feat: add numeric and symbolic scripts

scripts/dps_hierarchy/08_dps_level_k_bisection.py

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+"""
+08_dps_level_k_bisection.py
+
+General, RESUMABLE bisection for the DPS level-k noise-robustness
+threshold of the Tiles state family. Each run performs STEPS_PER_RUN
+bisection steps and saves progress to a JSON state file, so you can call
+it repeatedly (e.g. in a shell loop, or across separate sessions) without
+losing progress -- useful since each SDP solve can take anywhere from
+under a second (k=2) to a few minutes (k=3, with SCS) depending on k,
+your hardware, and the solver.
+
+Usage:
+    python3 08_dps_level_k_bisection.py
+
+Configure LEVEL, SOLVER, STEPS_PER_RUN, and EPS below.
+The state file is named dps_level{LEVEL}_bisection_state.json.
+
+--------------------------------------------------------------------
+Progress already made in the original chat session for LEVEL=3 (8 SCS
+solves, ~135-227s each) is included alongside this script as
+dps_level3_bisection_state.json:
+
+    bracket so far: [0.90982, 0.91080]   (i.e. p_c ~ 0.910-0.911)
+
+Just run this script (with LEVEL=3, the default) to continue narrowing
+it -- it will pick up automatically from that saved state. Delete the
+state file to start over, or change LEVEL to try a different extension
+order (4, 5, ... but see README.md for how fast the PPT-constraint size,
+and hence the cost, grows: 3*3^k).
+--------------------------------------------------------------------
+"""
+import json
+import os
+import time
+import cvxpy as cp
+from common import noisy_tiles
+from dps_hierarchy import build_dps_problem, dps_feasible
+
+LEVEL = 3
+SOLVER = cp.SCS            # swap to cp.MOSEK if available -- likely much faster
+STEPS_PER_RUN = 1          # raise this if your machine/solver is fast enough
+EPS = 1e-5                 # solver tolerance; tighten once you have a rough bracket
+DEFAULT_BRACKET = (0.70, 0.951)  # 0.951 is a proven-safe upper bound (= DPS level-2 threshold,
+                                  # since DPS level 3 can only detect at <= that noise level)
+
+STATE_FILE = f"dps_level{LEVEL}_bisection_state.json"
+
+if os.path.exists(STATE_FILE):
+    with open(STATE_FILE) as f:
+        state = json.load(f)
+    print(f"Resuming from saved state: bracket [{state['lo']:.5f}, {state['hi']:.5f}], "
+          f"{state['iter']} iterations so far.")
+else:
+    state = {"lo": DEFAULT_BRACKET[0], "hi": DEFAULT_BRACKET[1], "iter": 0, "log": []}
+    print(f"Starting fresh: bracket {DEFAULT_BRACKET}")
+
+prob, rho_param, sigma = build_dps_problem(d=3, k=LEVEL)
+print(f"sigma shape: {sigma.shape},  PPT-constraint (PSD cone) size: "
+      f"{3 * 3 ** LEVEL} x {3 * 3 ** LEVEL}\n")
+
+for _ in range(STEPS_PER_RUN):
+    lo, hi = state["lo"], state["hi"]
+    mid = (lo + hi) / 2
+    t0 = time.time()
+    feasible = dps_feasible(prob, rho_param, noisy_tiles(mid), solver=SOLVER,
+                             eps=EPS, max_iters=20000, warm_start=True)
+    dt = time.time() - t0
+    if feasible:
+        state["lo"] = mid
+    else:
+        state["hi"] = mid
+    state["iter"] += 1
+    state["log"].append({"iter": state["iter"], "p": mid, "feasible": feasible,
+                          "time_s": round(dt, 1), "status": prob.status})
+    print(f"[iter {state['iter']}] p={mid:.5f}  feasible={feasible}  "
+          f"status={prob.status}  ({dt:.1f}s)   "
+          f"bracket now [{state['lo']:.5f}, {state['hi']:.5f}]")
+
+with open(STATE_FILE, "w") as f:
+    json.dump(state, f, indent=2)
+
+print(f"\nCurrent bracket: [{state['lo']:.5f}, {state['hi']:.5f}]  "
+      f"(width {state['hi'] - state['lo']:.5f})")
+print("Run again to continue narrowing it further (progress is saved).")