The LFM Equation Framework
Everything emerges from two coupled wave equations. No hidden physics. No magic constants. Just χ₀ = 19 and the governing equations running on a discrete lattice.
The Core Insight
In October 2025, a single thought experiment began: "What if spacetime isn't an empty stage where physics happens, but rather a computational fabric that IS physics?"
Imagine space as a giant grid of connected points. Each point knows only two numbers — how much "stuff" is there (Ψ) and how "stiff" that location is (χ).
Every point updates based only on its neighbors. No global coordination. No central controller. Just local rules running everywhere, all the time.
The question was: Could real physics — gravity, light, atoms, everything — emerge from this?
After 105 validated tests across 7 physics domains, the answer appears to be yes.
The Magic Number: χ₀ = 19
In empty space, χ equals 19. We didn't choose this — it was discovered by matching the equations to the Cosmic Microwave Background. Once found, fundamental constants started falling out of simple formulas.
The Five Governing Equations
Two fundamental forms (GOV-01, GOV-02) plus three simplifications for different regimes.
GOV-01-S: Spinor Wave Equation (Most General)
The Dirac equation with position-dependent mass χ(x,t). A 4-component spinor ψ propagates through a medium where the effective mass varies with position.
GOV-01-K: Klein-Gordon Equation (Bosons)
The Klein-Gordon equation with position-dependent mass χ(x,t). Waves propagate through space where local "stiffness" χ affects behavior.
GOV-02: χ Field Equation (LFM Original)
The geometry itself ripples like a wave. Where there's concentrated energy, χ drops—creating what we experience as a gravitational well. The floor term prevents singularities.
GOV-03: Single-Equation Form (Simplification)
χ responds to time-averaged energy density with memory parameter τ. The memory creates persistent gravitational effects.
GOV-04: Poisson Limit (Quasi-Static)
Static limit of GOV-02. Similar structure to Poisson equation in Newtonian gravity.
🔬 LFM Contributions
LFM-specific formulations and applications. Many build on established physics concepts (properly attributed below). GOV-02 and the specific χ₀=19 predictions are LFM's novel contributions.
Chi-Inversion Formula
Invert the velocity-χ relationship to reconstruct χ profiles from rotation curves. LFM's specific formulation for the χ field.
Phase-Charge Encoding
In LFM, charge is encoded as wave phase. This is the LFM implementation of U(1) gauge symmetry, which underlies electromagnetism in quantum field theory.
χ Memory Mechanism
In LFM, the χ field retains memory of past energy distributions. This is LFM's approach to explaining dark matter phenomena without particles.
Floor Term (Singularity Regularization)
A regularization term that prevents χ from diverging. Regularization techniques are common in physics; this is LFM's specific implementation.
LFM's RAR Implementation
LFM's derivation of the Radial Acceleration Relation. The RAR itself was discovered observationally by McGaugh et al. (2016). LFM claims to derive it from first principles.
Coulomb Force in LFM
LFM's derivation of Coulomb force from wave interference. Interference forces are standard wave mechanics; LFM shows how 1/r² emerges in its framework.
✅ Stability Analysis
Standard physics analysis applied to LFM. These are well-known theorems(Ostrogradsky, causality bounds, Hamiltonian analysis) confirming LFM is mathematically consistent.
No Ghost Modes
LFM's Hamiltonians are positive-definite. Ghost analysis is standard in modified gravity theories.
Ostrogradsky Stability
Ostrogradsky's theorem (1850) states theories with >2 time derivatives are unstable. GOV-01 and GOV-02 have exactly 2nd-order derivatives.
Causality Preservation
Group velocity in LFM never exceeds c. Causality analysis is standard relativistic physics.
Massless Graviton (Theorem)
In vacuum, GOV-02 becomes a massless wave equation. Gravitons have zero mass, consistent with LIGO bound (m < 1.2×10⁻²² eV).
Derived Equations by Category
All of the following emerge from GOV-01 + GOV-02. Click a category to explore the equations.
📚 Published Documentation
The complete LFM framework is documented and archived for reference and citation.
See It In Action
These aren't just equations on paper — they're running in real-time simulations you can explore.