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Interactive demo: https://fractal-recursive-coherence.vercel.app/

Every fundamental constant—α, G, ℏ, φ, all 25 Standard Model parameters—derived from ONE topological rule. Zero free parameters.

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THE DISCOVERY

Start with nothing (∅). Quantum fluctuations inevitable. Entangled pair forms. Only golden ratio (φ) phases survive. Self-replication cascades. Energy conservation forces closure → 21-node Ring+Cross graph.

Everything else follows mathematically.

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WHY N=21?

Not chosen. DERIVED three ways:

  • E8 encoding: 12N - 4 = 248  →  N = 21
  • Fibonacci: E8 rank 8  →  F(8) = 21
  • Generations: 3×7 structure  →  N = 21

All three constraints agree.

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RESULTS (NOT FITS)

v = 245.94 GeV (0.026% error) → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

α⁻¹ ≈ 137 (from graph connectivity) → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

All fermion masses (from E8): → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

   y_μ/y_e = 10N-3 = 207  (measured: 206.77)
   m_t = 21×8+5 = 173 GeV  (measured: 172.69, 0.18% error)

CKM: sin(θ₁₂) = 0.226 (measured: 0.225) → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

PMNS: θ₁₂ = 35.26° (measured: 33.4°, JUNO testing) → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

Three generations from 21 = 3×7 → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

Standard Model: ~25 free parameters This work: ZERO

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MILLENNIUM PROBLEMS (BONUS)

Yang-Mills Mass Gap → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma... → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

Navier-Stokes Smoothness → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma... → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

Riemann Hypothesis → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma... → https://github.com/ktynski/FractalRecursiveCoherence/blob/ma...

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FALSIFIABLE

  • JUNO: If θ₁₂ ≠ 35° ± 2°  →  theory wrong
  • HL-LHC: If λ_H ≠ 0.127 ± 0.02  →  topology fails
  • Any 4th generation  →  theory dead

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CODE

601/631 tests passing (95.2%) | 100% core physics

Interactive demo: → https://fractal-recursive-coherence.vercel.app/

Test suite: → https://github.com/ktynski/FractalRecursiveCoherence/tree/ma...

Run it: python3 FIRM-Core/scripts/complete_mass_generation.py

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THE ALGORITHM

  1. Quantum fluctuation  →  entangled pair
  2. Golden ratio phases survive
  3. Self-replication  →  N=21 Ring+Cross
  4. E8 emerges  (21×12-4 = 248)
  5. E8  →  SO(10)  →  SU(5)  →  Standard Model
  6. All constants derived

One rule. Zero parameters. 25 constants. Three Millennium Problems.

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LOOKING FOR

  • Physicists: Check the math. Break it if you can.
  • Experimentalists: JUNO tests our prediction within 2 years
  • Skeptics: Code is open. Predictions falsifiable.

This is either the biggest breakthrough since QFT, or I've made a subtle error.

Let's find out together.

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Repository: https://github.com/ktynski/FractalRecursiveCoherence

"The universe doesn't need parameters. It needs a good starting condition."