1. K(3)=12, K(8)=240 are PROVEN theorems (Schütte 1953, Levenshtein 1979), not arbitrary choices. These are the only numbers that solve the sphere packing problem.
2. τ=7 derives from THREE independent sources: octonion imaginary dimension, Fano plane points, and M-theory compactification (11D−4D). Not days of week.
3. n=45 is not chosen – it's CALCULATED: (K²−K−2τD)/2 = (144−12−42)/2. Change any input, precision collapses.
4. The killer: sin²θ₁₃ = 1/45 in neutrino physics. Same 45, completely independent measurement. That's not fitting – that's prediction.
The code is open. If you can get 0.574 ppm with Barnes-Wall vectors and week days, I'd genuinely like to see it.
Author here. Important context: I'm not a physicist – this emerged from months of collaborative work with AI (Claude), exploring geometric patterns in fundamental constants.
There are 4320 vectors of norm 4 in the Barnes–Wall lattice.
7 is also the number of days in the week.
45(rpm) is the rotational speed of grammaphone records.
Substituting these into the paper also yields zero free paramers.
Fair point – numerology concern is valid.
Key differences:
1. K(3)=12, K(8)=240 are PROVEN theorems (Schütte 1953, Levenshtein 1979), not arbitrary choices. These are the only numbers that solve the sphere packing problem.
2. τ=7 derives from THREE independent sources: octonion imaginary dimension, Fano plane points, and M-theory compactification (11D−4D). Not days of week.
3. n=45 is not chosen – it's CALCULATED: (K²−K−2τD)/2 = (144−12−42)/2. Change any input, precision collapses.
4. The killer: sin²θ₁₃ = 1/45 in neutrino physics. Same 45, completely independent measurement. That's not fitting – that's prediction.
The code is open. If you can get 0.574 ppm with Barnes-Wall vectors and week days, I'd genuinely like to see it.
Author here. Important context: I'm not a physicist – this emerged from months of collaborative work with AI (Claude), exploring geometric patterns in fundamental constants.
Formula: M_Pl/m_e = π^45 × (1 + 2α + α/13 − (8/9)α²)
All coefficients derive from kissing numbers (proven theorems, not fitting).
Result: 5.74×10⁻⁷ precision. Cross-validated by sin²θ₁₃ = 1/45 from neutrino physics.
Everything is open:
- Paper: full derivation with references
- Code: deterministic (seed=42), CODATA 2022
- Live demo: https://colab.research.google.com/drive/1UtKmlkaYFHegx4S98Vv...
I can't debate field theory – but the math either holds or it doesn't. Looking for experts to verify or break it.