Four factors. Four sources. Each traced to the postulate. The only operation is multiplication.
Factor
Value
Source
μΛ
ρΛ1/4
Vacuum energy floor
Cgeom(ρ)
Geometric mean of C(e/D) over Kostant exponents
Phase operator on sunflower
(√ΩΛ)dist/30
√ΩΛ
McKay graph distance
T²(ρ ⊗ σ)
27 vacuum-twisted values
Reidemeister torsion
Mass Calculator
-
predicted mass
The 24 Predictions
Formula A applied to 8 nontrivial irreps × 3 vacua. Sorted by predicted mass.
#
ρ
dim
dist
σ
T²
Mass (GeV)
SM
Ratio
Dead zone: Ranks 4-9 (R₃ at dist 2, R₆ at dist 3) produce masses between 10⁻⁹ and 10⁻⁶ GeV. No known SM fermions occupy this range. Overlaps sterile neutrino and warm dark matter search windows.
SM Fermion Scorecard
10 of 12 within factor of 3. All 12 within factor of 10. Three predictions land within 6%.
Fermion
Observed (GeV)
Predicted (GeV)
ρ
σ
Ratio
≤3×?
Locked Data
Cgeom values (Kostant sunflower, computed live from exponents)
Irrep
Spin
D
Kostant exponents
Cgeom
Vacuum torsion T²(ρ ⊗ σ) (27 entries)
ρ
T²(triv)
T²(std)
T²(gal)
The Postulate
S¹ = ∂(Möbius) ↪ S³, ∂S³ = ∅
The temporal edge bounds the Möbius surface embedded in hypersphere space. The space has no boundary. Everything derived traces to this topology.
Five Foundations
Foundation
Statement
Wave-matter identity
λ = h/p is identity. Matter is wave, sampled.
Surface origin
Time is phase on the boundary of a 2D manifold.
Topology
ψ(y + L) = −ψ(y). A field traversing the manifold returns to minus itself.
Bounded evaluation
R_H / ℓ_P has definition at the limit ∞/0. The observer is the structural midpoint.
Embedded sampling
The observable's character selects the manifold (n = 1, 2, 3). Dimension follows the measurement.
The Cosmic Standing Wave
Ψ = cos(t/2)
Anti-periodicity requires period 4π. Cosine is inherited because the universe initiates at maximum amplitude Ψ = +1. The present epoch sits at t ≈ 5.22 rad, approximately 2.8 Gyr before turnaround.
The 120 Domain
The binary icosahedral group 2I is the largest exceptional discrete subgroup of SU(2) ≅ S³, with |2I| = 120.
Term
Resolution
Source
120 domain
120 positions
|2I| = 120 native to S³
Grid
120 (fermionic)
Half-integer modes on the domain
60R-grid
60 (even only)
|ψ|² projects 2I → I
Manifold Assignment
n
Manifold
Observables
(√Ω)⁻ⁿ
1
Temporal edge S¹
H₀, a₀
~10⁻⁶¹
2
Möbius surface
Λ
~10⁻¹²²
3/2
Gauss-Codazzi interface
Gravity
3
Space S³
Null "dark matter"
~10⁻¹⁸³
Derivation Chain
The calculator derives every scale from first principles. No hardcoded outputs.
Quantity
Formula
Value
Extended Scorecard
Blind outputs of a fixed structure, checked against observation.
Observable
Predicted
Observed
Agr.
Fibonacci Wells
Well
Θ
C(Θ)
Grid
n
Observable
Falsification
MIT has no free knobs. The framework stands or falls on locked predictions.
Prediction
Falsified if
Threshold
a₀(z) ∝ H(z)
a₀ consistent with constant at high z
≥ 2σ, z > 2
Λ constant
ρ_DE(z) shows significant evolution
≥ 2σ
CMB suppression
Wrong suppression scale
ℓ_cut ∉ [15, 50]
Null dark matter
Non-gravitational interaction detected
≥ 5σ, replicated
zcross ≈ 0.66
Phantom crossing outside window
[0.4, 0.9]
weff > −1
True phantom behavior confirmed
Model-independent 2σ
μΛ ≈ 2.25 meV
Lightest ν mass inconsistent
Direct measurement
Dead zone states
Particles at 10⁻⁹ to 10⁻⁶ GeV
If observed with suppressed couplings
Any SM fermion
Incompatible with 24-entry table at ×10
Ongoing
Falsification window: Euclid Data Release 1, October 21, 2026