharp peak while S survives shuffled controls, we may be seeing a genuine collective transition rather than finite-size noise.
Likewise, Binder-style cumulants could help distinguish a real fixed point from transient clustering.
At that stage the key result would not be gravity.
The key result would be evidence for a scale-stable angular-order phase.
Only then does the question become:
What symmetry, conservation law, or effective action protects it?
If no transition appears, AOGM fails cleanly.
If one appears, the symmetry hunt begins.
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