Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics

Herein we develop connections between zeta functions and some recent "mysterious" constants of nonlinear physics. In an important analysis of coupled Winfree oscillators, Quinn, Rand, and Strogatz [Quinn et al. 07] developed a certain N-oscillator scenario whose bifurcation phase offset small ⍉ is implicitly defined, with a conjectured asymptotic behavior sin ⍉ ~ 1−ᴄ₁/N, with experimental estimate ᴄ₁ = 0.605443657 . . .. We are able to derive the exact theoretical value of this "QRS constant" ᴄ₁ as a real zero of a particular Hurwitz zeta function. This discovery enables, for example, the rapid resolution of c1 to extreme precision. Results and conjectures are provided in regard to higher-order terms of the sin ⍉ asymptotic, and to yet more physics constants emerging from the original QRS work.