Recht's "Mates of Costate" argues mathematical equivalence (Lagrangian duality), not historical transmission — and never mentions Kelley

The duality argument, precisely. Attach Lagrange multipliers to a discrete-time LQ problem's dynamics constraint and the multipliers "become a trajectory of a related linear system called the adjoint or dual system," whose "dynamics are linear in the costate p_t, with time running in reverse and the state transition matrix being the transpose (also known as the adjoint) of A." Stationarity w.r.t. the multipliers recovers the forward pass; stationarity w.r.t. the states yields the backward costate recursion. Same transpose structure the AD literature states as claim-jvp-vjp-transpose-duality — control theory's clothing for it. He also derives Kalman filtering as a special case of the same machinery, placing Kalman (1960) and Bryson (1961) "very much at the birth of modern control theory."

What the post is and isn't evidence for. It is an explicit, Tier-1-worked equivalence claim ("the method of adjoints, which is equivalent to backpropagation"). It is not a transmission claim — Recht's own narrative frame is late rediscovery (a colleague showed him the method "a few years ago"), and his Bryson-1961 priority line is expressly relayed ("According to Dreyfus…" — he couldn't locate the 1961 proceedings; his "1968" book date is off by one, preserved not corrected). Checked against the full text: "Kelley" never appears — the post's chain is Kalman → Bryson → Bryson & Ho only, so it cannot carry the joint Kelley–Bryson priority story (claim-kelley-bryson-optimal-control-precursor, claim-bryson-ho-1969-curriculum-vector).

Equivalence-vs-transmission is the same distinction the cluster's spine keeps enforcing (claim-rhw-1986-demonstration-not-invention, claim-reverse-mode-multiple-independent-discovery): "these are the same mathematics" and "one caused the other" are different claims with different evidence, and this post — read carefully — only makes the first.