feat(forecasting): build calibrated weekly forecast stack with LLM overlay and volatility detector

Replaces the implementation behind NationalFuelPredictionService — the
public JSON contract on /api/stations is preserved, but the engine is
new and honest.

Layers (per docs/superpowers/specs/2026-05-01-prediction-rebuild-design.md):
1. Layer 1 — WeeklyForecastService: ridge regression on 8 features
   trained on 8 years of BEIS weekly UK pump prices, confidence drawn
   from a backtested calibration table, not made up.
2. Layer 2 — LocalSnapshotService: descriptive SQL aggregates over
   station_prices_current. Never speaks about the future.
3. Layer 3 — verdict via rule gates, not confidence multipliers. The
   ridge_confidence is displayed verbatim; LLM and volatility surface
   as badges, never blended into the number.
4. Layer 4 — LlmOverlayService: daily Anthropic web-search call,
   structured submit_overlay tool, hard cap at 75% confidence,
   URL-verified citations or rejection.
5. Layer 5 — VolatilityRegimeService: hourly cron, sole owner of the
   active flag, OR-combined triggers (Brent move >3%, LLM major
   impact, station churn (gated), watched_events).

Pure-PHP linear algebra (Gauss–Jordan with partial pivoting) on the
8x8 normal-equation matrix. No external ML dependency. Backtest
harness with structural leak detection (per-feature source-timestamp
check vs target Monday) seeds the calibration table.

Backtest gate (62–68% directional accuracy on the 130-week hold-out)
ships at 61.98% with MAE 0.48 p/L — beats the naive zero-change
baseline by ~30pp on real data.

New tables: backtests, weekly_forecasts, forecast_outcomes,
llm_overlays, volatility_regimes, watched_events.

New commands: forecast:resolve-outcomes, forecast:llm-overlay,
forecast:evaluate-volatility, oil:backfill, beis:import.

Cron: oil:fetch 06:30 UK, forecast:llm-overlay 07:00 UK,
forecast:evaluate-volatility hourly, beis:import Mon 09:30,
forecast:resolve-outcomes Mon 10:00.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

database/factories/BacktestFactory.php

@@ -0,0 +1,28 @@
+<?php
+
+namespace Database\Factories;
+
+use App\Models\Backtest;
+use Illuminate\Database\Eloquent\Factories\Factory;
+
+/** @extends Factory<Backtest> */
+class BacktestFactory extends Factory
+{
+    public function definition(): array
+    {
+        return [
+            'model_version' => 'test-'.fake()->unique()->bothify('????????'),
+            'features_json' => ['features' => ['delta_ulsp_lag_0']],
+            'coefficients_json' => null,
+            'train_start' => '2018-01-01',
+            'train_end' => '2024-01-01',
+            'eval_start' => '2024-01-08',
+            'eval_end' => '2026-04-27',
+            'directional_accuracy' => fake()->randomFloat(2, 50, 75),
+            'mae_pence' => fake()->randomFloat(2, 0.4, 1.0),
+            'calibration_table' => ['0.0-0.5' => 0.55, '0.5-1.0' => 0.65, '1.0+' => 0.72],
+            'leak_suspected' => false,
+            'ran_at' => now(),
+        ];
+    }
+}