baseState
plain-language theorem explainer
The base state for the obstruction counterexample is the false element in the Boolean state space of the alternating framework. Researchers checking the T5 to T6 bridge would cite this definition to build an explicit finite model whose orbit under negation alternates between readout values 1 and 2. The assignment is direct and supplies the starting point for showing that ClosedObservableFramework alone fails to enforce self-similar ratios or additive posting on levels.
Claim. In the closed observable framework with Boolean carrier set, negation dynamics, and readout sending false to 1 and true to 2, the base state is the element false.
background
The module exhibits an obstruction: ClosedObservableFramework is too weak to derive ratio self-similarity or additive posting for orbit levels k maps to r(T^[k] baseState). It supplies a finite counterexample whose states lie in Bool, dynamics is logical negation, and readout alternates between the values 1 and 2. The boolFramework instance is constructed exactly as states in Bool, T as not, r as the map sending false to 1 and true to 2. This concrete setup is the local theoretical setting for the honesty check on the T5 to T6 bridge.
proof idea
Direct definition that assigns the false Boolean value as the initial state for the obstruction orbit.
why it matters
This definition supplies the concrete starting state for the orbit levels used to prove that ClosedObservableFramework does not force the fields of RealizedHierarchy. It is referenced in the downstream results that establish failure of ratio self-similarity and additive posting. The construction fills the honesty check for the T5 uniqueness to T6 self-similar fixed point step in the forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.