Artian Small-x Proton Beam Access Framework: Collinear Baseline, Finite-Window Shadow Kernel, and Full Camera Gate

Artian Small-\(x\) Proton Beam Access Framework Version: 3.1 Concept DOI: 10.5281/zenodo.20938370 Author: Ali Attar Website: quantumtraction.org This paper develops the QTT small-\(x\) proton beam-access programme as a three-layer public-PDF shadow framework: a source gluon rail, an Artian collinear-shadow baseline, and a finite-window public-PDF shadow kernel. The source rail remains the QTT proton-gluon row \[ g_p^{\rm QTT}(x,\mu_A) = \frac{16/31}{B(2-\lambda_A,7)} x^{-\lambda_A}(1-x)^6, \] with no empirical PDF, \(K\)-factor, measured cross-section, or fitted exponent allowed into the constructor. Version 3.1 first prints the Artian collinear-shadow baseline. The source gluon is passed through the zero-fit collinear projector \[ \Pi_{\rm col}[g](x) = \frac{f_g\,x^{-1}(1-x)^2g(x)} {\int_0^1du\,u\,u^{-1}(1-u)^2g(u)}, \] which gives \[ g_A^{\rm col}(x) = \frac{f_g}{B(1-\lambda_A,9)} x^{-(\lambda_A+1)}(1-x)^8. \] At the top-threshold row this yields \[ \mathcal L_{\tau,13}^{\rm col}=40.1858566635, \qquad \frac{\mathcal L_{\tau,13}^{\rm col}}{\mathcal L_{\tau,13}^{\rm NNPDF40}}-1 = -0.0551373020. \] The public energy-scaling row is nearly locked, \[ R_{14/13}^{\rm col}(M_t)=1.174126228, \qquad R_{14/13}^{\rm NNPDF40}(M_t)=1.174811743, \] but the collinear baseline is still amber because its maximum central residual over \(100\)--\(1000\) GeV is \(15.87\%\). Version 3.1 then keeps the finite-window Artian public-PDF shadow kernel from v3.0: \[ \Xi_A(M) = 32^{-2}\sqrt{\frac43}\, \tau^{-\left(1+\frac{1}{2\rho}\right)} \exp\!\left[-\frac{u}{64}-\frac{u^2}{5}\right], \qquad u=\ln\frac{M}{343.116\,{\rm GeV}}, \qquad \tau=\frac{M^2}{s}. \] The public-PDF shadow luminosity is \[ \mathcal L_{\tau}^{\rm Artian\,shadow}(M,s) = \Xi_A(M)\, \mathcal L_{\tau}^{\rm QTT}(M^2/s,\lambda_A). \] Against the NNPDF40 central \(\tau\)-luminosity comparator over the \(100\)--\(1000\) GeV mass ladder at \(\sqrt{s}=13\) TeV, the finite-window kernel gives \[ \max|\Delta_{\rm rel}| = 2.878485301\times10^{-3}, \qquad {\rm RMS}_{\log} = 1.952489542\times10^{-3}. \] At the top-threshold row, \[ \Xi_{\rm PDF}^{t}=3.026254923273525, \qquad \Xi_A^{t}=3.02760861938158, \qquad \Delta_{\rm rel}^{t}=4.4731727577\times10^{-4}. \] The interpretation is intentionally scoped. The collinear-shadow baseline is amber: it explains the leading public-collinear shift but does not close the full public-PDF object. The finite-window kernel is a green-candidate execution against the NNPDF40 central corridor. The universal public-PDF replacement remains yellow until independent CT/MSHT/NNPDF replica and covariance tests are passed without changing the source rail, the collinear projector, or the finite-window kernel. Main status labels: Sigma-NO-FREE-PDF-SOURCE-FIREWALL-CLOSED Sigma-ARTIAN-COLLINEAR-SHADOW-BASELINE-THEOREM-PRINTED Sigma-COLLINEAR-PUBLIC-PDF-BASELINE-AMBER Sigma-PUBLIC-PDF-MINIMAL-ARTIAN-SHADOW-KERNEL-PRINTED Sigma-NNPDF40-TAU-CENTRAL-CORRIDOR-GREEN-CANDIDATE Sigma-PDF-FAMILY-COVARIANCE-REPLICATION-PENDING Sigma-FULL-PDF-CAMERA-SOURCE-VECTOR-KERNEL-PENDING Related QTT anchors: Main book: Quantum Traction Theory, concept DOI 10.5281/zenodo.17527179 Toponium / top-threshold parent harness: 10.5281/zenodo.20123498 Strong-coupling source theorem: 10.5281/zenodo.20625550 Two-clock projection constant: 10.5281/zenodo.19979595 Included files: PDF paper, Version 3.1 LaTeX source Verification script JSON reproducibility certificate CSV row tables for the QTT source rail, collinear-shadow baseline, and public-PDF shadow control Render audit SHA-256 manifest