R⁸ Lorentz-Consistency Module: A Technical Specification for Leaf–Bank–Projector EFTs / Clause-U (Luminal Island), Sequester No-Signaling, Projector Bundle Hygiene, and Governance Constraints

## Abstract (Zenodo Companion Note) This note is a **technical specification** for Lorentz and causality compliance in the R⁸ framework, titled *Lorentz-Consistency Module (R⁸): Leaf–Bank–Projector–Governance*. Its purpose is to provide a reviewer-grade, unambiguous **contract** for what the IR theory allows and forbids, and how “bank”, “projector”, discrete governance, and sequester can coexist without introducing preferred frames, superluminal signaling, or tensor-speed anomalies. We adopt a single physical spacetime (“leaf”) \((M,g_{\mu\nu})\) and treat the bank as an **internal bosonic sector** (e.g., scalar fields \(\phi^I(x)\)) living on the same Lorentzian manifold. Lorentz invariance in the bank therefore means **Lorentz-covariant operators on the leaf**, not a second spacetime with an independent lightcone. Discrete governance (e.g., \(\mathbb{Z}_k\) via a BF-type topological sector) acts on **internal channel structure** and can generate selection rules (“teeth”, such as \(Z_{48}\to Z_{24}\) visibility) without breaking leaf Lorentz symmetry. Clause-U is formalized as an **admissible operator locus** (“luminal island”): minimal Einstein–Hilbert gravity plus canonical/minimally coupled scalars, together with restricted portal terms. We list **hard exclusions** (e.g., Horndeski-type curvature–derivative operators that shift \(c_T\), parity-odd gravitational Chern–Simons terms, and IR preferred-frame/aether structures) and provide a PASS/FAIL gate checklist aligned with luminality, WEP/PPN safety, and stability (no ghosts). The vacuum-energy sequester is clarified as a **regulated global constraint** that fixes a spacetime-constant integration variable (DC filter) while preserving dynamical AC components—**not** a dynamically updated nonlocal signaling channel. We also disambiguate projector-bundle notation: \(P(x)\) is treated as a \(4\times N\) partial isometry with \(PP^\top=I_4\), while \(\Pi_g=P^\top P\) is the associated idempotent \(N\times N\) projector onto the selected 4D subspace. The induced connection \(\omega_\mu = P\mathcal{A}_\mu P^\top + P\partial_\mu P^\top\) is interpreted as a channel-holonomy structure compatible with discrete governance and projector dynamics; it is not assumed to be a new propagating gauge field in the IR. Finally, we include “governor” certification metrics (idempotency, jitter, locality/commutator proxies) that operationalize projector hygiene. This document **does not** claim an observational proof of emergent gravity, nor does it derive its content from EHT analyses. Instead, it provides the structure-level consistency conditions that any microphysical completion and any data-driven holonomy/“lattice” phenomenology must respect.