[MEDIUM] `ClosedFormStrategy` closure extraction grabs the first captured field with no type validation (silent wrong target)

[MEDIUM] ClosedFormStrategy closure extraction grabs the first captured field with no type validation (silent wrong target)

Summary

ext/ClosedFormExpectationsExt/ClosedFormExpectationsExt.jl:150-154:

field_names = fieldnames(F)
if isempty(field_names)
    error(...)
end
captured = getfield(argument, first(field_names))
return (strategy, Logpdf(captured))

When RxInfer-style closures capture more than one variable, the code silently takes the first captured field and wraps it in Logpdf, with no validation that it is a Distribution/ProductOf. This can silently project the wrong target distribution (or even a non-distribution), producing an incorrect exponential-family member with no error.

Evidence (Julia 1.12.6, ClosedFormExpectations 0.4.1)

• let a = 5, d = Normal(0,1); fn = (x) -> logpdf(d,x) + a; preprocess_strategy_argument(ClosedFormStrategy(), fn) returns arg.dist == 5 (the scalar a), not d.
• With two captured distributions (a = Gamma(3,3), d = Normal(0,1)), it returns arg.dist == Gamma(3,3) (the first captured), not the intended Normal.

The check isempty(field_names) only guards against zero captured variables; it does not ensure the captured value is the intended target.

Impact

Silent-wrong-inference class bug (produces a wrong distribution without failing). Trigger is narrow (multi-variable closures), but the failure mode is silent.

Suggested fix

After extraction, assert the captured value is a Distribution or ProductOf (and, if the closure has more than one field, either error or attempt to locate the distribution field). At minimum, captured isa Union{Distribution,ProductOf} || error(...).

Start at ext/ClosedFormExpectationsExt/ClosedFormExpectationsExt.jl:150-154 and inspect how preprocess_strategy_argument handles captured closure fields. Reproduce the multi-variable closure examples from the issue, then ensure an invalid captured value is rejected rather than silently wrapped; done means the reported wrong-target cases no longer return a scalar or unintended distribution.