History of Satisfiability thresholds of random $k$-XORSAT

 Title: Satisfiability thresholds of random $k$-XORSAT-Definition: Random $k$-XORSAT CITE{WikiXORSAT} is a random system of $m=\lfloor\alpha-  n\rfloor$ $k$-variable equations over $\mathbb{F}_2$ in $n$ Boolean variables. For-  $k\geq3$, $\alpha_k$ is the density such that, as $n\to\infty$, satisfiability has-  probability tending to $1$ when $\alpha<\alpha_k$ and to $0$ when $\alpha>\alpha_k$-  CITE{PittelSorkin}.+Definition: Random $k$-XORSAT CITE{WikiXORSAT} is a random system of $k$-variable+  equations over $\mathbb{F}_2$. For $k\geq3$, $\alpha_k$ is the density such that,+  as $n\to\infty$, satisfiability has limiting probability $1$ for $\alpha<\alpha_k$+  and $0$ for $\alpha>\alpha_k$ CITE{PittelSorkin}. Keywords: XOR-SAT, random linear systems over GF(2), p-spin model, cuckoo hashing Parameters:

     constraints: $k\geq3$ Comments:-  comment-conventions: The density is $\alpha=m/n$, equations per variable. The average-    degree of the underlying $k$-uniform constraint hypergraph is $k\alpha$. Each-    equation uses $k$ distinct variables and a uniform right-hand side. In cuckoo-    hashing CITE{WikiCuckoo} with $k$ hash functions and buckets that hold one key-    each, $\alpha_k$ is the threshold for the load, the number of keys per bucket-    CITE{DGMMPR}. Allowing repeated variable choices gives the same threshold CITE{PittelSorkin}.+  comment-conventions: The density is $\alpha=m/n$, equations per variable; in the+    finite model $m=\lfloor\alpha n\rfloor$. The average degree of the underlying+    $k$-uniform constraint hypergraph is $k\alpha$. Each equation uses $k$ distinct+    variables and a uniform right-hand side. In cuckoo hashing CITE{WikiCuckoo} with+    $k$ hash functions and buckets that hold one key each, $\alpha_k$ is the threshold+    for the load, the number of keys per bucket CITE{DGMMPR}. Allowing repeated variable+    choices gives the same threshold CITE{PittelSorkin}.   comment-k2: There is no $k=2$ row. In random $2$-XORSAT the limiting probability     of satisfiability is strictly between $0$ and $1$ below density $\alpha=1/2$,