The 8/3-plus stability conjecture for power-free binary morphism lengths

For every extended-real threshold $(8/3)^+\leq\alpha<3$, the admissible positive lengths of $\alpha$-free uniform binary morphisms are exactly all integers except $3$ and $6$. Every admitted length has a complementary witness, $h(1)=\overline{h(0)}$; the broader binary class has the same length set by the credited prior impossibility theorem. At the strict threshold $8/3$, length $5$ is impossible, whereas it is possible at $(8/3)^+$. The decisive bound for the prior endpoint family is $\operatorname{ce}(h(w))\leq\max(8/3,\operatorname{ce}(w))$ for every cubefree input. A length-12 seed covers the remaining doubling family through the established finite sufficient criterion. The proof includes finite and infinite admissible inputs with the stated critical-exponent convention. It does not classify every preserving morphism or settle all transitions in the lower interval $[(7/3)^+,8/3]$. Equal zero/one counts in one image are not assumed.

For every extended-real threshold $(8/3)^+\leq\alpha<3$, the admissible positive lengths of $\alpha$-free uniform binary morphisms are exactly all integers except $3$ and $6$. Every admitted length has a complementary witness, $h(1)=\overline{h(0)}$; the broader binary class has the same length set by the credited prior impossibility theorem. At the strict threshold $8/3$, length $5$ is impossible, whereas it is possible at $(8/3)^+$. The decisive bound for the prior endpoint family is $\operatorname{ce}(h(w))\leq\max(8/3,\operatorname{ce}(w))$ for every cubefree input. A length-12 seed covers the remaining doubling family through the established finite sufficient criterion. The proof includes finite and infinite admissible inputs with the stated critical-exponent convention. It does not classify every preserving morphism or settle all transitions in the lower interval $[(7/3)^+,8/3]$. Equal zero/one counts in one image are not assumed.