A Parameter-Free Einstein–Hilbert Coefficient from a Sink-Current Endurance Ledger
Year: 2026
Type: preprint
Abstract: From endurance current to the Einstein--Hilbert coefficient Version: 1.2 Concept DOI: 10.5281/zenodo.20042843 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 This paper separates the QTT-native gravity step from the continuum-geometric step. The native object is the A2 endurance current \(J_{\mathrm{end}}\), a sink-current ledger for how mass consumes space-quantum renewal. The primitive capacity units are \[ \widetilde t={\widetilde\ell\over c}, \qquad \widetilde m={\hbar\over c\widetilde\ell}, \qquad V_{\mathrm{SQ}}=4\pi\widetilde\ell^3, \qquad V_4=4\pi\widetilde\ell^4. \] The endurance continuity law is \[ \nabla\!\cdot J_{\mathrm{end}} = -{V_{\mathrm{SQ}}\over \widetilde m\,\widetilde t}\rho. \] The no-knob weak-field constitutive projection is \[ \mathbf g_N={c\over\widetilde\ell}J_{\mathrm{end}}. \] Together they give the Newton--Poisson coefficient \[ \nabla\!\cdot\mathbf g_N=-4\pi G\rho, \qquad G={\widetilde\ell^2c^3\over\hbar}. \] The continuum layer is then stated separately. In a regular coarse-grained Einstein-gauge limit, causal order fixes the conformal Lorentzian metric, the QTT four-volume count fixes the conformal factor, and the leading local second-order covariant infrared action is \[ S_{\mathrm{EH}} = \lambda\int d^4x\sqrt{-g}\,R, \qquad \lambda={c^3\over16\pi G}={\hbar\over16\pi\widetilde\ell^2}. \] The paper's useful distinction is this: \[ \boxed{\text{QTT fixes }G\text{ by endurance counting; Einstein--Hilbert is the infrared continuum completion.}} \] The result is therefore an infrared Einstein-gauge theorem, not a claim that the absolute QTT clock, creation sector, or higher-curvature capacity corrections disappear outside that regime. What to audit in the paper: the A2 sink-current continuity equation; the no-knob projection \(\mathbf g_N=(c/\widetilde\ell)J_{\mathrm{end}}\); the derived coupling \(G=\widetilde\ell^2c^3/\hbar\); the Lovelock/infrared continuum bridge to \(S_{\mathrm{EH}}\); the one-ruler falsifier: the same \(\widetilde\ell\) must stay consistent across the QTT sectors that use it.
Author: Attar, Ali
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160294319