Higher-Spin Fronsdal-Aether Coupling
$$\nabla^\mu \Phi_{\mu\ldots} = 0 + \xi\, u^\mu \Phi_{\mu\ldots} = 0$$
Status: Unproven.
The Fronsdal field equation itself ($\nabla^\mu\Phi_{\mu\ldots}=0$, describing free higher-spin fields) comes from real, published theoretical work — the Vasiliev-Fronsdal formalism for higher-spin gauge theory (Vasiliev, 1990). That underlying framework is itself genuinely speculative physics with no experimental confirmation — see Unproven Systems At Large, the same epistemic category as string theory. Paper 9 adds its own $\xi u^\mu\Phi_{\mu\ldots}$ aether-coupling term on top of that, claimed to resolve known ghost instabilities in higher-spin theories (the Rarita-Schwinger ghost problem) — an original PBT addition, not part of the published Vasiliev-Fronsdal literature.
What would make this proven: first, independent experimental evidence for higher-spin particles at all (none exists yet, for any theory); second, and separately, a demonstration that PBT’s specific aether-coupling term is what actually resolves the ghost problem, rather than the simulation-only “stable norms ~1” result reported, which doesn’t distinguish this specific mechanism from other known ghost-resolution approaches in the literature.