Exact invariant computations and Singer's conjecture for three degree families in rank four

W. Singer's conjecture asserts that the algebraic transfer is injective in every bidegree. In this article, we establish this conjecture in rank four for the three infinite families of degrees $5\\cdot2^r-2$, $17\\cdot2^r-2$, and $2^{r+s+u}+2^{r+s}+2^s-3$, with all parameters positive. More precisely, we prove that the fourth algebraic transfer is an isomorphism in bidegree $(4,n+4)$ for every degree $n$ in these families. The proof combines exact computations over $\\mathbb F_2$ of cohit representations and their invariant subspaces with established descriptions of the transfer codomain and known transfer images. Classical cohit dimension formulas certify quotient representations constructed by evaluation on primitive elements. For two exceptional subfamilies, four-term primitives replace dual spikes, and their translates are indexed by $2520$ cosets of explicitly specified subgroups. Binary coefficient extraction uses $35$ carry states. Twenty-one exact subspace identities establish isomorphisms of the full cohit modules as the parameters vary, reducing the unbounded parameter ranges to $39$ finite representatives. We determine admissible cohit bases, symmetric and general linear invariant bases, and primitive coinvariant bases. Explicit polynomial representatives describe the invariant classes, including formulas valid throughout the unbounded parameter ranges. These constructions and the established transfer images prove injectivity in every stated degree, thereby verifying Singer's conjecture for all three families. Degree-labelled computational data and verification programs accompany the finite calculations and parameter reductions.