Scientific Integrity

How to Falsify LFM

A theory that cannot be falsified is not physics — it is philosophy. This page lists explicit, quantitative criteria that would rule out the Lattice Field Medium framework. We update it as new data arrives.

13Falsifiable tests

8Currently consistent

2Under tension / watch

3Open / untested

⚠️

Honest assessment — what LFM does not yet explain

Fine structure constant: LFM gives α = 1/137.088 vs measured 1/137.036 — a 380 ppm discrepancy currently unexplained (loop corrections not computed).
Fine structure α loop corrections: LFM tree-level gives 1/137.088; the remaining 380 ppm gap requires 1-loop QED corrections not yet computed in the lattice framework.
Dark energy equation-of-state: DESI Y1 (2024) shows ≈2σ tension with w=−1. LFM predicts w=−1 exactly — this is real tension that needs watching.
Light quark absolute masses: Formulae give ratios well; absolute masses depend on unit conventions not yet fixed by the framework.
Entanglement (IT-05): The only remaining GAP in the equation emergence catalog. Phase-correlation mechanism proposed but not yet proven.

Falsifications Tests by Domain

Particle Physics

Higgs self-coupling λ_H

Open / Untested

LFM Prediction

λ_H = D_st/(2D_st²−1) = 4/31 ≈ 0.12903

Falsified If

HL-LHC measures λ_H outside 0.129 ± 0.013 (10% precision) — i.e., λ_H < 0.116 or λ_H > 0.142

Current Precision

±10% (current) → ±5% (HL-LHC)

Experiment

HL-LHC HH → bbγγ channel

Timeline

2028–2030

Reference

LFM-PAPER-075

Note: λ_H = 4/31 is derived from z₂ = 2D_st² second-coordination-shell lattice geometry — no free parameters. The denominator 31 is pure counting.

Particle Physics

CKM CP-violation phase δ_CKM

Consistent

LFM Prediction

δ_CKM = 3(χ₀+3) = 3×22 = 66.0°

Falsified If

Belle II or LHCb measures δ_CKM outside 66.0° ± 3.0°

Current Precision

Current: 65.8° ± 2.5° (0.08% error)

Experiment

Belle II + LHCb (B-meson decay CP asymmetry)

Timeline

2026–2028

Reference

LFM-PAPER-045

Note: Currently consistent at 0.3% error. As precision improves, this becomes a hard test.

Cosmology

Dark energy fraction Ω_Λ

Consistent

LFM Prediction

Ω_Λ = (χ₀ − 2D)/χ₀ = 13/19 = 0.6842

Falsified If

CMB+BAO combined (0.5% precision) measures Ω_Λ outside 0.684 ± 0.004

Current Precision

Current Planck: 0.685 ± 0.007 (0.12% error)

Experiment

Simons Observatory + DESI BAO (2026+)

Timeline

2026–2028

Reference

LFM-PAPER-071

Note: Derived from Jeans stability: 6 face modes (2D=6) collapse into matter; 13 remaining modes evacuate producing the dark-energy observational effect. Zero free parameters.

Cosmology

Dark energy equation of state w

Tension / Watch

LFM Prediction

w = −1 exactly. LFM forbids phantom crossing (w < −1) by Theorem C.3: χ ≤ χ₀ ⟹ w ≥ −1.

Falsified If

Any robust measurement confirms w < −1 at >3σ (phantom dark energy)

Current Precision

DESI Y1 (2024) already shows ~2σ tension with w=−1; LFM prediction is w=−1 exactly

Experiment

DESI, Euclid, Roman Space Telescope

Timeline

2024–2027 (ongoing)

Reference

LFM-PAPER-071

Note: Theorem C.7 (NO phantom crossing) is analytic and applies at all redshifts. If DESI/Euclid confirm w(z)<−1 at >3σ, LFM is ruled out as the dark energy explanation.

