Update README.md

README.md

@@ -1,12 +1,11 @@
 ---
-title: Agentic Reliability Framework
-emoji: 🤖
+title: Agentic Reliability Framework (ARF) – Technical Overview
+emoji: 🧠
 colorFrom: blue
-colorTo: green
+colorTo: indigo
 sdk: static
 pinned: false
 license: apache-2.0
-short_description: Bayesian governance for agentic systems
 ---
 
 # Agentic Reliability Framework (ARF) – Technical Overview
@@ -19,29 +18,46 @@ short_description: Bayesian governance for agentic systems
 
 ## 🧠 Core Engine (Protected)
 
-**Bayesian Risk Fusion** – Conjugate Beta priors (online) + HMC logistic regression (offline) + optional hierarchical hyperpriors.
+### Bayesian Risk Fusion
 
-\[
+Conjugate Beta priors (online) + HMC logistic regression (offline) + optional hierarchical hyperpriors.
+
+$$
 \text{risk} = w_{\text{conj}}\cdot\frac{\alpha}{\alpha+\beta} \;+\; w_{\text{hmc}}\cdot p_{\text{hmc}} \;+\; w_{\text{hyper}}\cdot \mu_{\text{hyper}}
-\]
+$$
+
+Weights are dynamic:
+
+$$
+w_{\text{hmc}} = \min\left(0.6,\; \frac{n}{n_0}\right), \qquad
+w_{\text{hyper}} = \min\left(0.3,\; \text{base}\cdot(1-w_{\text{hmc}})\right)
+$$
+
+Posterior variance → 90% HDI for uncertainty quantification.
 
-- Weights are dynamic: \(w_{\text{hmc}} = \min(0.6, n/n_0)\), \(w_{\text{hyper}} = \min(0.3, \text{base}\cdot(1-w_{\text{hmc}}))\)
-- Posterior variance → 90% HDI for uncertainty quantification.
+### Expected Loss Minimisation
 
-**Expected Loss Minimisation** – Chooses `APPROVE`, `DENY`, or `ESCALATE` by minimising:
+Chooses `APPROVE`, `DENY`, or `ESCALATE` by minimising:
 
-\[
+$$
 \begin{aligned}
 L_{\text{approve}} &= \text{COST\_FP}\cdot R + \text{COST\_IMPACT}\cdot b_{\text{mean}} + \dots \\
 L_{\text{deny}} &= \text{COST\_FN}\cdot(1-R) + \text{COST\_OPP}\cdot v_{\text{mean}} \\
 L_{\text{escalate}} &= \text{COST\_REVIEW} + \text{COST\_UNCERTAINTY}\cdot\psi
 \end{aligned}
-\]
+$$
+
+### Execution Ladder (Rust)
+
+Mechanical gates: `license`, `confidence`, `risk`, `rollback`, `causal`.
+
+### Lyapunov Stability
+
+Quadratic candidate $V(x,r) = \alpha r^2 + \beta\|x - x_{\text{des}}\|^2$ ensures healing actions converge.
 
-**Execution Ladder (Rust)** – Mechanical gates: `license`, `confidence`, `risk`, `rollback`, `causal`.  
-**Lyapunov stability** – Quadratic candidate \(V(x,r) = \alpha r^2 + \beta\|x-x_{\text{des}}\|^2\) ensures healing actions converge.
+### Cryptographic Signing
 
-**Cryptographic signing** – Ed25519 signatures for `HealingIntent` (Python `cryptography`, Rust `ed25519_dalek`).
+Ed25519 signatures for `HealingIntent` (Python `cryptography`, Rust `ed25519_dalek`).
 
 ---