Length-profile bounds and parity conjectures for hypercube drawings

Consider a length-regular drawing of the $d$-dimensional hypercube, with edge lengths $\ell_1\leq \ell_2\leq\cdots$. Length-profile conjectures. The following assertions are proposed: (1) for every $i$, $\ell_i\leq 2^{d-1}-2^{d-(i+1)}$; (2) there must exist edges of even length, with the dimension qualification left unresolved in the source; and (3) if a length $\ell$ is odd, it cannot occur twice, with the source suggesting a qualification of $d\geq 3$ or $d\geq 4$. These claims concern structural restrictions on length-regular hypercube drawings. The tentative dimension qualifications and the informal presentation make the precise scope unclear, and the source gives no resolution.