Electromagnetism

Fine structure constant α

Tension / Watch

LFM Prediction

α = 11/(480π) = 1/137.088

Falsified If

Electron g-2 or atomic clock measurements confirm α differs from 1/137.088 by more than 10 ppm

Current Precision

Current best measurement: 1/137.036 (electron g-2); LFM error = 0.04% = 380 ppm

Experiment

Electron g-2 (Harvard, Northwestern), atom interferometry

Timeline

Already testable — LFM has ~380 ppm discrepancy from best known value

Reference

LFM-PAPER-045

Note: LFM gives 1/137.088 vs measured 1/137.036. The ~380 ppm error is currently unexplained — it could indicate the formula needs loop corrections, or a deeper issue. This is an honest discrepancy.

Lorentz Symmetry

Directional photon dispersion (GRB timing)

Consistent

LFM Prediction

Anisotropy is O(k⁴); suppressed ~14 orders below current GRB bounds. Angular pattern of any residual must follow cubic-harmonic K₄(θ,φ).

Falsified If

GRB photon arrival times show (1) linear-in-k dispersion, or (2) direction-dependent timing with non-K₄ angular symmetry

Current Precision

Current Fermi-LAT bound: Δc/c < 10⁻¹⁶ at TeV energies

Experiment

Fermi-LAT GRB catalog, Cherenkov Telescope Array (CTA)

Timeline

2026+ (CTA first data)

Reference

Tutorial 16 (LFM website)

Note: The 19-point stencil gives 0.115% anisotropy at k=0.30 (near-Planck). At observable energies (k ~ 10⁻²⁰ Planck), anisotropy is ~10⁻³²%. See Tutorial 16 for quantitative details.

Strong Force

Linear quark confinement (string tension)

Consistent

LFM Prediction

v16 S_a auxiliary fields (ALL params derived from χ₀=19: γ=ε_W=0.1, L=β₀=7, κ_tube=30κ) predict V(r) = σ·r with σ ≈ 0.0275 (lattice units)

Falsified If

Higher-statistics 3D simulations show V(r) growth is unambiguously sub-linear (not r¹) — e.g., R² < 0.5 for linear fit at separations r = 1–20 lattice units

Current Precision

Session 143: H₀ REJECTED, R²=0.882, σ=0.0275. GOV-01/02 alone give R²≈0 (Yukawa screening only).

Experiment

LFM v16 S_a field GPU simulations; lattice QCD string tension comparison

Timeline

Session 143 complete; paper forthcoming 2026

Reference

LFM-PAPER-081 (forthcoming)

Note: GOV-01/02 alone do NOT produce confinement — mass gap gives Yukawa screening only (correct for W/Z analogy). Full linear confinement requires v16 S_a auxiliary fields, but all four S_a parameters are uniquely derived from χ₀=19 (no free parameters). Session 143 dynamic 3D test: H₀ REJECTED at R²=0.882. Needs higher-resolution follow-up before publication.

Strong Force

Strong coupling constant α_s at M_Z

Consistent

LFM Prediction

α_s = 2/(χ₀−2) = 2/17 ≈ 0.1176

Falsified If

Precision QCD measurements confirm α_s(M_Z) outside 0.1176 ± 0.005

Current Precision

Current PDG: 0.1179 ± 0.0010 (0.25% error). Currently consistent at 0.25% error.

Experiment

LHC jet cross-sections, τ decay, lattice QCD

Timeline

Ongoing

Reference

LFM-PAPER-045

Note: Numerator 2 = rank(SU(3)) is derived from corner theorem; ratio form 2/(χ₀−2) is motivated but not yet fully derived from first principles.

Gravity

Graviton mass m_g

Consistent

LFM Prediction

In vacuum, GOV-02 reduces to the massless wave equation ∂²χ/∂t² = c²∇²χ ⟹ m_g = 0 exactly

Falsified If

LIGO confirms graviton mass m_g > 10⁻²² eV at >3σ

Current Precision

Current LIGO bound: m_g < 1.2×10⁻²² eV (consistent)

Experiment

LIGO-Virgo-KAGRA, LISA

Timeline

2028+ (LISA)

Note: This is an analytic theorem from GOV-02 in vacuum. No free parameters.

