Scalar-Clock Geometry and Conditional Gravitational Dynamics in the Axis Model
Andrew Morton · Public preprint · Conditional geometry and dynamics
Connects scalar-clock metric reconstruction to explicit response-field dynamics and a conditional gravitational effective theory.
Abstract
We formulate a conditional geometric and gravitational interface for the Axis Model. A neutral scalar phase supplies a real temporal coframe on a clock-admissible branch. Three independently specified spatial one-forms complete a local Lorentzian metric; their normalization and completion data remain necessary inputs to metric selection. We distinguish this coframe metric from the expectation of a renormalized composite metric operator. For a declared two-response-scalar action on a fixed background, we derive the field equations and full quadratic fluctuation form. Its homogeneous reference contains two massless scalar modes, and a separate nonzero-phase-gradient diagnostic retains background-dependent mixing. These operators provide conditional inputs to a curvature calculation, with an independent renormalized Einstein–Hilbert coefficient and a separately specified physical species map. We derive the Newtonian limit of an admitted Einstein sector and the profile-dependent scaling of simple thin lenses. Metric reconstruction, fixed-background determinants, a constrained metric functional, and microscopic particle interpretation retain their distinct mathematical requirements. No measured observable selects the coframe, species roster, normalization, or matching scale.
Scope
The coframe completion, physical species map and finite gravitational normalization are supplied inputs. The paper establishes conditional field and metric relations, while physical metric selection, microscopic graviton support and observational predictions require additional work.
Paper and supporting files
The manuscript, source files and reproducibility calculations are available on Zenodo.
Read the current paper and supporting files on Zenodo