feat: add numeric and symbolic scripts

scripts/dps_hierarchy/07_dps_level3_single.py

@@ -0,0 +1,30 @@
+"""
+07_dps_level3_single.py
+
+A single DPS level-3 feasibility check on the pure Tiles state, to confirm
+the construction works and see its cost before committing to a full
+noise-threshold bisection (see 08_dps_level_k_bisection.py).
+
+In the original sandbox this took ~137s with SCS (single solve, cold
+start). Expect similar or better on a modern laptop; likely far faster
+with an interior-point solver (MOSEK, if you have a license) since the
+PSD cone here (81x81 complex Hermitian) is small by modern SDP standards
+-- SCS is a first-order method tuned for large sparse problems and is not
+especially fast on small/dense feasibility problems like this one.
+
+Expected result: status "infeasible" (i.e. entanglement IS detected).
+"""
+import time
+import cvxpy as cp
+from common import RHO_TILES
+from dps_hierarchy import build_dps_problem, dps_feasible
+
+SOLVER = cp.SCS  # try cp.MOSEK if available -- likely much faster at this size
+
+prob, rho_param, sigma = build_dps_problem(d=3, k=3)
+print(f"sigma shape: {sigma.shape}   "
+      f"PPT-constraint (PSD cone) size: {3 * 3 ** 3} x {3 * 3 ** 3}")
+
+t0 = time.time()
+ok = dps_feasible(prob, rho_param, RHO_TILES, solver=SOLVER, eps=1e-6, max_iters=20000)
+print(f"DPS level-3 feasible: {ok}  status={prob.status}  [{time.time() - t0:.1f}s]")