Gravity

Gravitational wave speed v_gw

Consistent

LFM Prediction

v_gw = c exactly (from GOV-02 in vacuum: same dispersion as GOV-01)

Falsified If

|v_gw − c|/c > 10⁻¹⁵ (current multimessenger bound from GW170817)

Current Precision

GW170817 + GRB 170817A: |v_gw − c|/c < 10⁻¹⁵ (consistent)

Experiment

Next neutron-star merger with optical counterpart

Timeline

Ongoing (LIGO O4/O5)

Note: GOV-02 in vacuum is ∂²χ/∂t² = c²∇²χ, identical wave structure to GOV-01. Both propagate at c by construction.

Cosmology

CMB spectral index n_s

Consistent

LFM Prediction

n_s ≈ 0.9726 (χ₀=19, κ=1/63 fit). Inflation e-folds N = D(χ₀+1) = 60 (exact).

Falsified If

Simons Observatory measures n_s outside 0.970 ± 0.003 at >3σ (current Planck: 0.9649 ± 0.0042)

Current Precision

LFM n_s = 0.9726 vs Planck n_s = 0.9649; 0.8% error — within 1.8σ of Planck best-fit.

Experiment

Simons Observatory, LiteBIRD

Timeline

2026–2030

Reference

LFM-PAPER-045

Note: χ₀=19 was fitted to n_s — it is the CMB anchor point. LFM uses this to derive all other constants.

Neutrinos

Neutrino CP phase δ_CP

Open / Untested

LFM Prediction

δ_CP = 180° + (χ₀−4) = 195°

Falsified If

Hyper-K or DUNE measure δ_CP outside 195° ± 15° at >3σ

Current Precision

Current measurement: 195° ± 35° (consistent, large uncertainty)

Experiment

Hyper-Kamiokande (2027+), DUNE (2030+)

Timeline

2027–2030

Reference

LFM-PAPER-045

Note: Currently consistent but error bar is large. As Hyper-K and DUNE reduce uncertainty to ±10°, this becomes a decisive test.

Black Holes

Black hole interior — no true singularity

Open / Untested

LFM Prediction

χ → −χ₀ = −19 inside horizon (Z₂ second vacuum). No curvature singularity. Child-universe interior.

Falsified If

Future quantum gravity theory or observation confirms a true curvature singularity at r=0 that cannot be resolved by any mechanism

Current Precision

Currently inaccessible observationally

Experiment

Indirect: Hawking radiation spectrum, black hole information paradox resolution

Timeline

Long-term (Hawking radiation not yet observed)

Note: Not directly falsifiable with current instruments. Hawking radiation from microscopic BHs (if produced at LHC) would carry imprint of interior structure. Currently a theoretical prediction only.

What Would Actually Falsify LFM?

Smoking guns (single observation)

Phantom dark energy confirmed: w < −1 at >3σ (rules out Theorem C.3)
Graviton mass m_g > 10⁻²² eV confirmed by LISA
Lorentz violation with non-K₄ angular symmetry in GRB photon timing
Higgs self-coupling λ_H < 0.10 or > 0.17 from HL-LHC
Gravitational wave speed |v_gw − c|/c > 10⁻¹⁵

Accumulation of tension

Multiple predictions off by >5% when precision reaches 1% (currently at 2–5%)
Fine structure α discrepancy not resolved after loop corrections computed
String tension σ from v16 S_a fields fails at high-resolution follow-up (R² drops below 0.5)
Ω_Λ measured at 0.5% precision outside 13/19 ± 0.004
δ_CP measured outside 195° ± 15° by Hyper-K

Scientific transparency commitment: We maintain this page as a first-class document, not an afterthought. Every new paper published by this project adds at least one entry here. If a test goes against LFM, it will be listed as Under Tension immediately and upgraded to Falsified if the result reaches >3σ significance.

Equations Reference →Tutorial 16: Lorentz Anisotropy →All Papers →About LFM →