"R⁸: The Constitution & The Court — A Test‑First Hidden‑Sector EFT, with an Audit‑Grade Lithium Toy Trial"

# Abstract This addendum refines the \(R^8\) lithium/BBN transfer layer by isolating the precise handoff between the primitive cubic phase-clock window and applied BBN microphysics. Previous notes already introduced a branch-aware toy rate of the form\[\lambda_X(T)=A_0\,p_7(q(T))\,W_Q(T),\]so the present contribution is not a rebranding of that result. Instead, it replaces the constant toy dial \(A_0\) by a dimensionful microscopic rate,\[A_0\to \Gamma_{\rm micro}(T),\]and formulates the referee-safe transfer ansatz\[\lambda_X(T)=W_Q^{\rm BBN}(T)p_7(q_\star(T))\Gamma_{\rm micro}(T),\]with the more complete scattering expression\[\lambda_X(T)=W_Q^{\rm BBN}(T)n_X(T)\left\langle p_7(q(E))\sigma_X(E)v(E)\right\rangle_T.\]Here \(W_Q^{\rm BBN}(T)\) is the BBN-epoch primitive cubic branch-window probability, \(p_7\) is a declared multi-scale momentum gate, and \(\Gamma_{\rm micro}\) is the ungated dimensionful microscopic input unless the gate is explicitly absorbed into the cross section. The note records the existing toy calibration \(A_{\rm new}=0.0153452~{\rm s}^{-1}\), \(W_Q^\star=0.915736\), and \(A_0^\star=0.0167572~{\rm s}^{-1}\), derives ungated and already-gated cross-section targets at the BBN toy peak, and states the required guardrails for full physics: epoch-specific \(W_Q^{\rm BBN}(T)\), no double counting of the momentum gate, proper unit conversion, reaction stoichiometry, reverse reactions, thermal-history effects, and full light-element constraints beyond lithium. No full BBN solution or new nuclear-channel discovery is claimed.