Do the primaries confirm the Ornstein–Uhlenbeck process's physics origin (Uhlenbeck & Ornstein 1930) and its use in the Vasicek interest-rate model?

Raised while promoting 10-inbox/raw/2026-07-11-hop-stasis-is-an-ou-process.md into claim-ornstein-uhlenbeck-process-links-brownian-motion-and-the-vasicek-model. That note rests on Wikipedia (Tier 4) — acceptable for settled definitional/historical content per the sourcing floor, but a pointer to the primaries, not evidence of them. The note stays seedling until read against the source texts. Two documents, two verifications:

1. Physics origin. G. E. Uhlenbeck & L. S. Ornstein, "On the Theory of the Brownian Motion," Physical Review 36 (1930), 823–841. Confirm that the process introduced there is the mean-reverting model of a massive Brownian particle's velocity under friction — i.e. that the recorded gloss ("original application in physics was as a model for the velocity of a massive Brownian particle under the influence of friction") is faithful to the paper, and that the friction term is what supplies mean reversion.

2. Finance application. Oldřich Vašíček, "An equilibrium characterization of the term structure," Journal of Financial Economics 5 (1977), 177–188. Confirm that the Vasicek short-rate model is an Ornstein–Uhlenbeck process — a mean-reverting diffusion of the interest rate toward a long-run level — i.e. that "the Ornstein–Uhlenbeck process is used in the Vasicek model of the interest rate" is the same equation with variables relabeled, not a loose resemblance.

Why it matters: the physics-to-finance identity is the second leg of the cross-domain OU bridge (observation-mean-reversion-to-an-optimum-recurs-across-fossil-stasis-bonds-and-sgd). It is uncontested textbook material, so priority is medium — but a cross-domain claim that a bridge note leans on should sit on its primaries rather than on Wikipedia. Both papers are widely available (Phys. Rev. archive; JFE / library routes).