A Closed Fixed-Ambient Realization: Nonlinear Normal-Graph Dynamics, Local Well-Posedness, and Operational Readout
Year: 2026
Type: preprint
Abstract: This paper constructs a local nonlinear realization of the fixed-ambient branch of the OFT/VGM research programme. It follows the physical-admissibility framework of Paper XXII and specifies the geometry, coupled action, evolution equations, admission conditions, and an operational readout within one declared model. A scalar normal displacement of a de Sitter reference hypersurface in Minkowski ambient space generates an exact induced metric. A massive scalar field couples to this metric with finite backreaction. Substitution into the action gives an explicit first-derivative Lagrangian and a quasilinear second-order two-field system. The induced-metric constraint is eliminated identically by the normal-graph parametrization. Strict geometric, temporal, and full fiber-Hessian coercivity margins define a nonempty open neighborhood of the vacuum. An explicit symmetric-hyperbolic first-order reduction, including derivative compatibility, supports local existence, uniqueness, and continuous dependence for the declared Sobolev data. Energy control uses the complete Cauchy state, and a continuation criterion identifies norm blow-up or loss of a positive geometric, causal, or hyperbolic margin. A calibrated proper-time functional provides a nonzero linear operational response along a family of admitted exact solutions. The paper distinguishes the frozen-geometry probe cone from the characteristic set of the fully coupled system and separates local energy control from global or asymptotic stability. The model is a background-dependent effective realization; empirical comparison remains a separate step. This deposit contains the English manuscript, revised version 1.1 dated 8 November 2026, its XeLaTeX source, and the accompanying Peaceful Civilian Use Licence. Version 1.1 makes the first-order reduction and norm conventions explicit, corrects a missing addition sign in the quadratic derivative density, and uses a positive-definite gradient norm in the joint weak-graph limit. Series: OFT/VGM Research Programme — Paper XXIII.DOI: https://doi.org/10.5281/zenodo.24058796
Author: SIGERGOK, Hasan
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225585024