miguel angel franco leon

From Simplicial Minimality to Spectral Dimension: Why 4 × 2 = 8 Does Not Yield ds = ln8

A non-degenerate simplex in three dimensions has four vertices. Separately, the SU(2)- invariant intertwiner space of a four-valent j = 1/2 node is two-dimensional. Their product is eight. It is tempting to set beff = 8 and ds = ln 8.That identification is not a theorem. This not...

From Simplicial Minimality to Spectral Dimension: Why 4 × 2 = 8 Does Not Yield ds = ln8

A non-degenerate simplex in three dimensions has four vertices. Separately, the SU(2)- invariant intertwiner space of a four-valent j = 1/2 node is two-dimensional. Their product is eight. It is tempting to set beff = 8 and ds = ln 8.That identification is not a theorem. This not...

The Minimal Simplex Principle: Tetrahedral Coordination as a Combinatorial Necessity in R³

Several independent approaches to quantum gravity employ tetrahedral or 4-valent building blocks — loop quantum gravity uses 4-valent spin-network nodes, causaldynamical triangulations sum over 4-simplices — but in each case the tetrahedron is introduced as a convenient discretiz...

The Minimal Simplex Principle: Tetrahedral Coordination as a Combinatorial Necessity in R³

Several independent approaches to quantum gravity employ tetrahedral or 4-valent building blocks — loop quantum gravity uses 4-valent spin-network nodes, causaldynamical triangulations sum over 4-simplices — but in each case the tetrahedron is introduced as a convenient discretiz...