⚠ RESEARCH AREA

This is active research, not validated science. The F-ZERO framework is being tested against observational data. Matches indicate consistency; discrepancies reveal areas for refinement.

Your testing helps: Plug in values, find gaps, propose improvements. Both confirmations and contradictions advance understanding.

⚠ A NOTE ON NUMBER MATCHES

    When numbers align with observation, that is not validation — it is a signal worth investigating. Try it yourself. Plug in values. Watch where it breaks.
  
    The derivations and papers are provided as a trail — not proof. What you should be looking for are the failures, the errors, and the fixes. That is where the real work is.
  
    Matches suggest consistency. Discrepancies reveal what still needs to break, bend, or be rebuilt. Both are useful. Neither is final.

Quick Start — Presets

Preset fills the fields below — you can edit any value before computing.

Gravitational System

Mass (solar masses or kg)

Spin (0–1)

Temperature (K)

Quantum / Particle

Fine Structure Constant α

Strong Coupling αs

Z Boson Mass (GeV)

Cosmic Scale

Hubble Constant H₀ (km/s/Mpc)

Master Constants
Fundamental parameters from F_n = E_n − T_n · S_n = 0

              Q = 1 + ln(2)/3 = 1.231049

              verlinde = 1 + 1/(4π) = 1.079577

              κ = c² / (2·R_P)

Cosmology & MOND

CMB, dark energy, and galactic acceleration scale

              n_s = 1 − 2(1+w)·verlinde/Q

              w_de ≈ −0.98

              a₀_MOND = κ·Q/verlinde·(1+α)

              η_B = α·Q³·β_GH²/(8π²)

Neutrino Physics

Masses, mixing angles (PMNS), baryon asymmetry

              m_ν3 = Ry·α/2

              Δm²₃₁ = (Ry·α/2)²

              sin²θ₂₃ = verlinde/2

              sin²θ₁₃ = verlinde/50

              sin²θ₁₂ = verlinde·(N+π)/50

Higgs & Electroweak

Higgs mass, W/Z bosons, Weinberg angle

              M_H = M_Z·(2Q−verlinde)·(1−α/verlinde)

              M_W = M_Z·√(1−sin²θ_W)

              sin²θ_W = λ·(1+αs/4)·(1+α/π)

              λ_H = (1+αs/4+α/π)/(N_f+2)

              v_H = M_H/√(2λ_H)

Quantum Chromodynamics (QCD)

Strong coupling, proton-to-electron mass ratio

              αs(M_Z) = 1/(N_c + β₀·ln(M_Z/m_e·π·N_c))

              β₀ = 7/(4π)

              mp/me = 2·N_c·π^(N_f−1)

CKM Quark Mixing

Cabibbo-Kobayashi-Maskawa matrix elements

              sin(θ_C) = λ = 0.25·(1−αs+αs²)

              A = 1 − (N_c/2)·αs

              |V_ub| = (2−Q)/(8(Q−1))·(1−αs/4)

              δ_CP = arccos((Q+λ)/4)

Site under active development. Built in under 3 hours. May break. All formulas preserved here. Unvalidated — in progress — open to collaboration.
The axiom
F_n = E_n − T_n · S_n = 0
Master constants

Q = 1 + ln(2)/3 = 1.2310490602

verlinde = 1 + 1/(4π) = 1.0795774715

κ = c² / (2·R_P)

β_GH = 1 / (exp(2π) − 1)

β0 = 7 / (4π)

P0 = H0·R_P / c
Exact identities

π·(verlinde − 1) = 1/4

3·(Q − 1) = ln(2)

β0·4π = 7

spin = 4π/(8π) = 1/2

Q = 1 + Ω_Λ/3

n_eq = 2/Q
Cosmology & MOND

n_s = 1 − 2(1+w)·verlinde/Q           obs: 0.9649 | gap: 0.002%

w_de = −1 + (1−n_s)·Q/(2·verlinde)    obs: −0.98 | gap: 0.001%

a0 = κ·Q/verlinde·(1+α)               obs: 1.21e−10 m/s² | gap: 0.10%

η_B = α·Q³·β_GH²·(1+πα/2)/(8π²)    obs: 6.104e−10 | gap: 0.013%

Ω_Λ = ln(2)                            obs: 0.6889 | gap: 0.617%
Neutrino physics — PMNS

m_ν3 = Ry·α/2                          (Ry = m_e·α²·c²/2eV)

Δm²31 = (Ry·α/2)²                     obs: 2.453e−3 eV² | gap: 0.46%

Δm²21 = (Ry·α/2)²·verlinde·(N+π)/(50π²) obs: 7.53e−5 eV² | gap: 0.57%

sin²θ23 = verlinde/2                    obs: 0.545 | gap: 0.96%

sin²θ13 = verlinde/50                  obs: 0.0218 | gap: 0.96%

sin²θ12 = verlinde·(N_modes+π)/50     obs: 0.307 | gap: 1.21%
Higgs & electroweak

sin²θ_W = λ·(1+αs/4)·(1+α/π)         obs: 0.23122 | gap: 0.04%

M_H = M_Z·(2Q−verlinde)·(1−α/verlinde) obs: 125.25 GeV | gap: 0.027%

M_W = M_Z·√(1−sin²θ_W)              obs: 80.377 GeV | gap: 0.52%

λ_H = (1+αs/4+α/π)/(N_f+2)          obs: 0.129 | gap: 0.017%

v_H = M_H/√(2λ_H)                    obs: 246.22 GeV | gap: 0.13%

g_w = 2·M_W/v_H                      obs: 0.652 | gap: 0.52%
QCD

αs(M_Z) = 1/(N_c + β0·ln(M_Z/(m_e·π·N_c))) obs: 0.118 | gap: 0.14%

mp/me = 2·N_c·π^(N_f−1)                obs: 1836.15 | gap: 0.002%
CKM quark mixing

λ = 0.25·(1−αs+αs²)                  obs: 0.22486 | gap: 0.39%

A = 1 − (N_c/2)·αs                    obs: 0.8271 | gap: 0.50%

V_ub = (2−Q)/(8(Q−1))·(1−αs/4)       obs: 0.40145 | gap: 0.57%

sinθ23_CKM = A·λ²                     obs: 0.04182 | gap: 1.27%

sinθ13_CKM = A·λ³·V_ub               obs: 0.003731 | gap: 0.07%

δ_CP = arccos((Q+λ)/4)                obs: 1.196 rad | gap: 0.21%
Input constants — NIST CODATA 2018

ℏ = 1.054571817e−34 J·s

c = 2.99792458e8 m/s

G = 6.67430e−11 m³/(kg·s²)

k_B = 1.380649e−23 J/K

m_e = 9.1093837015e−31 kg

α = 7.2973525693e−3

αs = 0.118 (default input)

M_Z = 91.1876 GeV (default input)

H0 = 67.4 km/s/Mpc (default input)

R_P = 4.2701e26 m (Hubble radius)

F-ZERO / COREA / EFU  ·  fzerogenesis.com  ·  unvalidated · in progress · open