This framework demonstrates the relationship between information recovery and objectivity for embedded observers, suggesting implications for understanding complex systems.
Inter-subjective objectivity for embedded observers is modeled with recursive constraints and local projections. The order parameter \( O_t \) measures information jointly recoverable from cumulative evidence, and for any finite constraint model its mean is non-decreasing by the data-processing inequality. Enumeration of all 256 elementary cellular automata yields a tripartite observer-threshold law. Going beyond cellular automata, a birthday collision bound \( K^* = 4 log_2 L / Hᵣ₂ \) is verified across 2D Ising, Potts, BEG, and Clifford MIPT systems, with exact Temperley-Lieb algebra decomposition of the orbit count verified to \( ≤ 0.01 \) bits.
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Xinlei Wang (2026) studied this question.
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