wip(assembler): round L32 -- smooth Gradient interface at full amplitude (no rings, not flat)

Band faces now use signed distance to the displaced solid intervals, continuous across bands, so
MC interpolates the interface instead of terracing at density levels. The Gradient amplitude is
restored to width/8 (about 4 m peak-to-peak at 16 m). Ring/terrace audit at LOD0-8 on the FI floor and SW
ceiling passes; negative controls: L30 (rings) and L31 (flat) both fail. Hole/interface audits,
16 passage rows and 24/24 determinism pass. Evaluator 20. Cost vs L31 SW +1.9%, FI +1.5%.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01CSFYgsdW8ejZSyiMf4qRSX

Standalone/Research/WorldAssemblerM3/Linux32/ProbeTransitionCacheL32.py

@@ -0,0 +1,62 @@
+#!/usr/bin/env python3
+"""Compare the v20 transition-column cache with the uncached v20 binary."""
+import re
+import subprocess
+import time
+from pathlib import Path
+
+
+ROOT = Path(__file__).resolve().parents[4]
+OUT = ROOT / "Saved/Linux/l32"
+BINARIES = {
+    "base": OUT / "bin/VoxelForgeCoreHeadless-l32-clang-v20",
+    "cache": OUT / "bin/transition-cache/VoxelForgeCoreHeadless-l32-transition-cache",
+}
+ORDER = (("base", "cache"), ("cache", "base"), ("base", "cache"),
+         ("cache", "base"), ("base", "cache"))
+READY = re.compile(r"\bwhole_view_ready=([0-9.]+)s")
+rows = []
+failed = False
+
+for pair, builds in enumerate(ORDER, 1):
+    for build in builds:
+        name = f"cache-compare-sw-pair{pair}-{build}"
+        logfile = OUT / f"{name}.log"
+        command = [
+            "taskset", "-c", "0-11", "prlimit", "--as=6442450944", "--",
+            str(BINARIES[build]), str(ROOT / "Standalone/data/owner_world.json"),
+            "--workers=12", "--world-assembler-prototype", "--stream-benchmark",
+            "--stream-pipeline", "--force-generate", "--clip-radius=3",
+            "--max-clip-level=8", "--max-level=-1", "--recipe=surface-world",
+        ]
+        started = time.monotonic()
+        try:
+            with logfile.open("w", encoding="utf-8") as stream:
+                result = subprocess.run(command, stdout=stream, stderr=subprocess.STDOUT,
+                                        timeout=900, check=False)
+        except subprocess.TimeoutExpired:
+            result = None
+        elapsed = time.monotonic() - started
+        text = logfile.read_text(encoding="utf-8", errors="replace")
+        matches = READY.findall(text)
+        valid = result is not None and result.returncode == 0 and len(matches) == 1
+        ready = float(matches[0]) if len(matches) == 1 else float("nan")
+        rows.append((pair, build, ready, elapsed,
+                     result.returncode if result else "TIMEOUT", valid))
+        print(f"pair={pair} build={build} whole_view_ready={ready:.3f}s "
+              f"process_elapsed={elapsed:.1f}s {'PASS' if valid else 'FAIL'}", flush=True)
+        failed |= not valid
+
+csv = OUT / "transition-cache-compare.csv"
+csv.write_text(
+    "pair,build,whole_view_ready_seconds,process_elapsed_seconds,exit_code,status\n" +
+    "".join(f"{pair},{build},{ready:.6f},{elapsed:.3f},{code},"
+            f"{'PASS' if ok else 'FAIL'}\n"
+            for pair, build, ready, elapsed, code, ok in rows), encoding="utf-8")
+for build in BINARIES:
+    values = [row[2] for row in rows if row[1] == build]
+    values.sort()
+    median = values[len(values) // 2]
+    print(f"[TransitionCacheCost] build={build} median_whole_view_ready_s={median:.3f}")
+print(f"[TransitionCacheCost] runs={len(rows)} status={'FAIL' if failed else 'PASS'}")
+raise SystemExit(1 if failed or len(rows) != 10 else 0)