ABSTRACT This paper presents a comprehensive interpretation of the _Algorithmic Response (AR)_ formula and applies it to planetary science as a predictive framework for the occurrence and stratification of standard planetary substances (water, ice, methane, nitrogen, ammonia mixtures, metallic hydrogen, etc.). It is a direct continuation and mathematical elaboration of my previous work (HSH Series Paper No. 45: “Life is not Memory but Algorithmic Response: On New Elements and the Origin of Life via Particle–Environment–Algorithm Interaction”). While all conceptual ideas of the AR formula are authored by SEOKHOUN HONG , the detailed mathematical construction and explicit formulation were generated in collaboration with GPT-5 . This explicit acknowledgement is crucial: the mathematics is co-produced with GPT-5, while the physical interpretation, structural framework, and theoretical originality are mine.

This paper extends the concept of “quantum remembered response,” previously introduced in an FQXi essay, into a more rigorous scientific definition: _Algorithmic Response (AR)_. AR is defined as a probabilistic policy that outputs the distribution of possible reaction channels given an internal state and environment. With this framework, we unify the explanation of (i) Earth’s water oceans, (ii) Titan’s methane seas, and (iii) the non-persistence of water on Mars, as well as propose a predictive approach for the synthesis of new elements and a redefinition of the origin of life as the accumulation of algorithmic responses. Life is not memory in the anthropocentric sense but the structural evolution of algorithmic responses accumulated in particle–environment interactions.