A quantum Planck field: Coupled algebra and preparation-dependent predictions

This preprint develops a quantum model in which a positive scalar field sets the action scale. It derives the coupled commutator algebra with the Planck-field operator on the right-hand side of the field–momentum commutators and constructs an ordered evolution generator. Dividing the Lagrangian density by the local action scale resolves a time-evolution conflict between the stipulated algebra and the undivided dynamics. The calculations connect specified field preparations to spectral distributions, exchange with a calibrated quantum probe, and singlet-positronium annihilation statistics in a specified electron–photon extension. Decay is expressed relative to a clock frequency, making the observable a dimensionless ratio. The atomic treatment distinguishes field statistics over all annihilation outcomes from statistics conditioned on surviving atoms. It compares an illustrative broad preparation, a cosmologically matched case, strong confinement, and the same confined-state preparation evolved after removal of the added potential. The work also develops the cosmological comparison cases, field-preparation distributions, and the evaluated equivalence-principle constraint under a specified nuclear completion. The predictions depend on the preparation, coupling assumptions, clock reference, and effective annihilation model; the calculations do not establish a detectable experimental signal or a fit to experimental data. This v26 deposit contains the complete paper and Appendices A–I in PDF and editable Word formats, the separate main article and technical supplement, full mathematical sources, numerical and symbolic calculation code, input parameters, generated model data, all main and supplemental figures, and reproduction and verification instructions. The scientific documents contain 219 numbered equations, six main figures, fifteen supplemental figures, and a shared 147-entry bibliography. The archive includes a manifest and maps from figures and calculations to their source files. Documents, mathematical sources, figures, and generated data are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). Original software and build scripts are licensed under the MIT License. These licenses apply to their respective components, not as alternative licenses for every file. See Planck_Field_v26_LICENSES.txt for the scope and license notices.