This working paper develops a minimal structural framework—subsystem epistemics—to investigate the conditions under which observational closure can be consistently defined for an observer embedded within a physical system. The starting point is deliberately minimal. Two assumptions are adopted: (i) information consists in the registration of a difference between two events, and (ii) all observation is performed by subsystems subject to the same resource constraints as the systems they observe. Combined with the principle that logical operations are physical processes requiring finite resources and time, these assumptions are used to examine the structural compatibility between observational closure and continuous spacetime models. Three independent structural difficulties are identified for continuous spacetime: (1) indeterminacy in the completion of observational processes under arbitrarily divisible time, (2) limits on confirming invariance across uncountably extended domains using finite operations, and (3) the loss of informational uniqueness under arbitrarily fine spatial separation. These are formulated as structural tensions rather than impossibility claims. To address these tensions, the paper introduces a discrete minimal-step framework. The existence event unit (xent) is defined as the minimal unit of observational closure, and the Information-Spacetime Stepping Framework (ISSF) is proposed as a discrete background within which closure and information propagation are consistently defined. Within this setting, an informational uniqueness condition (IUP) is derived from closure constraints, and the TECUM equivalence (Triadic Equivalence under Closure of Unified Manifestation) is introduced as a structural characterisation of stable systems. A further development is the introduction of an information field density (ρᵢnfo), arising from a verification congestion mechanism. This quantity provides a unified structural interpretation of effective signal propagation, with potential connections to refractive behaviour in media, slow-light phenomena, and horizon effects. These connections are presented at varying levels of evidential strength and are explicitly open to empirical scrutiny. The framework does not claim to establish the necessity of spacetime discreteness as a final conclusion. Rather, it identifies a set of structural conditions under which minimal step models provide a natural and coherent resolution. Several testable predictions are proposed, including lattice-level anisotropy in cellular automaton simulations and quantitative relationships between information density and effective propagation speed. This work is intended as a conceptual and structural contribution at a pre-theoretical level. It does not presuppose quantum mechanics or general relativity, and instead seeks to clarify what spacetime must be like if embedded observation is to be physically realisable. Keywords: observational closure, discrete spacetime, information theory, embedded observers, structural realism, cellular automata, foundations of physics
Ruipeng Shi (Wed,) studied this question.