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Canonical correction · 2026-07-30
The earlier single-value radix exchange claim is superseded. For even base $b$, modular negation $N_b(k)=-k\pmod b$ fixes the endpoint pair $\{0,b/2\}$, while half-cycle translation $H_b(k)=k+b/2\pmod b$ exchanges it.
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$$ N_b^2=H_b^2=I,\qquad N_bH_b=H_bN_b. $$
$$ \operatorname{Fix}(N_b)=\{0,b/2\},\qquad D_bN_bE_b=I_2. $$
$$ H_bE_b=E_bJ,\qquad D_bH_bE_b=J. $$
Thus reflection and exchange are distinct commuting involutions, generating
$$ \{I,N_b,H_b,N_bH_b\}\cong C_2\times C_2. $$
DH-C01 → DH-J-01 as an alias/deduplication edge, not two independent citizens.