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This analysis constructs a self-adjoint operator representing interactions in a prime oscillator system, highlighting implications for number theory.
We construct an explicit self-adjoint operator L= A+ V on ℓ2(N,1/n) arising from a dynamical system of prime oscillators. The free Hamiltonian A= log n generates dilations; the interaction V = Re(TΛ) encodes prime-power firing events via Dirichlet convolution with the von Mangoldt function.
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Guillermo Garcia (2026) studied this question.
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