We examine the inertial regime of scalar–conformal NUVO space and establish its correspondence with the kinematic structure of special relativity. In this framework spacetime geometry is determined by a scalar–conformal metric of the form
where represents locally available structural capacity.
We show that when the scalar diagnostic field is spatially uniform, the resulting geometry reduces to a constant conformal deformation of Minkowski spacetime. In this limit the null structure, invariant propagation speed, and Lorentz symmetry of the reference metric are preserved. Persistent anchored structures maintained by steady boundary flux states follow geodesic worldlines with constant four–velocity, reproducing the inertial motion of special relativity.
The analysis establishes that inertial kinematics arise as a limiting regime of scalar–conformal geometry rather than as an independent postulate. No assumptions regarding dynamical laws, time dilation, or measurement structure are introduced at this stage. Instead, the results identify the geometric conditions under which the NUVO framework recovers the inertial structure of relativistic spacetime.
This work provides the geometric foundation for subsequent developments in the SR-series, where relativistic time dilation is derived from transport-modified internal structural cycles and acceleration is interpreted as boundary-state evolution. It also prepares the connection to phase-based coherence phenomena developed in the Q-series.
The preceding papers of the M–series establish the scalar–conformal
framework of NUVO space, in which spacetime is modeled as a Lorentzian
manifold equipped with a scalar diagnostic field
representing locally available structural capacity.
The physical metric is given by
Persistent matter structures are modeled as anchored configurations
maintained by admissible boundary flux states. Motion modifies the
boundary flux presentation encountered by the structure, and admissible
trajectories are those for which this presentation remains compatible
with the structural intake requirement.
A distinguished class of trajectories arises when the boundary flux
state remains stationary. In this regime the structure follows a
geodesic of the scalar–conformal metric and exhibits inertial motion.
The purpose of the present paper is to examine the regime in which the
scalar diagnostic field is spatially uniform and to establish that this
regime reproduces the kinematic structure of Minkowski spacetime.
This result provides the inertial correspondence limit of the
scalar–conformal framework. Subsequent SR papers examine how time
dilation arises from transport-modified internal structural cycles and
how acceleration corresponds to structural adjustment.
We consider the regime
Then
Introducing rescaled coordinates
yields
Thus the geometry is diffeomorphic to Minkowski spacetime.
Even in a uniform scalar background, transported structures experience an effective scalar modulation distinct from the ambient field due to local structural adjustment. This distinction will be central in the derivation of relativistic time dilation.
Null directions satisfy
Thus causal structure is preserved.
The invariant transport speed is defined by propagation along null
directions of the scalar–conformal metric and coincides with the causal
speed of Minkowski spacetime.
Lorentz transformations preserve both and constant
, hence
Thus Lorentz symmetry emerges naturally in the uniform scalar regime.
In steady state:
Geodesic equation:
With constant :
Thus inertial motion corresponds to constant four–velocity.
Uniform scalar state yields:
Thus special relativity emerges as the inertial limit of NUVO space.
Internal structural cycles correspond to phase accumulation governing coherence in the Q-series. Variations in effective scalar modulation induce corresponding variations in phase evolution.
The uniform scalar regime reproduces Minkowski kinematics. Inertial
motion corresponds to steady boundary flux states. This establishes the
kinematic limit of the NUVO framework.