feat: signal math upgrade — probabilistic, regime-aware scoring pipeline

Implement full probabilistic signal processing pipeline gated behind
probabilistic_scoring_enabled feature flag in risk_configs:

- Bayesian log-likelihood accumulator with Beta posterior and entropy
- Regime detector (trend-following, panic, mean-reversion, uncertainty)
- Source accuracy tracker with per-source historical prediction accuracy
- Sigmoid confidence gate replacing binary gate
- Information gain surprise weighting for rare events
- Adaptive recency decay with event-specific half-lives
- Regime multiplier replacing market context multiplier
- Weighted disagreement entropy for contradiction detection
- Multiplicative macro exposure with conditional integration
- Graph-distance attenuated competitive signal propagation
- Exponentially weighted momentum with volatility scaling
- Expected value recommendation gate

All changes backward-compatible: flag=false preserves exact current behavior.
New outputs stored in existing JSONB columns (no schema changes except
source_accuracy table via migration 034).

Tests: 26 property-based tests (14 correctness properties), 99 unit tests,
1789 total tests passing with zero regressions.

services/recommendation/eligibility.py

@@ -9,10 +9,11 @@ Evaluates trend summaries against configurable thresholds to decide:
 All decisions are rule-based with no model involvement. The LLM is only
 used downstream for optional thesis wording (a separate task).
 
-Requirements: 7.1, 7.2, 7.3, 7.4
+Requirements: 7.1, 7.2, 7.3, 7.4, 14.1, 14.2, 14.3, 14.4, 14.5, 14.6
 """
 from __future__ import annotations
 
+import math
 from dataclasses import dataclass, field
 from enum import Enum
 
@@ -78,6 +79,10 @@ class EligibilityConfig:
     # Contradiction penalty: higher contradiction → smaller position
     contradiction_sizing_penalty: float = 0.5
 
+    # --- Expected value gate (Requirement 14) ---
+    # EV threshold: minimum expected value to allow recommendation through
+    ev_threshold: float = 0.005
+
 
 DEFAULT_ELIGIBILITY_CONFIG = EligibilityConfig()
 
@@ -98,6 +103,11 @@ class EligibilityResult:
     time_horizon: str = ""
     invalidation_conditions: list[str] = field(default_factory=list)
 
+    # Probabilistic pipeline fields (Req 14.5, 16.2)
+    ev_value: float | None = None
+    p_bull: float | None = None
+    pipeline_mode: str = "heuristic"
+
 
 # ---------------------------------------------------------------------------
 # Gate checks
@@ -318,6 +328,57 @@ def _derive_invalidation_conditions(
     return conditions
 
 
+# ---------------------------------------------------------------------------
+# Expected value computation (Requirements: 14.1–14.6)
+# ---------------------------------------------------------------------------
+
+# Horizon days mapping for EV computation
+_EV_HORIZON_DAYS: dict[str, float] = {
+    "intraday": 1.0,
+    "1d": 1.0,
+    "7d": 7.0,
+    "30d": 30.0,
+    "90d": 90.0,
+}
+
+
+def compute_expected_value(
+    p_bull: float,
+    strength: float,
+    sigma_20: float,
+    horizon_days: float,
+) -> float:
+    """Compute expected value for the recommendation gate.
+
+    Formula:
+        R_up   = strength · σ_20 · √(horizon_days)
+        R_down = (1 - strength) · σ_20 · √(horizon_days)
+        EV     = P_bull · R_up - P_bear · R_down
+
+    where P_bear = 1 - P_bull.
+
+    Args:
+        p_bull: Bayesian bullish probability in [0, 1].
+        strength: Trend strength in [0, 1].
+        sigma_20: 20-day return standard deviation.
+        horizon_days: Number of days for the projection horizon.
+
+    Returns:
+        Expected value (can be negative).
+
+    Requirements: 14.1, 14.2
+    """
+    p_bear = 1.0 - p_bull
+    sqrt_horizon = math.sqrt(max(horizon_days, 0.0))
+    r_up = strength * sigma_20 * sqrt_horizon
+    r_down = (1.0 - strength) * sigma_20 * sqrt_horizon
+    ev = p_bull * r_up - p_bear * r_down
+    # Guard against NaN/infinity from extreme inputs
+    if math.isnan(ev) or math.isinf(ev):
+        return 0.0
+    return ev
+
+
 # ---------------------------------------------------------------------------
 # Main entry point
 # ---------------------------------------------------------------------------
@@ -326,6 +387,10 @@ def _derive_invalidation_conditions(
 def evaluate_eligibility(
     summary: TrendSummary,
     config: EligibilityConfig = DEFAULT_ELIGIBILITY_CONFIG,
+    *,
+    probabilistic: bool = False,
+    p_bull: float | None = None,
+    sigma_20: float = 0.01,
 ) -> EligibilityResult:
     """Evaluate a trend summary for recommendation eligibility.
 
@@ -335,8 +400,27 @@ def evaluate_eligibility(
     3. Determines the highest allowed execution mode
     4. Computes position sizing from portfolio rules
     5. Derives invalidation conditions
+    6. (probabilistic) Applies EV gate: EV > threshold to proceed
+
+    When ``probabilistic=True``:
+    - Computes EV = P_bull · R_up - P_bear · R_down
+    - When EV > threshold (default 0.005), allows recommendation through
+    - When EV ≤ threshold, forces recommendation to informational mode
+    - Populates expected_value, p_bull, pipeline_mode on result
+
+    When ``probabilistic=False``:
+    - Skips EV gate entirely (existing behavior)
+
+    Args:
+        summary: The current trend summary.
+        config: Eligibility configuration thresholds.
+        probabilistic: Use EV gate when True.
+        p_bull: Bayesian bullish probability (required when probabilistic=True).
+        sigma_20: 20-day return standard deviation for EV computation.
 
     Returns an EligibilityResult with the full decision trace.
+
+    Requirements: 14.1, 14.2, 14.3, 14.4, 14.5, 14.6
     """
     rejection_reasons = _check_gates(summary, config)
 
@@ -353,6 +437,21 @@ def evaluate_eligibility(
     if not eligible:
         mode = RecommendationMode.INFORMATIONAL
 
+    # EV gate (Requirement 14.1–14.6)
+    ev_value: float | None = None
+    if probabilistic and p_bull is not None:
+        horizon_days = _EV_HORIZON_DAYS.get(summary.window.value, 7.0)
+        ev_value = compute_expected_value(
+            p_bull=p_bull,
+            strength=summary.trend_strength,
+            sigma_20=sigma_20,
+            horizon_days=horizon_days,
+        )
+
+        if ev_value <= config.ev_threshold:
+            # Force to informational mode (Req 14.4)
+            mode = RecommendationMode.INFORMATIONAL
+
     return EligibilityResult(
         eligible=eligible,
         action=action,
@@ -361,4 +460,7 @@ def evaluate_eligibility(
         rejection_reasons=rejection_reasons,
         time_horizon=horizon,
         invalidation_conditions=invalidation,
+        ev_value=ev_value,
+        p_bull=p_bull if probabilistic else None,
+        pipeline_mode="probabilistic" if probabilistic else "heuristic",
     )