configDim

Module GapDerivation closes boundary item B-22: the coherence-energy exponent equals the configuration dimension of a recognition event. A recognition event is assigned $D$ spatial degrees of freedom (forced by T8), one temporal degree of freedom (tick advance, T2), and one balance degree of freedom (ledger neutrality $J(x)=J(x^{-1})$, T3). The local spatial dimension is fixed as the constant $D := 3$.

Coherence energy is charged at $\varphi^{-1}$ per independent degree of freedom, so $E_{\mathrm{coh}} = \varphi^{-(D+2)}$. At $D=3$ this is $\varphi^{-5}$, matching the RS-native constant. The same $D+2$ factor appears in the gap product $D^2(D+2)$ that yields 45 at $D=3$, and in cosmology as the configuration factor in the baryon-rung decomposition of the CMB first peak.

Pure definition: the map sends any natural $d$ to $d+2$. No lemmas, no tactics. Downstream results specialize at the forced spatial dimension $D=3$ (via configDim_at_D3) or keep $d$ symbolic in gap and $\eta_B$ factorizations.

This is the B-22 count that makes $E_{\mathrm{coh}}=\varphi^{-5}$ a consequence of $D=3$ alone, rather than an independent input. It feeds configDim_at_D3, Constants_E_coh_eq_configDim, and the gap identity $D^2(D+2)=45$ at $D=3$. Downstream cosmology reuses the same integer: CMB certification decomposes the first peak as baryonRung × configDim (=220), and the exact $\eta_B$ rung derivation factors through parityCount($d$) × configDim($d$). In the forcing chain it sits between T2/T3 (temporal and balance axes) and T8 ($D=3$), and supplies the $+2$ in the exponent that links the eight-tick octave and $\hbar=\varphi^{-5}$.