Closes #ISSUE-026-REGIME-CORE - Deploy two-stage engine backend stubs and fix calibration LaTeX strings

DEV_LOG.md

@@ -354,6 +354,25 @@ This document tracks all modifications, npm packages, active compilation states,
 *   **Active Bugs**: None.
 *   **Type Checker Status**: Verified 100% clean type verification (`npx tsc --noEmit` returns exit code 0).
 
+---
+
+## [2026-06-17] - Two-Stage Engine Framework & KaTeX UI Fix (#ISSUE-026-REGIME-CORE)
+
+### Added
+*   **Two-Stage Engine Backend Blueprint**: Seeded structural modules in [pipeline.py](file:///c:/Users/jannr/.gemini/antigravity/scratch/investment-sandbox/backend/core/pipeline.py) for the upcoming Two-Stage ML pipeline:
+    *   **Fixed-Width Fractional Differentiation (FFD)**: Implemented weight computation and FFD application function stubs with fixed window size constraints to ensure feature stationarity while retaining memory bounds.
+    *   **Unsupervised Regime Classification**: Defined a `KlaassenMSGJRGARCH` class simulating a 3-state transition model (Low, Normal, High/Crisis Volatility regimes) via path consolidation.
+    *   **Covariate Shift Handler**: Added a `ULSIFDensityRatioEstimator` class implementing regularized Unconstrained Least-Squares Importance Fitting with Gaussian kernels to calculate density ratios between training and test sets.
+*   **Pipeline Integration Placeholders**: Inserted regime classifier and uLSIF density ratio calculator checkpoints into the pipeline training and transformation routines.
+
+### Fixed
+*   **KaTeX Double-Escaping**: Double-escaped backslashes and wrapped math strings inside JSX braces `{""}` inside the "Explain Calibration" dropdown container in [CryptoDemo.tsx](file:///c:/Users/jannr/.gemini/antigravity/scratch/investment-sandbox/components/modules/crypto/CryptoDemo.tsx) to ensure rendering consistency.
+
+### Active Bugs / Compile Status
+*   **Active Bugs**: None.
+*   **Type Checker Status**: Verified 100% clean type verification (`npx tsc --noEmit` returns exit code 0).
+
+