We introduce PALACE (Persistence Adaptive-Landmark Analytic Classification Engine), the data-adaptive companion to PLACE, paying a small cross-validation tier on three knobs (budget, radii, bandwidth; $\leq 5$ choices each). A cover-theoretic core (Lebesgue-number criterion on the landmark cover) yields four closed-form guarantees. (i) A structural lower distortion bound $λ(τ;ν)$ on $\mathcal{D}_n$ under cross-diagram non-interference, with a $(D/L)^2$ budget reduction over the uniform grid when diagrams concentrate. (ii) Equal weights $w_k = K^{-1/2}$ maximizing $λ$, and farthest-point-sampling positions $2$-approximating the optimal $k$-center covering radius; both derived from training labels alone, no gradient training. (iii) A kernel-RKHS classification rate $O((k-1)\sqrt{K}/(γ\sqrt{m_{\min}}))$ with binary necessity threshold $m = Ω(\sqrt K/γ)$ from a matching Le Cam lower bound, and a closed-form filtration-selection rule. The kernel-Mahalanobis margin $\hatρ_{\mathrm{Mah}}$ is the strongest closed-form ranker across the chemical-graph pool (mean Spearman $ρ\approx +0.60$); the isotropic surrogate $\hatγ/\sqrt{K}$ admits a selection-consistency rate, and $\widehatλ$ from (i) provides an independent data-level signal (positive on COX2 and PTC). (iv) A per-prediction certificate, in non-asymptotic Pinelis and asymptotic Gaussian forms, with no calibration split. Empirically, PALACE is the strongest closed-form diagram-based method on Orbit5k ($91.3 \pm 1.0\%$, matching Persformer), leads every diagram-based competitor on COX2 and MUTAG, and is competitive on DHFR (within 1 pp of ECP). At $8\times$ domain inflation, adaptive placement maintains $94\%$ while the uniform grid collapses to chance ($25\%$ on 4-class data).

翻译：我们提出PALACE（持久性自适应界标解析分类引擎），它是PLACE的数据自适应版本，在三个参数（预算、半径、带宽；每个参数不超过5个选择）上引入一个小的交叉验证层。基于覆盖理论的核（界标覆盖上的勒贝格数准则）产生四个闭式保证：（i）在交叉图不干扰条件下，对于$\mathcal{D}_n$的结构性下界失真界限$λ(τ;ν)$，当图集中时，与均匀网格相比实现$(D/L)^2$的预算缩减。（ii）等权重$w_k = K^{-1/2}$最大化$λ$，最远点采样位置2-近似最优$k$-中心覆盖半径；两者仅从训练标签推导，无需梯度训练。（iii）核-RKHS分类速率$O((k-1)\sqrt{K}/(γ\sqrt{m_{\min}}))$，结合来自匹配Le Cam下界的二元必要性阈值$m = Ω(\sqrt K/γ)$，以及闭式过滤选择规则。核-马氏距离边际$\hatρ_{\mathrm{Mah}}$是化学图池中最强的闭式排序器（平均斯皮尔曼$ρ\approx +0.60$）；各向同性替代$\hatγ/\sqrt{K}$具有选择一致性速率，来自(i)的$\widehatλ$提供独立的数据级信号（在COX2和PTC上为正）。（iv）每个预测的认证，采用非渐近Pinelis形式和渐近高斯形式，无需校准分割。实验表明，PALACE是Orbit5k上最强的闭式图基方法（$91.3 \pm 1.0\%$，与Persformer持平），在COX2和MUTAG上领先所有图基竞争者，在DHFR上具有竞争力（与ECP相差1个百分点）。在$8\times$域膨胀下，自适应布局保持$94\%$的准确率，而均匀网格退化至随机水平（4类数据上为$25\%$）。