docs: update paper and generated artifacts for ILP<V>

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: GiggleLiu

docs/paper/reductions.typ

@@ -584,7 +584,7 @@ Equivalent to the Ising model via the linear substitution $s_i = 2x_i - 1$. The
 ]
 
 #problem-def("ILP")[
-  Given $n$ integer variables $bold(x) in ZZ^n$, constraint matrix $A in RR^(m times n)$, bounds $bold(b) in RR^m$, and objective $bold(c) in RR^n$, find $bold(x)$ minimizing $bold(c)^top bold(x)$ subject to $A bold(x) <= bold(b)$ and variable bounds.
+  Given $n$ variables $bold(x)$ over a domain $cal(D)$ (binary $cal(D) = {0,1}$ or integer $cal(D) = ZZ_(>=0)$), constraint matrix $A in RR^(m times n)$, bounds $bold(b) in RR^m$, and objective $bold(c) in RR^n$, find $bold(x) in cal(D)^n$ minimizing $bold(c)^top bold(x)$ subject to $A bold(x) <= bold(b)$.
 ][
 Integer Linear Programming is a universal modeling framework: virtually every NP-hard combinatorial optimization problem admits an ILP formulation. Relaxing integrality to $bold(x) in RR^n$ yields a linear program solvable in polynomial time, forming the basis of branch-and-bound solvers. When the number of integer variables $n$ is fixed, ILP is solvable in polynomial time by Lenstra's algorithm @lenstra1983 using the geometry of numbers, making it fixed-parameter tractable in $n$. The best known general algorithm achieves $O^*(n^n)$ via an FPT algorithm based on lattice techniques @dadush2012.
 

docs/src/reductions/problem_schemas.json

@@ -119,11 +119,6 @@
         "type_name": "usize",
         "description": "Number of integer variables"
       },
-      {
-        "name": "bounds",
-        "type_name": "Vec<VarBounds>",
-        "description": "Variable bounds"
-      },
       {
         "name": "constraints",
         "type_name": "Vec<LinearConstraint>",