target_D3

The public spine packages Recognition Science forcing as named campaign targets. One target is spatial dimension three (T8): nontrivial linking is detectable only at $D=3$. An Alexander linking bridge is the content-typed witness of that forcing; the target statement is simply that this type is inhabited. The statement is kept as a Prop-valued def so it cannot be discharged by a free-Prop cheat.

Historically the spine used an axiom linking_requires_D3. This module replaces that axiom with topology. Upstream, arc-complement acyclicity (Hatcher 2B.1, arc case) says every topological embedding of the unit interval into $S^D$ has $H_1$-acyclic complement, in every dimension $D$. The assembly lemma reduces the campaign target to that frontier: if arc complements are acyclic for all $D\ge 2$ with $D\ne 3$, the bridge is inhabited.

Constants modules already fix $D:=3$ as the forced spatial dimension; the present result is the topological justification that lands on the public spine.

Term-mode one-liner. Apply the assembly theorem that, given arc-complement acyclicity for every $D$ with $2\le D$ and $D\ne 3$, inhabits the Alexander linking bridge (via an intermediate lemma converting arc-acyclicity into $D=3$ forcing). Discharge the hypothesis by a lambda that ignores the numeric side conditions and invokes the unconditional arc-complement acyclicity theorem in every dimension. No further case splits or constructions appear at this layer.

Closes campaign P-d3link's main $D=3$ target on the public spine (2026-07-18), replacing the DimensionForcing axiom with a real topological construction. Downstream, any inhabited bridge yields the forcing law: if $D$ detects nontrivial linking then $D=3$. That law feeds the public spine certificate, which bundles forced tower, continuum purchase, cost selection, $\phi$ from iota, and circle $H_1$ into one cert.

Framework landmark: T8 ($D=3$ spatial dimensions) in the unified forcing chain. Adjacent on the same spine is T7 (eight-tick octave, period $2^3$); the cube-period bound is the related counting argument, though it does not itself depend on the linking bridge. With this target closed, the public spine no longer carries an open linking axiom for dimension forcing.