This paper proves that the Epistemic Support-Point Filter (ESPF) is the unique optimal recursive estimator within the class of epistemically admissible evidence-only filters. Where Bayesian filters minimize mean squared error and are driven toward an assumed truth, the ESPF minimizes maximum entropy and surfaces what has not been proven impossible -- a fundamentally different epistemic commitment with fundamentally different failure modes. Two results locate this theorem within the broader landscape of estimation theory. The first is a unification: the ESPF's optimality criterion is the log-geometric mean of the alpha-cut volume family in the Holder mean hierarchy. The Popperian minimax bound and the Kalman MMSE criterion occupy the p=+inf and p=0 positions on the same curve. Possibility and probability are not competing frameworks: they are the same ignorance functional evaluated under different alpha-cut geometries. The Kalman filter is the Gaussian specialization of the ESPF's optimality criterion, not a separate invention. The second result is a diagnostic: numerical validation over a 2-day, 877-step Smolyak Level-3 orbital tracking run shows that possibilistic stress manifests through necessity saturation and surprisal escalation rather than MVEE sign change -- a direct consequence of the Holder ordering, not an empirical observation. Three lemmas establish the result: the Possibilistic Entropy Lemma decomposes the ignorance functional; the Possibilistic Cramer-Rao Bound limits entropy reduction per measurement; the Evidence-Optimality Lemma proves minimum-q selection is the unique minimizer and that any rule incorporating prior possibility risks race-to-bottom bias.

翻译：本文证明了认知支持点滤波器（ESPF）是认知可接受的纯证据滤波器类中唯一的最优递归估计器。贝叶斯滤波器通过最小化均方误差来逼近假设的真相，而ESPF则通过最小化最大熵来揭示尚未被证明为不可能的状态——这是一种根本不同的认知承诺，具有根本不同的失效模式。两项研究结果将该定理置于更广泛的估计理论图景中。首先是统一性结果：ESPF的最优性准则对应于霍尔德均值体系中α截集体积族的对数几何平均。波普尔极小极大界与卡尔曼最小均方误差准则分别位于该曲线p=+∞和p=0的位置。可能性与概率并非竞争框架：它们是在不同α截集几何下评估的同一无知泛函。卡尔曼滤波器是ESPF最优性准则的高斯特例，而非独立发明。其次是诊断性结果：在为期2天、877步的Smolyak三级轨道跟踪数值验证中显示，可能性压力通过必要性饱和与惊异度上升（而非最小体积椭圆符号变化）显现——这是霍尔德序的直接推论，而非经验观察。三个引理支撑该结论：可能性熵引理分解了无知泛函；可能性克拉美-罗界限定了每次测量的熵减幅度；证据最优性引理证明最小q选择是唯一极小化解，且任何包含先验可能性的规则都可能引发逐底竞争偏差。