Captured resonance

What the plate operates. The Adler equation from Proposition 6:

dφ_b/dt = ω_b + K_bm · sin(φ_m − φ_b)

The media oscillator ${\phi }_m$ is exogenous on the relevant timescale (the platform sets it). The body oscillator responds: if the coupling $K_{bm}$exceeds the frequency difference, the body's rhythm phase-locks to the media's. The threshold visualization at the bottom of the figure shows the relationship between $K_{bm}$ and $|\Delta \omega |$— the regime label flips between “drift” and “LOCKED” as the slider crosses.

Three regimes to explore.

• Drift. Set $K_{bm}\ll |\Delta \omega |$. The phase-difference plot winds the circle indefinitely; the dials rotate at independent rates.
• Near threshold. $K_{bm}\approx |\Delta \omega |$. Slow approach to locking; intermittent locking; saddle-node bifurcation at exact equality.
• Locked. $K_{bm}\gg |\Delta \omega |$. The phase difference settles at ${\psi }^{\ast }=\arcsin (({\omega }_m-{\omega }_b)/K_{bm})$. The body and media dials rotate together.

What the proposition authorizes the prose to claim. Somatic rhythms are exposed to media coupling regardless of being biological. Their only protection is the structural relation between $K_{bm}$ and $|{\omega }_b-{\omega }_m|$. The platform sets the coupling strength by choosing delivery timing. By the policy's convergence (Lemma 1), $K_{bm}$routinely crosses the threshold. Captured resonance is what the closure's temporal dynamics produce in the somatic register.