Zero free parameters. Here are the top three predictions:
1. Stack 12 oranges around one. Square it: 144. Multiply by electron mass.
Result: Σ−Λ = 73.58 MeV
This is the mass difference between two types of baryons (Σ and Λ particles).
Experiment: 73.60 MeV. Error: 0.02%
2. α⁻¹ = 4π³ + π² + π = 137.036
The fine structure constant — it controls how strongly light interacts with matter.
Feynman called it "the greatest damn mystery in physics."
Turns out: 4π³ (volume) + π² (surface) + π (circumference). Just geometry.
Error: ~2 ppm
3. ρ_Λ/ρ_Pl = π⁻²⁴⁷
The ratio of dark energy density to Planck density.
Quantum theory predicted this wrong by 10¹²² — the "worst prediction in physics."
This formula fixes it. Error: 1.1%
The notebook verifies 7 "Crown Jewel" predictions (mean error 0.014%) plus additional tests across particle physics and cosmology. Runtime: ~5 seconds.
This isn't numerology — the kissing number K₃=12 is a proven theorem (Schütte-van der Waerden 1953). The E₈ lattice (K₈=240) won Viazovska the Fields Medal in 2022.
a) "Any number expressible in base π" true, but the claim isn't
that 137 ≈ something×π. It's that α⁻¹ = 4π³ + π² + π with
INTEGER coefficients {4, 1, 1} arising from kissing number geometry.
b) "Units issue" these are dimensionless coefficients, not literal
m³ + m² + m. The "volume/surface/circumference" is structural
(π³, π², π¹ powers), not dimensional.
Fair questions thanks for the rigor check!
Jblx2•1mo ago
What if I like Euler's number better than pi?
e^4 + 5*e^2 + 16*e + 2*e^0 = 137.03594
That's a lot closer to 137.035999177 than the pi approximation (137.03630)
Excellent numerology! But here's the key question: can your e-polynomial derive OTHER constants?
UCT's π-formula α⁻¹ = 4π³ + π² + π isn't chosen because it's "close" it's chosen because the SAME geometric framework derives:
Numerology: Find ONE formula that fits ONE number
Physics: Find ONE framework that predicts MANY numbers
Your e⁴ + 5e² + 16e + 2 = 137.036 is impressive! Now use those same coefficients (1, 5, 16, 2) to predict the proton mass. If you can't, it's a coincidence. If you can, publish immediately.
UCT coefficients (4, 1, 1) come from π-exponents in the Duality Theorem connecting α to E₈ geometry. They're not fitted they're derived.
Jblx2•1mo ago
This is not my area. I've never seen powers of pi used in geometry or anywhere else for that matter. Where is a good introductory resource for geometry that uses powers of pi? Why does the tau mass need the natural log of 10?
AlekseN•1mo ago
Zero free parameters. Here are the top three predictions:
1. Stack 12 oranges around one. Square it: 144. Multiply by electron mass. Result: Σ−Λ = 73.58 MeV This is the mass difference between two types of baryons (Σ and Λ particles). Experiment: 73.60 MeV. Error: 0.02%
2. α⁻¹ = 4π³ + π² + π = 137.036 The fine structure constant — it controls how strongly light interacts with matter. Feynman called it "the greatest damn mystery in physics." Turns out: 4π³ (volume) + π² (surface) + π (circumference). Just geometry. Error: ~2 ppm
3. ρ_Λ/ρ_Pl = π⁻²⁴⁷ The ratio of dark energy density to Planck density. Quantum theory predicted this wrong by 10¹²² — the "worst prediction in physics." This formula fixes it. Error: 1.1%
The notebook verifies 7 "Crown Jewel" predictions (mean error 0.014%) plus additional tests across particle physics and cosmology. Runtime: ~5 seconds.
This isn't numerology — the kissing number K₃=12 is a proven theorem (Schütte-van der Waerden 1953). The E₈ lattice (K₈=240) won Viazovska the Fields Medal in 2022.
Visual summary: https://raw.githubusercontent.com/AIDoctrine/fpc-ae1r/main/U...
Paper: https://doi.org/10.5281/zenodo.18167072
Happy to discuss the math.
Jblx2•1mo ago
2. Aren't all numbers expressible in base pi? Also, doesn't adding a volume plus an area plus a length have a units consistency issue?
AlekseN•1mo ago
1. You're right I should clarify: the formula uses Σ⁺ (1189.37 MeV), not Σ⁰ (1192.642 MeV). Different isospin states.
2. Two parts: Fair questions thanks for the rigor check!Jblx2•1mo ago
EDIT
better yet:
AlekseN•1mo ago
Proton mass: m_p/m_e = 6π⁵ (0.0017% error) Muon mass: m_μ/m_e = 2π⁴ + 12 (0.024% error) Tau mass: m_τ/m_e = (π⁷·ln10)/2 (0.0003% error) Weinberg angle: sin²θ_W = φ/7 (0.027% error) Cosmological constant: ρ_Λ/ρ_P = π^(-247) (1.1% error)
The difference between numerology and physics:
Numerology: Find ONE formula that fits ONE number Physics: Find ONE framework that predicts MANY numbers
Your e⁴ + 5e² + 16e + 2 = 137.036 is impressive! Now use those same coefficients (1, 5, 16, 2) to predict the proton mass. If you can't, it's a coincidence. If you can, publish immediately. UCT coefficients (4, 1, 1) come from π-exponents in the Duality Theorem connecting α to E₈ geometry. They're not fitted they're derived.
Jblx2•1mo ago