The motivic period conjecture for prime weighted multiple harmonic sums

Let $\mathcal{P}_{\geq 3}$ denote the set of primes at least $3$, let $\alpha\in\mathbb{N}^{\ast}$, and let $I$ be one of $\mathcal{P}_{\geq 3}\times\{\alpha\}$, $\{p\}\times\mathbb{N}^{\ast}$, or $\mathcal{P}_{\geq 3}\times\mathbb{N}^{\ast}$. Consider the weight-filtered algebras of prime weighted multiple harmonic sums and their motivic counterparts, together with the map from the motivic algebra that factorizes through the corresponding completed diagonal algebra. Motivic period conjecture. The map between these weight-filtered algebras is an isomorphism of filtered algebras for each of the three specified types of $I$. Equivalently, any absolutely convergent identity between prime weighted multiple harmonic sums $\operatorname{har}_{p^{\alpha}}$ valid for all $p$ or all $\alpha$ is already valid in the motivic setting. The source presents this as an analogue of the period conjecture and gives no evidence of a proof or disproof.