This paper develops a finite certificate calculus for ambient release systems, staged probabilistic environments in which a protected coordinate is not observed directly but can remain statistically readable through visible roles, timing, repeated movement, bounded attention, linked rooms, and post-release state. The security notion, choric masking, requires the trace law induced by a protected locus to lie inside or near the convex hull of admissible cover traces under the tests available to a specified audience. For finite horizons, trace laws form polytopes, audiences induce measurement operators, and masking becomes intersection in the projected measurement space. Exposure is certified by separating hyperplanes, kernel obstructions, hypothesis-testing bounds, Fano-type localization lower bounds, and support separation in downstream rooms. The calculus distinguishes trace residue from carrier localization, full-trace exposure from attention-filtered exposure, first-room masking from delayed post-release exposure, and unresolved system pressure from carrier hazard. It proves measurement-polytope equivalence for exact and approximate masks, dual separation certificates, data-processing laws for attention lenses, aperture identities for gaze-thinned observation, lower bounds for mandatory unique gestures, composition rules for linked releases, and a repeated-room debt theorem showing how unresolved pressure can broaden selection and shift cost onto cover populations without localizing the source. The result is a finite, checkable language for auditing privacy, unlinkability, side-channel leakage, and accountability in public-facing release systems.

翻译：本文为环境释放系统（即分阶段概率环境）开发了一种有限证书演算。在该系统中，受保护坐标虽非直接可观测，但可通过可见角色、时序、重复移动、有界注意力、关联房间及释放后状态保持统计可读性。安全概念“时间遮蔽”要求：受保护位点诱导的迹分布律，应位于或接近指定受众可用测试下所允许覆盖迹的凸包之内。对于有限时域，迹分布律构成多面体，受众诱导测量算子，而遮蔽转化为投影测量空间中的交集。暴露通过分离超平面、核障碍、假设检验界、Fano型定位下界及下游房间中的支持分离进行认证。该演算区分了迹残差与载体定位、全迹暴露与注意力过滤暴露、首房间遮蔽与延迟释放后暴露，以及未解系统压力与载体风险。它证明了精确遮蔽与近似遮蔽的测量-多面体等价性、对偶分离证书、注意力透镜的数据处理定律、凝视稀释观测的孔径恒等式、强制唯一手势的下界、关联释放的组合规则，以及重复房间债务定理——该定理表明未解压力如何扩大选择范围并将成本转移至覆盖群体而不定位源头。最终成果是一种用于审计公开释放系统中隐私、不可链接性、侧信道泄露及可问责性的有限可验证语言。