Verification Portal
Every mathematical claim in this framework is backed by a SymPy verification script. No calculation appears in documentation without a passing script. Below are curated highlights — the full set of 735+ scripts is available on GitHub.
Start here(8 scripts)
Fine Structure Constant (alpha)
Derives 1/alpha = 137 + 4/111 entirely from division algebra dimensions. Sub-ppm accuracy (0.3 ppm) with zero free parameters.
Weinberg Angle (tree + one-loop)
Tree-level sin^2(theta_W) = 28/121 from democratic bilinear principle, plus one-loop correction structure. 800 ppm tree gap analyzed.
Hubble Constant (H_0)
Derives H_0 = 337/5 = 67.4 km/s/Mpc from fourth-power prime family. Exact match to Planck 2018 CMB value within measurement uncertainty.
Dark Energy Density (Omega_Lambda)
Derives Omega_Lambda = 137/200 = 0.685 connecting the fine structure constant to cosmological expansion.
Matter Density (Omega_m)
Derives Omega_m = 63/200 from Hilbert-Schmidt equipartition with dual-channel counting. 63 dual-role generators out of 200 total contributions.
CONJ-A3: Algebraic Independence (pure math)
Proves R^4 and R^7 structures cannot coexist in a common norm-multiplicative algebra. Forces n_d^2 + n_c^2 = 137, not (n_d + n_c)^2 = 225. Uses Radon-Hurwitz obstruction.
Three Generations of Fermions
Three independent mechanisms trace the generation count to dim(Im(H)) = 3. Strongest: Hom(H, R^7) decomposes into exactly 3 quaternionic channels.
Schrodinger Equation from Projection
Derives the Schrodinger equation, Born rule, and uncertainty principle from dimensional projection of a higher-dimensional wave onto 3D.
Run them yourself
Python 3.8+ and SymPy. That's it.
pip install sympy mpmath
Each script is self-contained with PASS/FAIL output.
cd verification/sympy/
python alpha_enhanced_prediction.py Every script prints explicit PASS or FAIL for each test.
Test 1: 137.036036... [PASS]
Test 2: error < 1 ppm [PASS] Verification methodology
What each script does
- ✓ States all assumptions explicitly with [A]/[I]/[D] tags
- ✓ Performs the calculation using exact rational arithmetic (SymPy)
- ✓ Compares against measured values (CODATA 2022 / PDG 2022)
- ✓ Prints explicit PASS/FAIL for every test assertion
What this proves (and doesn't)
- ✓ The arithmetic is correct (verified computationally)
- ✓ The formulas match measurement to stated precision
- ! Does NOT prove the derivation chain is physically correct
- ! Numerology risk: right numbers, possibly wrong reasons
Full script repository
All 735 verification scripts are open source. Clone the repo and run them all.
GitHub repository link will be available at launch.