Meaning
The Measurement Markov Interface exports a certified relaxation system in a form that downstream measurement research can use.
Its data are an algebra M, state φ and Hilbert realization, Dirichlet form, generator L, semigroup T_t, fixed-point algebra N_fix, equilibrium map E_fix, and rate κ. The central estimate is ‖T_tx−E_fix x‖₂,φ≤e^(−κt)‖x−E_fix x‖₂,φ on the stated domain.
Example (illustrative)
For the symmetric two-state chain, E_fix replaces both values by their mean and κ=2 controls decay of their difference. This supplies an explicit equilibrium and relaxation example.
Scope and limits
The word “measurement” identifies the intended downstream interface. GAT VIII does not thereby identify the fixed-point algebra with experimental records or derive an empirical probability rule.
Source
GAT VIII — Indexed Admissible Distributors and Selected Cofinal Čech Transport in Semisimple Yang–Mills Theory. GAT VIII, Equation 15.10.