Home / Simulations / P19 — Standard Model Parameters from One Substrate Density
BFUT P19 · Interactive Derivation Dashboard
Standard Model from One Substrate Density
The Standard Model requires 19–26 free parameters inserted by hand.
BFUT P19 derives six of them from a single physical quantity: the intrinsic equilibrium density of the Spaticle field.
Click any quantity to expand its physical mechanism.
ρs
SINGLE INPUT · SPATICLE SUBSTRATE EQUILIBRIUM DENSITY
5.9 × 10−27 kg/m³
Intrinsic equilibrium density of the Spaticle field. Not a cosmological constant.
Anchored by the proton charge radius rp = 0.8409 fm and independently
validated across three physical sectors.
1
FREE PARAM INPUT
TIER 1 — FROM ρs AND P16 FUNCTIONAL COEFFICIENTS A, B, C, D
STRONG COUPLING
αs
B · R₀⁴ / A ratio of binding to kinetic energy at condensation scale
0.120
vs measured
0.1179 at mZ
1.8%
P16 coefficients A (localisation cost) and B (bulk displacement) fix the ratio directly. Running with energy scale follows from effective coherence volume.
FINE STRUCTURE CONSTANT
α
ωc² R₀² / c² circulation energy / propagation energy at condensation scale
1/137.1
vs measured
1/137.036
0.05%
Unique dimensionless combination from three-sphere geometry. Once rp and ρs are fixed, α has no freedom. Not a free parameter.
ELECTROWEAK MIXING
sin²θW
1 mode out of 4 at Q = 235 MeV running to mZ via SM RGE
0.232
vs measured
0.2312 at mZ
0.1%
Bifurcation chirality of the P16 3+e topology: 1 W-mode out of (1+3) modes gives sin²θW = 1/4 at tree level, running to 0.2312 at mZ.
MODEL-UNIT-TO-SI MAPPING · rp ANCHOR
TIER 2 — BOSON MASSES · RECONFIGURATION ENERGY WITH SI ANCHOR
W BOSON MASS
mW
(4ρsc⁴/3) · Vcond · (ΔΨ/Ψvac) charged reconfiguration: 1/3 of 3-core
80.0 GeV
vs measured
80.377 GeV
0.5%
Depends only on ρs and rp once the SI anchor is applied. The ABCD coefficients cancel through the ℓmodel = rp/R₀ substitution.
Z BOSON MASS
mZ
mW / cos θW neutral channel: full symmetric reorganisation
91.8 GeV
vs measured
91.19 GeV
0.7%
Ratio mZ/mW = 1/cos θW derives from bifurcation geometry alone. Z0 requires symmetric reorganisation of all three internal modes.
HIGGS BOSON MASS
mH
√(mt · mZ) geometric mean of top quark and Z boson
125.51 GeV
vs measured
125.25 GeV
0.21%
Collective substrate excitation at the geometric mean of the fermionic and bosonic mass scales. Not a free parameter — derived from quantities already fixed by the condensation topology.
ELECTROWEAK THRESHOLD · n=4 BIFURCATION
TIER 3 — STRUCTURAL CONSTRAINTS FROM CIRCULATION TOPOLOGY
KOIDE RELATION
(me+mμ+mτ) / (√me+√mμ+√mτ)²
= 2/3 exactly three-fold circulation vector projected at 120°
Q = 0.666661
vs exact
2/3 = 0.666667
0.001%
Three charged leptons are projections of a single internal circulation vector onto three axes separated by 120° in circulation phase space — a direct consequence of the P16 three-sphere geometry.
LEPTON MASS SCALE
M₀² = mW/256
4⁴ = 256 from n=4 bifurcation threshold charged-lepton electroweak anchor
313.97 MeV²
vs measured
313.84 MeV²
0.042%
The factor 4⁴ = 256 arises from the n=4 P16 bifurcation threshold that selects the 3+e topology as the unique stable condensation. Lepton mass scale anchored to the electroweak sector without additional free parameters.