object_distinction_forced

This module sits at the absolute floor of Recognition Science: T-2 to T-1, forcing distinction out of absolute nothing with no axioms. Absolute nothing is encoded as the empty type Empty (initial object: no inhabitants, unique map into every type). Naming Empty already populates Type, and Empty cannot equal the terminal type Unit, so a first type-level inequality appears.

From that seed the module derives three distinction layers: type-level ($\exists,\alpha,\beta,,\alpha\neq\beta$), propositional ($\exists,P,Q:\mathrm{Prop},,P\neq Q$), and object-level ($\exists,x,y,,x\neq y$). The present theorem is the object-level layer. Its concrete carrier is Bool; the two Boolean values are treated as the first realized bit that later floors consume.

The prior absolute-floor module had taken propositional distinguishability and a non-singleton universe as given. Here those preconditions are theorems, not hypotheses.

Pure term proof. The existential is inhabited by the 4-tuple $(\mathrm{Bool},,\mathrm{true},,\mathrm{false},,p)$ where $p:\mathrm{true}\neq\mathrm{false}$ is discharged by the decidable-equality tactic decide. No lemmas are invoked; the carrier and the two distinct points are written explicitly.

Feeds the field object_distinction of nothingToDistinctionCert, the theorem-backed certificate that packages universe population, type distinction, prop distinction, object distinction, and the Bool instance. That certificate is the public hand-off from T-2/T-1 into the Recognition forcing chain (T0–T8): eight-tick octave, $D=3$, $J$-uniqueness, and $\varphi$ as self-similar fixed point all sit above a floor that previously assumed distinction. Closing object distinction means the meta-language fact “there are two different things” is no longer an external hypothesis. The module stays strictly below the later spine and does not import it.