Algorithm 1 Offline Confidence-Gated Iterative Refinement

Require:  Training partition ${\mathcal{D}}_{\mathrm{train}}$, validation partition ${\mathcal{D}}_{\mathrm{val}}$; initial primary system ${\theta }_P$, verification system ${\theta }_V$; high-confidence threshold ${\tau }_h=0.92$; feedback scaling factor $\lambda$ (empirically determined on ${\mathcal{D}}_{\mathrm{val}}$); maximum iterations $T=4$; early stopping tolerance $\epsilon =0.001$ Ensure:  Refined parameters ${\theta }_P^{*}$, ${\theta }_V^{*}$  1:Pre-train ${\theta }_P$ on ${\mathcal{D}}_{\mathrm{train}}$ (Adam optimiser, cosine annealing, early stop on validation $F_1$)  2:Pre-train ${\theta }_V$ on ${\mathcal{D}}_{\mathrm{train}}$ (stratified 5-fold cross-validation)  3:for $t=1$ to T do  4:    Run fixed-weight inference with ${\theta }_P$ and ${\theta }_V$ over ${\mathcal{D}}_{\mathrm{val}}$; compute $S\left(x\right)$ via Equation (19) for each x  5:    Construct refinement pool (curriculum gate):          ${\mathcal{R}}_t\leftarrow \left\{x\in {\mathcal{D}}_{\mathrm{val}}:S\left(x\right)>{\tau }_h\right\}$▹ Equivalent to dual-agreement; see Equation (19) with $\beta =0.6$  6:    All cases with $S\left(x\right)\le {\tau }_h$ excluded from ${\mathcal{R}}_t$; disagreement cases routed for clinician review  7:    Compute TreeSHAP attributions over ${\mathcal{R}}_t$; aggregate and ${\ell }_1$-normalise per feature to obtain ${\Phi }_t\in {\mathbb{R}}^F$  8:    FSG modulation via Equation (20): $W_{g,t}^{\prime }\leftarrow W_g\odot (1+\lambda {\mathbf{1}}_H^{\top }\otimes {\Phi }_t)$; row-wise ${\ell }_2$-normalise  9:   Freeze Mamba SSM and Bi-LSTM backbone; fine-tune FSG parameters ($W_{g,t}^{\prime }$) and classification head of ${\theta }_P$ on ${\mathcal{D}}_{\mathrm{train}}\cup {\mathcal{R}}_t$ (ground-truth labels) 10:    Retrain ${\theta }_V$ on ${\mathcal{D}}_{\mathrm{train}}\cup {\mathcal{R}}_t$ (ground-truth labels) 11:    Evaluate ${\mathrm{AUC}}_t$ of ${\theta }_P$ on ${\mathcal{D}}_{\mathrm{val}}$ 12:    if $t>1$ and ${\mathrm{AUC}}_t-{\mathrm{AUC}}_{t-1}<\epsilon$ then 13:        break ▹ Early stopping: marginal AUC gain below convergence threshold 14:    end if 15:end for 16:return ${\theta }_P^{*}\leftarrow {\theta }_P^{\left(t\right)}$,${\theta }_V^{*}\leftarrow {\theta }_V^{\left(t\right)}$