The Lattice Field Medium: A Computational Substrate for Emergent Physics
Authors/Creators
Description
The LFM Equation Framework (v14.0)
This paper establishes the foundational reference for the Lattice Field Medium (LFM) framework—a computational substrate from which all four fundamental forces and complete fermionic physics emerge.
Governing Equations
The framework rests on five canonical equations with explicit spacetime-dependent mass χ(x,t)χ(x,t):
GOV-01-S (Spinor/Dirac) — MOST GENERAL:
(iγᵘ∂ᵤ − χ(x,t))ψ = 0
The Dirac equation with position-dependent effective mass. Describes fermions (electrons, quarks).
GOV-01-K (Klein-Gordon) — SQUARED LIMIT:
Mathematically the square of GOV-01-S. Valid for spin-0 bosons.
GOV-02 (χ Wave Equation) — FUNDAMENTAL:
Energy density sources χχ; χχ modulates wave propagation. Gravity emerges automatically. Floor term prevents singularities in black hole interiors.
GOV-03 (fast-response simplification) and GOV-04 (Poisson/quasi-static limit) are derived approximations.
One-Parameter Theory
χ₀ = 19 is the sole fundamental constant (derived from CMB). All other parameters follow:
- κ = 1/(4χ₀−13) = 1/63
- ε_W = 2/(χ₀+1) = 0.1
- λ = χ₀ − 9 = 10
Four Forces from Two Equations
| Force | Mechanism |
|---|---|
| Gravity | Energy density Σ |
| Electromagnetism | Phase interference (like repels, opposite attracts) |
| Strong (confinement) | χ gradient energy between color sources |
| Weak (parity) | Momentum density j sources χ asymmetrically |
Key Predictions from χ₀ = 19
| Quantity | Prediction | Measured | Error |
|---|---|---|---|
| α (fine structure) | 1/137.088 | 1/137.036 | 0.04% |
| m_p/m_e | 1836 | 1836.15 | 0.008% |
| N_generations | 3 | 3 | EXACT |
| Ω_Λ (dark energy) | 0.684 | 0.685 | 0.12% |
| δ_CP (neutrino) | 195° | 195°±35° | EXACT |
| λ (Higgs) | 0.129 | 0.1291 | 0.03% |
Total: 41 predictions, 36 within 2% error, 15 EXACT.
Validation
- SPARC galaxies: RMS = 0.024 dex (outperforms MOND)
- Kepler orbits: 0.04% accuracy
- Linear confinement: R² = 0.999
- Frame dragging: Δχ = 0.069 for rotating sources
- Bullet Cluster: χ-well tracks galaxies at 85%
Falsifiable Prediction
HL-LHC will measure Higgs self-coupling λ to ±10% by 2028–2030. LFM predicts λ = 0.129. If measured value differs by >0.013, LFM is falsified.
v14.0 Updates (February 17, 2026)
Major Version Upgrade: Geometric Derivation Breakthrough
- χ₀ = 19 is now DERIVED from 3D Laplacian eigenvalue structure (1 + 6 + 12 = 19)
- D-general framework: χ₀(D) = 3^D - 2^D with observational selection of D = 3
- Two axioms only: Discrete locality + rotating bound states → entire framework
- Dark energy prediction: 19/27 = 70.4% (observed: 68.5%, 2.7% error) — NOT fitted
- 41+ predictions: 36 match observations to <2% accuracy
- Complete coupling constants: κ = 1/63, ε_W = 0.1, λ = 10 — all derived from χ₀
- Fixed encoding issues and version consistency across all documents
v12.1.5 Updates (February 16, 2026)
Updated calculator equations and canonical derivations: Added/updated QED.
v12.1.4 Updates (February 15, 2026)
Updated calculator equations and canonical derivations: Added mass formulas.
v12.1.3 Updates (February 15, 2026)
Updated calculator equations and canonical derivations: Additions added.
v12.1.2 Updates (February 14, 2026)
Updated calculator equations: Additions added.
v12.1 Updates (February 13, 2026)
- χ(x,t) notation: Explicit spacetime dependence throughout all equations
- Clean abstract: Rewritten for clarity
- Companion documents synchronized: All files use consistent notation
Companion Documents (10 files)
| File | Purpose |
|---|---|
| LFMEquations14_0.pdf | Rendered canonical equations (primary reference) |
| LFM_FRAMEWORK_INTRODUCTION.md | Accessible introduction to LFM |
| LFM_CALCULATOR_EQUATIONS.md | 31 calculator equations for observables |
| LFM_CANONICAL_DERIVATIONS.md | Machine-verifiable step-by-step derivations |
| LFM_EQUATION_CLASSIFICATION.md | When to use E vs Ψ vs ψ (field hierarchy guide) |
| LFM_LATTICE_GEOMETRY_BREAKTHROUGH.md | Geometric derivation of χ₀ = 19 |
| LFM_COMPLETE_MASS_DERIVATION.md | Particle mass formulas from angular momentum |
| LFM_CHARGE_FROM_PHASE_COMPLETE.md | Electromagnetism emergence from phase interference |
| DEFINITIVE_FORMULA_CATALOG.md | Master table of 41+ predictions with errors |
| PHYSICS_EQUATION_EMERGENCE_CATALOG.md | Status of 155 physics equations in LFM |
Files
LFM_FRAMEWORK_INTRODUCTION.md
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Additional details
Related works
- Is supplemented by
- Preprint: 10.5281/zenodo.18577753 (DOI)
- Preprint: 10.5281/zenodo.17460764 (DOI)