Sequential Detection of Non-Classical Coordination in the Limited Communication Regime: Orthogonal Divergence and the Internal Observer Detection Problem

Paper 3 in the Limited Communication series. The first two papers asked what an outside observer sees when quantum coordination affects their environment. This paper asks the opposite question: what does the coordinating party themselves see? If a physical mechanism exists that shifts the measurement statistics of an entangled partner — even slightly — the partner can detect that shift over time using sequential statistical testing, without any classical communication channel. This paper develops the complete detection architecture: how to detect the shift, how long it takes, how confident you can be, and how to verify pre-agreed signals using a codebook established before separation. The paper does not claim this capability exists today. It derives what follows if it becomes possible, using the mathematical framework established in Papers 1 and 2. The theory is built before the technology, so the formal tools are ready if the physics arrives. Technically: derives the detection-theoretic consequences when a coordinating party observes their own marginal statistics under a hypothesized non-linear bias mechanism. Develops sequential hypothesis testing (SPRT) architecture for detecting orthogonal divergence — environmental divergence at the entangled partner's location — without any classical communication channel. Proves the detection protocol saturates the Shannon capacity bound. Positions the conditional within a trilemma relative to Gisin's (1990) theorem on non-linear signaling. Extends the LCT framework inward, from the excluded observer to the coordinating party.