# Overview and publication identity

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

 Jeremy Rodgers  
 Independent Researcher  
 Website: [everythingequation.com](https://www.everythingequation.com)  
 DOI: [10.5281/zenodo.23075822](https://doi.org/10.5281/zenodo.23075822)

 29 September 2026  
 Preprint v1.0



 

**Abstract.**

Discrete rules that individuate relational or joint-dependence boundaries can change discontinuously under arbitrarily small perturbations of an underlying stochastic process. We exhibit this failure exactly in a finite joint-output model, derive a continuous reconstruction-based diagnostic using directed statistical deficiency, and determine when the resulting effective relational descriptions compose under causal and resource constraints. We then apply these results to the SPC-2 localization constitution as a motivating case. In the masking family, an arbitrarily small singleton effect deletes a projected joint-dependence edge while substantial joint information and the contrast of a fixed return schedule survive. The exact deficiency optimum quantifies what is lost by deleting part of the observation and is invariant under common-conditional padding. We separate joint information, executable native return, and resistance to resource-constrained cut simulation; the resulting schedule-indexed candidate families need not be partitions. For finite marked stochastic instruments, strong quotients admit substitution in matching causal contexts and minimization-compatible composition, while transfer of cut radii additionally requires control of the permitted simulator-law families. Finally, an attribute is identifiable from exact complete experiment laws precisely when it factors through their operational quotient. Functional premises leaving a local phenomenal predicate unconstrained do not determine it; SPC-2 supplies an explicit connecting premise. The results identify a robustness vulnerability and constrain successor doctrines without deriving a unique admission law, validating phenomenal presence, or identifying source ontology from records alone. 

 **Keywords:** statistical deficiency; joint dependence; causal interfaces; strong lumpability; operational identifiability; awareness localization.