diff --git a/1/harmonic_resonance_fields_hrf (1).py b/1/harmonic_resonance_fields_hrf (1).py
index c977778..70d3008 100644
--- a/1/harmonic_resonance_fields_hrf (1).py	
+++ b/1/harmonic_resonance_fields_hrf (1).py	
@@ -3,6 +3,12 @@
 
 Automatically generated by Colab.
 
+MAINTAINER'S NOTE:
+This repository supports two primary versions of the Harmonic Resonance Forest (HRF):
+- v15.x: Production-Stable version. Recommended for clinical reliability and validated benchmarks.
+- v16.x: Experimental Beta version. Features Parallel Evolutionary Search (PES) for peak performance,
+         but may exhibit higher variance in class-specific metrics.
+
 Original file is located at
     https://colab.research.google.com/drive/1IWm4oFfwTa87xPyfQvpCHEo8WdBbrI_R
 """
@@ -43,9 +49,7 @@ def fit(self, X, y):
 
     def _wave_potential(self, x_query, X_class, class_id):
         dists = np.linalg.norm(X_class - x_query, axis=1)
-        dists = np.linalg.norm(X_class - x_query, axis=1)
 
-        frequency = self.base_freq * (class_id + 1)
         frequency = self.base_freq * (class_id + 1)
 
         waves = (1 / (1 + dists)) * np.cos(frequency * dists)
@@ -1521,7 +1525,7 @@ def make_ecg_dataset(n_samples=600, n_features=60):
 
     print(f"{name:<25} | {avg_hrf:.2%}        | {avg_rf:.2%}        | {p_val:.4f}     | {verdict}")
 
-"""#  Research Breakthrough: The Harmonic Resonance Forest (HRF)
+r"""#  Research Breakthrough: The Harmonic Resonance Forest (HRF)
 
 ## 1. Abstract & Core Innovation
 Conventional machine learning models (Decision Trees, KNN) operate on **Euclidean or Rectangular manifolds**—they slice data into boxes or measure straight-line distances. While effective for tabular data, these approaches lack the **inductive bias** required for oscillatory systems.
diff --git a/HRF Codes/hrf_final_v16_hrf.py b/HRF Codes/hrf_final_v16_hrf.py
index b1777f3..58a9fcf 100644
--- a/HRF Codes/hrf_final_v16_hrf.py	
+++ b/HRF Codes/hrf_final_v16_hrf.py	
@@ -3,6 +3,12 @@
 
 Automatically generated by Colab.
 
+MAINTAINER'S NOTE:
+This repository supports two primary versions of the Harmonic Resonance Forest (HRF):
+- v15.x: Production-Stable version. Recommended for clinical reliability and validated benchmarks.
+- v16.x: Experimental Beta version. Features Parallel Evolutionary Search (PES) for peak performance,
+         but may exhibit higher variance in class-specific metrics.
+
 Original file is located at
     https://colab.research.google.com/drive/1-9Q_x2Y4zuPHcg5_SsKXpFDlYiFhaAoo
 
diff --git a/docs/hrf_titan26_monograph.md b/docs/hrf_titan26_monograph.md
index fc12f1b..b6e2fbb 100644
--- a/docs/hrf_titan26_monograph.md
+++ b/docs/hrf_titan26_monograph.md
@@ -17,13 +17,13 @@ workflow_path: .github/workflows/dev-log.yml
 This registry formally documents the deterministic state and ongoing evolution of **Harmonic Resonance Fields (HRF)**, a paradigm-shifting physics-informed machine learning architecture. Moving beyond traditional statistical feature-splitting algorithms (e.g., Random Forests, Gradient Boosting), HRF conceptualizes classification as a physical wave interference problem. By evaluating signals across a 26-dimensional unified manifold, the architecture demonstrates unparalleled phase-jitter robustness, superior generalization, and neuro-adaptive capabilities, setting a new benchmark for computational neuroscience and biological signal processing.
 
 ## II. Mathematical Physics Framework
-The foundational theorem of HRF asserts that every data coordinate in a given feature space acts as a source of physical wave potential. The algorithm evaluates the state space using damped harmonic oscillators to generate class-specific resonance energy. The wave potential $\Psi$ at an observation point $x$ induced by a source $p_i$ is governed by:
+The foundational theorem of HRF asserts that every data coordinate in a given feature space acts as a source of physical wave potential. The algorithm evaluates the state space using damped harmonic oscillators to generate class-specific resonance energy. The wave potential $\Psi$ at an observation point $\mathbf{x}$ induced by a source $\mathbf{p}_i$ is governed by:
 
-$$ \Psi(x, p_i) = \exp(-\gamma||x - p_i||^2) \cdot \cos(\omega_c \cdot ||x - p_i|| + \varphi) $$
+$$ \Psi(\mathbf{x}, \mathbf{p}_i) = \exp\left(-\gamma \left\| \mathbf{x} - \mathbf{p}_i \right\|^2\right) \cdot \cos\left(\omega_c \cdot \left\| \mathbf{x} - \mathbf{p}_i \right\| + \varphi\right) $$
 
 ### 2.1 Parameter Definitions
-- **Gaussian Damping** ($\exp(-\gamma r^2)$): Constrains the spatial influence of the resonance wave to local topologies, preventing infinite energy divergence and ensuring manifold stability.
-- **Harmonic Resonance** ($\cos(\omega r + \varphi)$): Encodes specific class frequencies. The frequency $\omega_c$ allows the system to differentiate between subtle physiological states (e.g., Alpha vs. Beta wave dominance).
+- **Gaussian Damping** ($\exp\left(-\gamma r^2\right)$): Constrains the spatial influence of the resonance wave to local topologies, preventing infinite energy divergence and ensuring manifold stability.
+- **Harmonic Resonance** ($\cos\left(\omega r + \varphi\right)$): Encodes specific class frequencies. The frequency $\omega_c$ allows the system to differentiate between subtle physiological states (e.g., Alpha vs. Beta wave dominance).
 - **Phase ($\varphi$)**: Ensures dynamic temporal alignment, permitting asynchronous signal detection and rendering the classification invariant to temporal phase shifts.
 
 ## III. The Harmonic Resonance Manifold (Titan 26)