Gravity in GCV: Four-Layer Role Map, Einstein-Hilbert Coupling, and the Denominator Target: fixed GR-exact coefficient, local sources, bounded-geometry interface, probe-effective gravity, and denominator-open closeout

Version v1.0.0. Technical pre-paper / timestamp record. This record fixes the gravity-role map used in the Gauged Constant Vacuum-Mode (GCV) framework. It clarifies how the gravitational coefficient in the GR-exact local equation should be distinguished from local sources, bounded geometry-response language, and probe-effective gravity reconstructed by observations. The standard GCV local equation may continue to be written with the usual gravitational coefficient G. In this record the same Einstein-Hilbert coefficient is denoted G_EH when it must be separated from downstream effective quantities. This notation is not a new gravity law, not a new Governance gate, not a branch label, and not a running Newton constant. The timestamped four-layer map is: 1. G_EH: the fixed Einstein-Hilbert coefficient in the GR-exact landed equation. 2. T_loc: the local source sector containing local excitations, while excluding the strictly spacetime-constant vacuum mode. 3. delta_geo: the bounded geometry-response interface used by downstream bounded-transient modules. This is not a running G_EH and is not derived or selected in this record. 4. G_eff^P: probe-effective gravity in a channel P, such as growth, lensing, or local reconstruction. This is not a new fundamental coupling. The record also states the denominator-open closeout. The current GCV / Governance / UV stack defines the GR-exact Einstein-Hilbert coefficient, but does not yet source-derive the absolute denominator M_EH. The paper therefore defines the inverse target that any future hard denominator theorem must reproduce: M_EH,target^2 = (1 + Delta_local) / (8 pi G_eff^local). This relation is a target condition, not a derivation of Newton’s constant. Claim boundary: this record does not modify the main GCV Governance/Lambda papers, does not claim that GCV currently derives Newton’s constant, does not claim that UV v1.2.0 derives M_EH, does not claim that bounded geometry is observed or selected here, and does not identify delta_geo with running G_EH. The package includes the rendered PDF, LaTeX source, citation metadata, manifest and checksum files, supplementary CSV audit ledgers, a numerical inverse-target table, constants used in the numerical illustration, and a small Python script that regenerates the inverse-target table. The PDF carries the scientific claim; the CSV files are machine-readable audit supplements. homepage: https://johansson.digital