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 GEH 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. GEH: the fixed Einstein-Hilbert coefficient in the GR-exact landed equation. 2. Tₗoc: the local source sector containing local excitations, while excluding the strictly spacetime-constant vacuum mode. 3. deltageo: the bounded geometry-response interface used by downstream bounded-transient modules. This is not a running GEH and is not derived or selected in this record. 4. GₑffP: 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 MEH. The paper therefore defines the inverse target that any future hard denominator theorem must reproduce: MEH, target² = (1 + Deltaₗocal) / (8 pi Gₑffˡocal). 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 MEH, does not claim that bounded geometry is observed or selected here, and does not identify deltageo with running GEH. 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