Generalized Becker finiteness conjecture for higher Pythagoras numbers

Let $R$ be a commutative ring with identity. For a positive integer $s$, let $p_{2s}(R)$ denote the least number of $2s$-th powers needed in the relevant representation defining the higher Pythagoras number, when this number is finite. Generalized Becker finiteness conjecture. The following conditions are equivalent:

1. $p_2(R)<\infty$.
2. $p_{2s}(R)<\infty$ for some $s$.
3. $p_{2s}(R)<\infty$ for all $s$.

Becker's theorem establishes this equivalence for fields, while the conjecture asks for the corresponding statement for arbitrary commutative rings with identity. Its status is open in the source.