Objectivity as an Information-Theoretic Ratchet: A Framework for Embedded Observers

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 \( K^* = \lceil 4 \log_2 L / H_{r2} \rceil \) is verified across 2D Ising, Potts, BEG, and Clifford MIPT systems, with exact Temperley-Lieb algebra decomposition of the orbit count verified to \( \leq 0.01 \) bits.