fix(research): avoid double split() call and potential IndexError (#2229)

cat.split()[0] was called in the condition and again in the body,
wasting a second split. More importantly, if cat were ever
whitespace-only, split() returns [] and [0] raises IndexError.
Assign to a local variable and guard with a truthiness check.

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/deep_research.py

@@ -439,7 +439,8 @@ class DeepResearcher:
             )
             cat = (result or "").strip().lower()
             # Clean one-word answer first.
-            first = cat.split()[0].strip(".,\"'*:") if cat.split() else ""
+            parts = cat.split()
+            first = parts[0].strip(".,\"'*:") if parts else ""
             if first in CATEGORY_PROMPTS:
                 return first
             # Weak local models often wrap the label in preamble ("the category