feat: show FIP path-smoothness in ticker technicals

Display-only Da/Gurun/Warachka information discreteness on the ticker
indicator panel. Shared compute with the backtest harness; not wired into
gate or rank.

tests/unit/test_indicator_service.py

@@ -8,6 +8,7 @@ from app.services.indicator_service import (
     compute_atr,
     compute_ema,
     compute_ema_cross,
+    compute_fip_id,
     compute_pivot_points,
     compute_rsi,
     compute_volume_profile,
@@ -262,3 +263,31 @@ class TestComputeEMACross:
         closes = _rising_closes(30)
         with pytest.raises(ValidationError, match="EMA Cross requires"):
             compute_ema_cross(closes, short_period=20, long_period=50)
+
+
+# ---------------------------------------------------------------------------
+# FIP ID (display / research context — not a gate)
+# ---------------------------------------------------------------------------
+
+class TestComputeFipId:
+    def test_steady_climber_is_continuous(self):
+        # Many small up days → low (negative) ID for a positive-return path.
+        closes = [100.0 * (1.002 ** i) for i in range(280)]
+        result = compute_fip_id(closes)
+        assert result["fip_id"] < 0
+        assert result["path"] == "continuous"
+        assert result["display_only"] is True
+        assert 0 <= result["score"] <= 100
+
+    def test_jump_then_flat_is_more_discrete_than_steady(self):
+        steady = [100.0 * (1.002 ** i) for i in range(280)]
+        jumpy = [100.0] * 252
+        jumpy.append(100.0 * 1.5)
+        jumpy.extend([100.0 * 1.5] * 40)
+        id_steady = compute_fip_id(steady)["fip_id"]
+        id_jumpy = compute_fip_id(jumpy)["fip_id"]
+        assert id_jumpy > id_steady
+
+    def test_insufficient_data_raises(self):
+        with pytest.raises(ValidationError, match="FIP ID requires"):
+            compute_fip_id(_rising_closes(50))