Artian's HVP Source-Access Reference Framework

Abstract

Which HVP object is the source, which one is the apparatus, and which one is only statistics? A resolved hadronic-vacuum-polarization test passes through several mathematically different layers before it becomes a laboratory verdict. This framework now types that full chain: \[ \mathcal S_{\rm src} \xrightarrow{\mathcal A_d^{\rm QTT}} \mathcal S_{{\rm acc},d} \xrightarrow{\mathcal C_d^{\rm phys}} \mathcal Y_d^{\rm prebin} \xrightarrow{\mathsf P_d} \mathbb R^{N_d} \xrightarrow{\Pi_d^\perp} \mathcal Q_d. \] Here \(\mathcal A_d^{\rm QTT}\) is the source-access word, \(\mathcal C_d^{\rm phys}\) is the calibrated physical camera, \(\mathsf P_d\) is finite binning, and \(\Pi_d^\perp\) removes only the declared statistical nuisance directions. The canonical Access-Law object is a different mathematical species: \[ M_d:\mathcal H_d\rightarrow\mathcal H_d, \qquad M_d^2=M_d=M_d^\dagger, \qquad \eta_d=\operatorname{Tr}(\rho_dM_d). \] A camera response or attenuation cannot be promoted into \(M_d\) by notation. For the frozen BaBar \(n_B=4\) access topology, \[ \lambda_4=e^{-4\chi_0}=0.9800147422281654, \] but \[ \lambda_4^2-\lambda_4 =-0.0195858472436279\neq0. \] The BaBar access factor is therefore non-idempotent and is not a projector. The paper also separates four uncertainty roles that must not be mixed: external camera calibration, profileable statistical nuisance, sealed finite model branches, and source uncertainty. When nuisance directions are marginalized rather than explicitly profiled, the typed covariance is \[ \Sigma_d^{\rm tot} =\Sigma_d^{\rm lab} +J_{C,d}\Sigma_{u,d}J_{C,d}^{\mathsf T} +U_dV_{\nu,d}U_d^{\mathsf T} +J_{{\rm src},d}\Sigma_{\rm src}J_{{\rm src},d}^{\mathsf T} +\Sigma_d^{\rm model}. \] The same uncertainty may not be both profiled and inserted into covariance, and no source or model covariance may be invented after reading the residual. At the BaBar public-row interface, the detector reconstruction has already been applied: \[ \mathcal C_{{\rm BaBar},{\rm public}}^{\rm phys}=I. \] This does not mean the experiment had no camera. It means that applying its acceptance, radiation, resolution, or unfolding response again would double count a completed reconstruction. The scientific tension remains sharply localized. In the 140-bin window \(0.600<\sqrt{s}<0.880\,{\rm GeV}\), the two frozen source executions give \[ z_{a_\mu}\in\{+1.361223,\,-0.593757\}, \] while the covariance-orthogonal lineshape gives \[ \chi^2_{\rm sh} \in\{57765.6144,\,85030.2611\}, \qquad \nu_{\rm sh}=139, \] against \[ \chi^2_{0.95}(139)=167.514304991. \] The integrated HVP direction can remain moderate while the resolved function beneath it fails decisively. The source remains frozen: \[ \frac{\delta R_{2\pi}^{\rm src,QTT}} {\delta\{\mathbf y_d,\Sigma_d^{\rm lab},\chi_d^2\}} =0. \] The typed-access theorem changes no V50 source value, covariance object, scientific hash, scalar pull, lineshape statistic, or status. It preserves the red BaBar full-covariance verdict and leaves one explicit open gate: constructing a genuine canonical HVP central projector from a declared state algebra. The package contains the 359-page framework, the complete executable history, the V50 independent verification passing 31/31 checks, and the V51 typed-access certificate passing 28/28 checks. Version: 51.0 Concept DOI: 10.5281/zenodo.20732034 Main book: Quantum Traction Theory: Main Book v10.01 Companion access theorem: Observation as Access in Quantum Traction Theory Website: quantumtraction.org