Algorithm 3: Online Open-Set Recognition
	Require: Test sample: $x_{\mathrm{test}}$; Trained encoder parameters $\varphi$ and prototype set $C={\left\{c_k\right\}}_{k=1}^K$; Global GPD model parameters: threshold ${\omega }_{\mathrm{global}}$, scale $\sigma$$\xi$ (obtained from Algorithm 2); Significance level ${\delta }_w$ for decision-making (e.g., 0.01). Ensure: Predicted label $\widehat{y}\in \{1,\dots ,K\}\cup \{‘\mathrm{Unknown}’\}$.
1	//Compute Test Statistics:
2	Extract feature: $z_{test}\leftarrow E_{\varphi }\left(x_{\mathrm{test}}\right)$;
3	Compute distances to all prototypes: $d_k\leftarrow {‖\begin{array}{c}{z}_{test}-c_k\end{array}‖}_2^{2}fork=1,\dots ,K$;
4	Find the minimum distance and its corresponding candidate class:
5	$d_{min}\leftarrow \min \left({\left\{d_k\right\}}_{k=1}^K\right)$$,\widehat{k}\leftarrow {\mathrm{argmin}}_k\left({\left\{d_k\right\}}_{k=1}^K\right)$.
6	//Decision Based on Extreme Value Model
7	If $d_{\min }\le {\omega }_{\mathrm{global}}$ then:
8	$d_{\min }$ outside tail distribution, classify as known class: $\widehat{y}\leftarrow \widehat{k}$.
9	else
10	$d_{\min }$ falls into the tail distribution, perform hypothesis testing:
11	//(a) Compute p-value:
12	$p-\mathrm{value}\leftarrow {\left(1+{\displaystyle \frac{\xi (d_{min}-{\omega }_{global})}{\sigma }}\right)}^{-1/\xi }$;
13	//(b) Compare with Significance Level:
14	if $p-\mathrm{value}<{\delta }_w$ then:
15	Low probability event occurs; reject null hypothesis:
16	classify as unknown: $\widehat{y}\leftarrow \text{‘}\mathrm{Unknown}’.$
17	else
18	Null hypothesis cannot be rejected:          classify as known class: $\widehat{y}\leftarrow \widehat{k}$.
19	end if
20	End if
21	Return $\widehat{y}$