This paper provides an independent axiomatic mechanism definition thatfixes the generative conditions under which a visibility-scoring structure emerges indigitally mediated socio-technical environments. It is not a sequel, follow-up, or extensionof the AI-Scored Society; rather, it specifies a Root Mechanism Layer thatmakes the emergence of an AI-scored visibility regime a conditional structural outcomeunder explicitly stated constraints. The AI-Scored Society identifies a visibilityredistribution structure in which conclusions without process reallocate social visibility. The present work complements that descriptive target class by formalising theminimal state space, symbol system, and axioms required to state bounded emergenceconditions.We declare a compact state vector Omega(t) = (E(t), S(t),R(t), V (t), τ, I), where E(t)denotes mediated environment intensity, S(t) scoring signal intensity, R(t) recommendation-as-control input, V (t) the visibility distribution, τ a strictly positive variabledelay, and I an irreversibility threshold. An axiomatic set constrains the system as:inference-mediated allocation (Decision Substrate), recursive coupling of visibility andsignal production (Recursive Mediation), asynchronous variable-delay coupling (VariableDelay), injected control inputs (Control Signal Injection), and threshold-inducednon-reversibility (Irreversibility Threshold). A lightweight difference mechanism linksa feasibility gap to control adjustment, yielding a minimal operational bridge fromaxioms to an emergence theorem.Under these axioms and within an explicit scope boundary (digitally mediated environments;excluding biological evolution and direct physical control systems), we statea conditional theorem: a non-degenerate dependency of visibility allocation on delayedscoring signals and injected control inputs necessarily emerges, and stabilises whenthe irreversibility threshold is crossed. The resulting system class is identified as anasynchronous recursive variable-delay socio-technical control environment.
Kawazoe Tsutomu (Tue,) studied this question.