Newton's Constant Is Not Primitive in Quantum Traction Theory: Artian Angular Capacity, Universal Endurance Ceilings, and G = ℓ_A² c³ / ℏ Without Planck-Length Circularity
Year: 2026
Type: preprint
Abstract: Newton's Constant Is Not Primitive in Quantum Traction Theory Version: 4.0Concept DOI: 10.5281/zenodo.20057430Current public record: 10.5281/zenodo.20057431Author: Ali AttarWebsite: quantumtraction.org This paper gives the QTT endurance derivation of Newton's constant. The structural theorem is kept exactly scoped: \[ G_A=\frac{\ell_A^2c^3}{\hbar} =\frac{\hbar c^5}{E_\ast^2}. \] This does not claim to obtain the SI value of \(G\) from pure numbers alone. One dimensional Artian ruler \(\ell_A\) must be primitive or independently measured. The theorem says that once Artian Geometry supplies that ruler, Newton's constant is no longer an independent primitive. Version 4.0 adds the five-face Artian \(G\) ledger from the main book v10.01. The paper keeps a clean separation: Face 1 is the structural theorem of this paper, while Faces 2-5 are cross-sector convergence rows that test whether independent sectors read the same Artian capacity endpoint \(E_\ast\) without using observed \(G\) as a constructor. Five-face master equation: \[ \boxed{ \begin{gathered} \texttt{FIVE\_FACE\_ARTIAN\_G\_MASTER\_LEDGER}\\[0.35em] G_A^{({\rm end})} =\frac{\ell_A^2c^3}{\hbar} =\frac{\hbar c^5}{E_\ast^2}, \\[0.55em] m_0E_\ast=(2\pi)^5v_Q^2 \quad\Longrightarrow\quad G_A^{(\nu)} =\hbar c^5\left[\frac{m_0}{(2\pi)^5v_Q^2}\right]^2, \\[0.55em] U_{\rm cap}^{(1)}=\frac{\alpha_{\rm QTT}}{2}E_\ast \quad\Longrightarrow\quad G_A^{({\rm EM})} =\frac{\alpha_{\rm QTT}^{\,2}\hbar c^5} {4\left(U_{\rm cap}^{(1)}\right)^2}, \\[0.55em] v_{G_F}=\sqrt2\,\mathcal R_H^{\rm EW}q_HE_\ast \quad\Longrightarrow\quad G_A^{(H\to{\rm lab})} =2\sqrt2\,(\mathcal R_H^{\rm EW}q_H)^2G_F \frac{\hbar c^5}{(1\,{\rm GeV})^2}, \\[0.55em] m_t c^2=q_HR_tE_\ast \quad\Longrightarrow\quad G_A^{(t)} =\hbar c^5\left(\frac{q_HR_t}{m_tc^2}\right)^2 . \end{gathered} } \] The Higgs/Fermi face uses \[ \rho=2\pi\cos(\pi/8), \qquad q_H=2\exp\!\left[-4\pi^2-\frac{1}{8\rho^2}\right], \] and the finite electroweak readout gate \[ \mathcal R_H^{\rm EW} = \exp\!\left[ -\frac{\alpha_{\rm QTT}}{8\rho^2}\sqrt{6+\rho^{-2}} \right]. \] The raw scalar source gives \[ G_A^{(H,{\rm raw})} =6.67518877\times10^{-11}\ {\rm m^3\,kg^{-1}\,s^{-2}}, \qquad z_G=+5.93\sigma, \] while the legal \(H\to{\rm lab}\) readout gives \[ G_A^{(H\to{\rm lab})} =6.67430141\times10^{-11}\ {\rm m^3\,kg^{-1}\,s^{-2}}, \qquad z_G=+0.009\sigma. \] The top-unit MARIAM face uses \[ \ell_t=0,\qquad \widehat{\mathcal T}_t=1,\qquad m_tc^2=q_HR_tE_\ast, \] with \[ R_t=\exp\!\left[-\frac{\alpha_s^{\rm QTT}(m_H)}{4\pi}\right], \qquad \alpha_s^{\rm QTT}(m_H)=0.11289736198, \qquad R_t=0.99105614971. \] The central audit is \[ G_A^{(t)} =6.67413881\times10^{-11}\ {\rm m^3\,kg^{-1}\,s^{-2}}, \qquad \frac{G_A^{(t)}-G_{\rm CODATA}}{G_{\rm CODATA}} =-24.15\,{\rm ppm}, \] or \(-1.07\sigma\) on the CODATA \(G\) uncertainty. The inverse capacity lock asks for \[ m_{t,{\rm lock}}^{(G)} =172.5579163\,{\rm GeV}. \] The top row remains guarded by the declared top-mass convention: direct, event-template, pole, threshold, and \(\overline{\rm MS}\) masses are not the same readout. The no-smuggling firewall is printed explicitly: \[ \frac{\partial q_H}{\partial G_{\rm obs}} = \frac{\partial \mathcal R_H^{\rm EW}}{\partial G_{\rm obs}} = \frac{\partial G_F}{\partial G_{\rm obs}} =0, \] \[ \frac{\partial q_H}{\partial m_t^{\rm obs}} = \frac{\partial R_t}{\partial m_t^{\rm obs}} = \frac{\partial R_t}{\partial G_{\rm obs}} =0, \] and, for the full ledger, \[ D_{\rm obs} \left( G_A^{({\rm end})}, G_A^{(\nu)}, G_A^{({\rm EM})}, G_A^{(H\to{\rm lab})}, G_A^{(t)} \right)_{\rm src} =0. \] Plainly: the paper's theorem removes \(G\) as a primitive once the Artian ruler is admitted. The five-face ledger says that the same capacity endpoint is being read from several unrelated sectors without observed \(G\) being allowed to write the source equations. Main status labels: Σ-NEWTON-G-ENDURANCE-SOURCE-IDENTITY-CLOSED Σ-FIVE-FACE-ARTIAN-G-MASTER-LEDGER-PRINTED Σ-HIGGS-FERMI-G-FACE-GREEN-AUDIT Σ-G-FROM-TOP-UNIT-MARIAM-SOURCE-EQUATION-CLOSED Σ-TOP-MASS-SCHEME-GUARDRAIL-ACTIVE Σ-EM-CAPACITY-EDGE-NON-G-PENDING Σ-NEUTRINO-ABSOLUTE-METRE-ANCHOR-PENDING Related QTT anchors: Main book v10.01: 10.5281/zenodo.20394203 Artian A2 Endurance to Einstein-Field Dynamics: 10.5281/zenodo.20763263 Newton's Second Law / inertia companion paper: 10.5281/zenodo.20059780 Existing Newton/G public record: 10.5281/zenodo.20057431 Included files: PDF paper, Version 4.0 LaTeX source Numerical audit script for the five-face rows Render audit SHA-256 checksum file Release package zip
Author: Attar, Ali
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160424391