fix: recalibrate FIP path labels to live equity scale

Replace inert ±0.25 bands with ~p25/p75 cutoffs from the prod snapshot
(−0.08 / 0.00). Document zero-return dilution and left-skewed distribution.

app/services/indicator_service.py

@@ -408,6 +408,17 @@ def compute_pivot_points(
     }
 
 
+# Path labels for display only. Calibrated on the ~505-name prod snapshot
+# (2026-07, n=502 with full history): empirical p25 ≈ −0.082, p75 ≈ +0.004,
+# mean ≈ −0.043. Paper-style |ID| ≳ 0.25 almost never appears in live equities
+# (only ~0.2% of names); real momentum winners cluster around −0.04…−0.12.
+# Thresholds are therefore ~quartile cutoffs, not ±0.25 textbook extremes.
+# Distribution is left-skewed (bullish sample → more "continuous" than "discrete"),
+# so the discrete band is not symmetric.
+FIP_PATH_CONTINUOUS_MAX = -0.08  # ~p25: smoother quartile
+FIP_PATH_DISCRETE_MIN = 0.00  # ~p75: less-continuous quartile
+
+
 def compute_fip_id(closes: list[float], as_of_index: int | None = None) -> dict[str, Any]:
     """Da/Gurun/Warachka information discreteness over the 12-1 formation window.
 
@@ -418,8 +429,13 @@ def compute_fip_id(closes: list[float], as_of_index: int | None = None) -> dict[
         ID = sign(PRET) × (%neg − %pos)
 
     Lower ID ⇒ smoother / more continuous path (for a winner: many small up days).
-    Higher ID ⇒ jumpy / discrete path (few large moves). Zero-return days count
-    in neither numerator but remain in the denominator.
+    Higher ID ⇒ jumpy / discrete path (few large moves).
+
+    Zero-return days count in neither numerator but remain in the denominator
+    (paper definition). Quirk: a flat series with one big jump can still land
+    near zero ("mixed") because zeros dilute %pos/%neg — faithful to the paper
+    and to real equities (exact zero daily returns are rare). Synthetic jump
+    tests assert ordering vs a steady climber, not the discrete label itself.
     """
     i = len(closes) - 1 if as_of_index is None else as_of_index
     if i < 252 or closes[i - 252] <= 0 or closes[i - 21] <= 0:
@@ -448,12 +464,13 @@ def compute_fip_id(closes: list[float], as_of_index: int | None = None) -> dict[
     else:
         sign = 0.0
     fip = sign * (pct_neg - pct_pos)
-    # Map [-1, 1] → score where lower ID (smoother) is higher for display only.
+    # Map observed ID range (~[-0.3, 0.15]) loosely to 0–100 for the card chrome;
+    # lower ID (smoother) → higher score. Display only.
     score = max(0.0, min(100.0, 50.0 * (1.0 - fip)))
-    if fip <= -0.25:
+    if fip <= FIP_PATH_CONTINUOUS_MAX:
         path = "continuous"
         path_label = "smooth grind (continuous information)"
-    elif fip >= 0.25:
+    elif fip >= FIP_PATH_DISCRETE_MIN:
         path = "discrete"
         path_label = "jumpy path (discrete information)"
     else: