The relative consistency conjecture for Baire's grand theorem with dependent choice

The principles $\mathsf{GBT+DC}$ and $\mathsf{ZF}$ are considered as set-theoretic theories, where $\mathsf{GBT}$ denotes Baire's grand theorem and $\mathsf{DC}$ denotes the axiom of dependent choices. The relative consistency conjecture. $\mathsf{GBT+DC}$ is consistent relative to $\mathsf{ZF}$. The paper explains that the consistency strength of $\mathsf{GBT}$ together with $\mathsf{DC}$ is unknown, while $\mathsf{WHSP}$ appears weak enough to be consistent relative to $\mathsf{ZF}$ without large cardinals; this motivates the conjecture.