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diff --git a/ui/code_templates.py b/ui/code_templates.py
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+"""
+ui/code_templates.py
+
+Python code templates for built-in derived channel kinds.
+Shown as read-only previews in the UI; clicking "Edit as Custom Script"
+converts the channel to custom_script kind with the template pre-filled.
+
+Templates use the enhanced expression namespace:
+  x      — list of source values in order
+  <name> — each source's channel_id as a named variable
+  t      — elapsed time (seconds)
+  math   — Python math module
+  vars   — shared SignalProcessor._script_vars dict (read/write)
+  state  — per-channel persistent dict (survives between evaluations)
+  result — assign the computed value here (expression-style exec)
+"""
+
+BUILTIN_TEMPLATES: dict = {
+
+    "derivative": """\
+# dy/dt — backward finite difference
+prev_v = state.get("v", x[0])
+prev_t = state.get("t", t)
+state["v"] = x[0]
+state["t"] = t
+result = (x[0] - prev_v) / (t - prev_t) if t != prev_t else 0.0
+""",
+
+    "second_derivative": """\
+# d²y/dt² — two-pass finite difference
+prev_v   = state.get("v", x[0])
+prev_t   = state.get("t", t)
+prev_vel = state.get("vel", 0.0)
+
+cur_vel = (x[0] - prev_v) / (t - prev_t) if t != prev_t else 0.0
+result  = (cur_vel - prev_vel) / (t - prev_t) if t != prev_t else 0.0
+
+state["v"]   = x[0]
+state["t"]   = t
+state["vel"] = cur_vel
+""",
+
+    "rms": """\
+# Rolling RMS over a sliding window
+import math as _math
+buf = state.setdefault("buf", [])
+buf.append(x[0])
+window = 20          # adjust window size (samples) here
+if len(buf) > window:
+    buf.pop(0)
+result = _math.sqrt(sum(v * v for v in buf) / len(buf))
+""",
+
+    "power": """\
+# Electrical power  P = V × I
+# source 0 = voltage,  source 1 = current
+result = x[0] * x[1]
+""",
+
+    "difference": """\
+# Difference  A − B
+# source 0 = A,  source 1 = B
+result = x[0] - x[1]
+""",
+
+    "sum": """\
+# Sum of all sources
+result = sum(x)
+""",
+}