What question did this study set out to answer?

The research aims to identify the unique cosmogenetic constant C_Θ as a solution among various topological invariant combinations from Platonic solids.

February 14, 2026Open Access

The Fourth Golden Number...

Puntos clave

The research aims to identify the unique cosmogenetic constant C_Θ as a solution among various topological invariant combinations from Platonic solids.
Analyzed combinations of the form a + b√5 using defined sets of topological invariants
Calculated geometric relationships associated with Platonic solids
Examined the structure of C_Θ through continuous fractions and Fibonacci relationships
Established connections with the exceptional Lie group F₄
Identified C_Θ = 8 + 20√5 as the unique solution among 36 combinations
Demonstrated a 0.007% deviation from the fine structure constant
Confirmed a gap factor of 541 compared to the second-best combination
Revealed a palindromic structure in the continued fraction of C_Θ
Presented a testable prediction of f(D₂O) = 99.57 Hz for experimental validation

Resumen

We demonstrate that the cosmogenetic constant C_Θ = 8 + 20√5 emerges as the unique solution among 36 possible combinations of the form a + b√5, where a and b belong to the set 4, 6, 8, 12, 20, 30 of topological invariants of the Platonic solids. This combination (8, 20) encodes the Cube-Octahedron duality (8 vertices) and Dodecahedron-Icosahedron duality (20 vertices/faces), reproducing the geometric value of the fine structure constant with 0. 007% deviation, the residual gap corresponding to QED corrections. The gap with the second-best combination is a factor of 541, ruling out coincidence. The continued fraction of C_Θ reveals a palindromic structure containing consecutive Fibonacci numbers (3, 5) and the lock 88 = F₁₁ - 1. We establish the exact connection C_Θ = dim (F₄) + 4 (5√5 - 11) with the exceptional Lie group F₄. This constant constitutes the "Fourth Golden Number, " governing the coupling scale (mass/charge) after φ (linear ratio), φ² (surface), and φ³ (volume). The testable prediction f (D₂O) = 99. 57 Hz offers a direct experimental validation pathway. Nous démontrons que la constante cosmogénétique C_Θ = 8 + 20√5 émerge comme unique solution parmi les 36 combinaisons possibles de la forme a + b√5, où a et b appartiennent à l'ensemble 4, 6, 8, 12, 20, 30 des invariants topologiques des solides de Platon. Cette combinaison (8, 20) encode la dualité Cube-Octaèdre (8 sommets) et Dodécaèdre-Icosaèdre (20 sommets/faces), et reproduit la valeur géométrique de la constante de structure fine avec un écart de 0. 007%, l'écart résiduel correspondant aux corrections QED. Le gap avec la deuxième meilleure combinaison est d'un facteur 541, excluant toute coïncidence. La fraction continue de C_Θ révèle une structure palindromique contenant les nombres de Fibonacci consécutifs (3, 5) et le verrou 88 = F₁₁ - 1. Nous établissons la connexion exacte C_Θ = dim (F₄) + 4 (5√5 - 11) avec le groupe de Lie exceptionnel F₄. Cette constante constitue le « Quatrième Nombre d'Or », gouvernant l'échelle de couplage (masse/charge) après φ (ratio linéaire), φ² (surface) et φ³ (volume). La prédiction testable f (D₂O) = 99. 57 Hz offre une voie de validation expérimentale directe.

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