Corrected result
The kernel condition $\ker\Pi_{\mathrm{adm}}\subseteq\ker\Phi$ gives linear factorisation through the admissible quotient. It imposes no $\mathrm{SU}(2)$ equivariance by itself.
After supplying the conditional O23 carrier, admissible saturation $\operatorname{Im}\Pi_{\mathrm{adm}}=\mathsf{Ntrl}$ and parity transport, representation theory gives the canonical action $\rho:\mathfrak{su}(2)\to\operatorname{End}(V_\rho)$. The complex equivariant intertwiner space is one-dimensional; over the underlying real representations it is two-dimensional.
Open bridge. No non-zero $\mathfrak{su}(2)$-equivariant map $3_{\mathrm{ad}}\to2_{\mathrm{fund}}$ exists. O27 therefore does not provide the vector lift $\mathcal V_q\to V_\rho$ required by O26 Hypothesis 4.4, which remains open.
What version 2.0 corrects
- Parity is transported by an adjoint action, not by global negation; the relevant lift in $\mathrm{SU}(2)$ has order four although its adjoint action has order two.
- The norm condition is Hilbert–Schmidt on $\operatorname{End}(V_\rho)$ and is not established for the canonical map.
- The earlier target-exclusion and “quaternionic rigidity” claims are removed: conditions (a)–(c) do not impose full equivariance.
- The pair-observable corollary is conditional on the unproved norm condition.
Reference
Admissible Morphisms on the Weil Pair Sector: The su(2) Action on End(Vρ) and the Open Vector Lift.