RMB Core Theory 2.1 The Unified Lagrangian Structure of the Space–Matter–Motion Theory

RMB Core Theory 2.1 presents the unified and mathematically consistent foundation of the Space–Matter–Motion (RMB) framework.
This work consolidates all field definitions, the Lagrangian formulation, and the resulting master equation that underlies every previous RMB publication (RMB I–VII).

Core Contributions

1. Definition of the central RMB fields

• Potential field: Φᵤ = ρ c² vᵤ

• Field tensor:  Fᵤᵥ = ∂ᵤΦᵥ − ∂ᵥΦᵤ

• Motion tensor:  Mᵤᵥ = ρ vᵤ vᵥ + αᴿᴹᴮ Fᵤᵥ

These objects unify matter flow and spatial deformation into a single dynamical structure.

2. Full Lagrangian formulation

The RMB Lagrangian yields the master field equation
  ∇ᵘ Mᵤᵥ = 0
which replaces the geodesic equation of General Relativity in the RMB framework.

3. Linearisation and wave equations

The theory predicts non-dispersive inertial-vorticity waves with wave speed
  cᴿᴹᴮ = c √(αᴿᴹᴮ / ρ₀).

4. Newtonian limit and rotation curves

The RMB correction term
  aᴿᴹᴮ(r) = −(αᴿᴹᴮ / ρ₀) · d/dr [v(r)/r]
produces flat galactic rotation curves without invoking dark matter.
This is validated using SPARC data.

Scope

Chapters 1–7 define the core theory.
Speculative phenomena (φ-scaling, resonance structures, Schumann–LHC correlations, the 800 Hz signal) are placed strictly in Appendix A and are not part of the core model.

Purpose

This is the official consolidated reference for all RMB field equations, ensuring consistency across all future RMB publications and offering a clear, testable physical framework that connects laboratory physics, astrophysics, and cosmology.