Relational Boundaries and Awareness Localization: Robustness, Composition, and Identification Limits

How robust are the boundaries used to distinguish a relational system, and what can its observable behavior establish about its internal organization or awareness? This theoretical paper shows that boundaries defined by exact information-dependence rules can change discontinuously under arbitrarily small perturbations of a stochastic process. A finite masking construction demonstrates the problem: a tiny new signal can remove a projected relational edge even while substantial joint information and a scheduled return remain. The paper develops a continuous reconstruction-based diagnostic using directed statistical deficiency. It asks whether one source-independent stochastic decoder can reproduce the complete family of response laws after part of a joint observation is removed. An exact optimization characterizes the information lost in the masking construction. The analysis distinguishes joint information, physically executable return, and resistance to resource-constrained cut simulation. It establishes conditions under which effective relational interfaces can replace lower-level systems in larger causal contexts, including the need to preserve the relevant comparison class when transferring approximate guarantees. Finally, the paper separates operational identification from phenomenal interpretation. Exact experimental laws determine an attribute only when it is constant across operationally equivalent realizations. This does not automatically provide finite-data certification, determine source ontology, or establish the presence of phenomenal consciousness. The results are applied to SPC-2, the candidate psychophysical constitution developed in Shadow Theory and Consciousness. They identify a robustness vulnerability in its original candidate construction and constrain possible successor rules without deriving a unique replacement admission law. This is a mathematical and conceptual preprint. It contains analytic arguments and illustrative finite calculations; it reports no empirical validation of consciousness. Independent external mathematical review remains outstanding. Author: Jeremy Rodgers, Independent ResearcherWebsite: https://everythingequation.comPaper 2 DOI: 10.5281/zenodo.23075822 Related works:Shadow Theory and Consciousness, Version 2: https://doi.org/10.5281/zenodo.22853774Paper 3 — Learning Effective Interfaces from Opaque Stochastic Systems: Capacity, Selection, and Validation Limits: https://doi.org/10.5281/zenodo.23075824Paper 4 — Identifying Binary Realizations from Intervention Laws: Certificates, Recoding Obstructions, and a Bounded SPC-2/IIT Comparison: https://doi.org/10.5281/zenodo.23075828