Using the discrete ±J bond distribution for the Sherrington-Kirkpatrick spin glass, all ground states for the entire ensemble of the bond disorder are enumerated. Although the combinatorial complexity of the enumeration severely restricts attainable system sizes, here N ≤ 9, some remarkably intricate patterns found in previous studies already emerge. The analysis of the exact ground state frequencies suggests a direct construction of their probability density function. Against expectations, the result suggests that its highly skewed appearance for finite N evolves logarithmically slow towards a Gaussian distribution. The Sherrington-Kirkpatrick (SK) model [1] of glassy behavior in magnetic materials has provided a conceptual framework for the effect of disorder and frustration that are observed in systems ranging from materials [2] to combinatorial optimization and learning [3]. It's conceptual simplicity is expressed through the Hamiltonianin which all pairs of binary Ising spin-variables σ i = ±1 are mutually connected through a bond matrix J i,j , which is symmetric and whose entries are random variables drawn from a distribution P (J) of zero mean and unit variance. We note that this Hamiltonian possesses a local "gauge"-invariance under the transformation ofat any site i and the bonds to all its adjacent sites j [4]. The SK model has reached significant prominence because, despite of its apparent simplicity, its solution proved surprisingly difficult, revealing an amazing degree of complexity in its structure [3]. While it is solvable in principle, many of its features have not been derived yet. One such feature concerns the probability density function (PDF) of its ground state energies. Being an extreme element of the energy spectrum, the distribution of e 0 is not necessarily normal but instead may follow a highly skewed "extreme-value statistics" as can be derived for the Random Energy Model [5]. If the energies within that spectrum are uncorrelated, it can be shown that the PDF for e 0 is among one of only a few universal functions. This extreme-value statistics of the ground states has been pointed out in Ref.[5] and has received considerable attention recently [6,7,8,9]. For instance, if the sum for H in Eq. (1) were over a large number of * Electronic address: sboettc@emory.edu † Electronic address: tkott@bucknell.edu independent terms, H would be Gaussian distributed. In such a spectrum, the probability of finding H → −∞ decays faster than any power, and ground states e 0 should be distributed according to a Gumbel PDF, [5]with m = 1, here generalized to the case where m refers to the m-th lowest extreme value [7]. In a spin glass the individual terms in Eq. (1) are not independent variables and deviations from any universal behavior may be expected. In particular, these deviations should become strongest when all spin variables are mutually interconnected such as here in the SK model, but may be less so for sparse graphs, such as low-dimensional lattices. (Although it should be noted that sparsely...