Fourth-Face Talbot-Lau Completed-Event Preregistration: An Activation-Gated Blind Test of A7U Matter-Wave Transport

Abstract

Can a finite Talbot chamber produce a nonconstant visibility shape after the ordinary interferometer kernel is frozen? \[ \boxed{ \begin{aligned} H_0:&\ \mathbf y_\perp=0,\\ H_{\mathrm{A7U}}:&\ \mathbf y_\perp=P_{\mathrm{prof}}\mathbf g^{\mathrm{phys}},\\ g_r^{\mathrm{phys}}=&\ \log\left|\frac{\int_{\Delta v_r}W_r(v)B_1^{\mathrm{QM/env}}(v)F_1^{\mathrm{A7U}}(v)\,dv}{\int_{\Delta v_r}W_r(v)B_1^{\mathrm{QM/env}}(v)\,dv}\right|,\\ &\ \frac{\partial\mathbf g^{\mathrm{phys}}}{\partial\mathbf y}=0. \end{aligned}} \] Version: 1.2 State: Stage-0 sealed; physical target activation pending; observation pending Concept DOI: 10.5281/zenodo.22010227 Author: Ali Attar, ORCID 0009-0008-9931-2691 Version note: v1.2 is an append-only source-projector-camera scope upgrade. The historical v1.0.1 branch, source equations, seven-bin vector, thresholds, PDF hash, and protocol-seal hash remain preserved. The v1.1 calibration-orthogonality gate also remains unchanged. The new outer wrapper separates the sealed A7U source-harmonic verdict from any stronger interpretation as a measurement of the central Access-Law projector weight. This preregistration asks for a seven-bin, first-harmonic matter-wave shape, not a constant loss of fringe contrast. The source branch is fixed before observation, but the final laboratory prediction is legal only after the ordinary complex Talbot kernel, event weights, operating point, calibration uncertainty object, physics-generated tangent basis, covariance, extraction operator, and the apparatus proof of kappa = 1 are independently frozen. The finite source law is \[ \Delta_n(v)=\left\|n^2\frac{hL}{d^2mv}\right\|_{\mathbb Z},\qquad N_{\Gamma,n}=\left\lceil\Delta_n^{-1}\right\rceil,\qquad F_n^{\mathrm{A7U}}=\sqrt{1-2\kappa_n\frac{2}{N_{\Gamma,n}}\left(1-\frac{1}{N_{\Gamma,n}}\right)}. \] The release seals a high-precision source-only feasibility vector, but proves why that vector cannot be substituted for the physical instrument prediction. Complex Talbot coefficients must be combined inside each velocity-bin integral before taking their modulus. This is the central wrong-falsification firewall: source-only forecast ≠ physical instrument prediction ≠ observation. A central Access-Law interpretation requires the additional prospectively frozen certificate \[ W^\dagger M W=P_a, \qquad C_n^{\mathrm{obs}}=(1-\eta)C_{n,u}+\eta C_{n,a}, \qquad \frac{\partial(W,M,C_{n,u},C_{n,a})}{\partial\mathbf y}=0. \] Without it, the test still adjudicates the activated A7U Talbot-Lau branch, but the lawful projector label is INELIGIBLE_NO_ACCESS_LAW_ETA_VERDICT. This prevents both wrong falsification and false promotion without weakening the sealed test. The calibration-orthogonality gate is \[ U_{\mathrm{phys}}=[\mathbf 1,\partial_{\theta_1}\log|\bar B_1^0|,\ldots],\qquad R_{\mathrm{sens}}^{\mathrm{cal}}= \sqrt{(P_{\mathrm{phys}}\mathbf g^{\mathrm{phys}})^T (P_{\mathrm{phys}}\Sigma P_{\mathrm{phys}}^T)^+ (P_{\mathrm{phys}}\mathbf g^{\mathrm{phys}})}\ge5. \] If the apparatus or data packet does not pass every activation gate, the deterministic result is TARGET-NOT-ACTIVATED or INELIGIBLE_NO_THEORY_VERDICT. The source-only forecast is 96.51% linear in velocity, so a generic constant-only nuisance model is not sufficient; the activated mass, phase, velocity-width, grating, and separation derivatives must be projected explicitly. These pre-data gates cannot be altered after a null. A qualified null therefore remains a real scoped falsifier. The public Pedalino sodium-nanoparticle archive establishes that the high-mass Talbot-Lau platform is real and experimentally mature, but it does not contain the complete velocity-resolved visibility, covariance, ordinary-kernel, and path-provenance packet required for a retrospective execution. Its published ordinary theory curves share a fitted global contrast factor of 0.78, so a constant additional suppression is not separately identifiable. This is therefore a prospective sealed test, not an observation claim. Stable scientific anchors: A7U Molecular Visibility Transport A7U source framework Quantum Traction Theory: Main Book Pedalino et al., Nature experiment Public experimental archive QTT Observatory · DOI map