Update README.md

README.md

@@ -12,23 +12,34 @@ short_description: Eigenvalue early warning for power grid stability — the phy
 Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference
 
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-TaiScience CSD-EWS Simulator
-TaiScience CSD-EWS is an educational simulator for critical slowing down (CSD) as an early-warning signal in power grid stability. It visualizes how system eigenvalues (poles) approach the stability boundary, using a Jacobian eigenvalue proxy and damping-ratio thresholds.
-This work is part of the TokaMind transfer-learning framework, which adapts a tokamak-plasma foundation model to power-grid dynamics. While Microsoft's GridSFM addresses static AC-OPF feasibility, this system targets dynamic CSD precursors — complementary directions for grid security analysis, relevant to cascading-failure events such as the 2025 Iberian blackout and the 2016 South Australia blackout.
-What It Shows
-Complex s-plane map — conjugate pole pair (s = σ ± jω) with real-time position relative to the stability boundary (Re = 0)
-Damping ratio — ζ = −σ / √(σ² + ω²), with a 5% threshold separating adequate damping from warning and danger zones
-Time-domain response — illustrative y(t) = e^(σt)·cos(ωt) showing how a near-critical mode decays or diverges
-Core Concept
-Critical slowing down is a generic precursor to instability across dynamical systems: as a control parameter pushes a system toward a bifurcation, its dominant eigenvalue's real part approaches zero, recovery from perturbations slows, and damping collapses. In power systems, detecting this slowing before a mode crosses into the right-half plane provides an early-warning window for operators.
+**TaiScience CSD-EWS** is an educational simulator for *critical slowing down* (CSD) as an early-warning signal in power grid stability. It visualizes how system eigenvalues (poles) approach the stability boundary, using a Jacobian eigenvalue proxy and damping-ratio thresholds.
+
+This work is part of the TokaMind transfer-learning framework, which adapts a tokamak-plasma foundation model to power-grid dynamics. While Microsoft's GridSFM addresses static AC-OPF feasibility, this system targets *dynamic* CSD precursors — complementary directions for grid security analysis, relevant to cascading-failure events such as the 2025 Iberian blackout and the 2016 South Australia blackout.
+
+## What It Shows
+
+- **Complex s-plane map** — conjugate pole pair (s = σ ± jω) with real-time position relative to the stability boundary (Re = 0)
+- **Damping ratio** — ζ = −σ / √(σ² + ω²), with a 5% threshold separating adequate damping from warning and danger zones
+- **Time-domain response** — illustrative y(t) = e^(σt)·cos(ωt) showing how a near-critical mode decays or diverges
+
+## Core Concept
+
+Critical slowing down is a generic precursor to instability across dynamical systems: as a control parameter pushes a system toward a bifurcation, its dominant eigenvalue's real part approaches zero, recovery from perturbations slows, and damping collapses. In power systems, detecting this slowing *before* a mode crosses into the right-half plane provides an early-warning window for operators.
+
 The full CSD detection pipeline (time-domain Jacobian proxy + spectral LFPR engine) is released as open source:
 https://github.com/chihsingwu/CSD-dual-engine
-Use Case
+
+## Use Case
+
 Teaching and intuition-building for power-system stability monitoring, transient stability assessment (TSA), and PMU-based early-warning research. This page is a manual teaching demo — not a live PMU or Toeplitz identification system. The waveform shows e^(σt)·cos(ωt) only, without modal amplitude or phase.
-Related Work
-TaiScience Research Group (Fu Jen Catholic University): https://taiscience.org
-StromaPath platform: https://stromapath.com
-TokaMind PMU transfer-learning preprint: https://arxiv.org/abs/2605.11033
-CSD dual-engine (open source): https://github.com/chihsingwu/CSD-dual-engine
-Keywords
-`critical slowing down` · `power grid early warning system` · `Jacobian eigenvalue proxy` · `damping ratio monitoring` · `transient stability assessment` · `PMU` · `TokaMind transfer learning` · `s-plane pole map`
+
+## Related Work
+
+- TaiScience Research Group (Fu Jen Catholic University): https://taiscience.org
+- StromaPath platform: https://stromapath.com
+- TokaMind PMU transfer-learning preprint: https://arxiv.org/abs/2605.11033
+- CSD dual-engine (open source): https://github.com/chihsingwu/CSD-dual-engine
+
+## Keywords
+
+`critical slowing down` · `power grid early warning system` · `Jacobian eigenvalue proxy` · `damping ratio monitoring` · `transient stability assessment` · `PMU` · `TokaMind transfer learning` · `s-plane pole map`