What determines the critical density of the universe? An information-theoretic approach.

I've been working on connecting the Standard Model particle content to cosmological observables through the Bekenstein entropy of the cosmological horizon. The main result:

ρ_crit = (N_SM / S_horizon) × M_P⁴ / (32π²)

where N_SM = 118 is the Standard Model helicity count (45 Weyl fermions × 2 + 28 bosons), S_horizon = πR_H²/l_P² is the Bekenstein entropy, and M_P is the Planck mass.

This simplifies to ρ_crit(predicted)/ρ_crit(observed) = N_SM/(12π²) = 118/118.435 = 0.9963.

The interesting property: the Hubble constant cancels algebraically. Both S_horizon and ρ_crit depend on H₀², but the ratio doesn't. The cancellation follows from l_P² × M_P⁴ × G = c⁴ (exact from Planck unit definitions). The only free input is N_SM, which is a discrete count.

The 32π² decomposes as 2 × 16π², where 16π² is the standard one-loop phase space factor in 3+1D and the factor of 2 comes from the Bures metric normalization in quantum state space.

Full derivation with proofs: 10.5281/zenodo.19372857

I'm looking for feedback on whether this relationship has appeared elsewhere in the literature, and whether the physical interpretation (heat engine efficiency of the cosmological horizon) holds up.

One of the biggest mysteries in physics is why the universe has the energy density it does. We can measure it, but nobody can explain why it's that specific number.

I found a formula that gets within 0.37% of the observed value using just two inputs: how many types of particles exist (118 in the Standard Model) and how much information the universe's horizon can hold (the Bekenstein entropy).

The formula boils down to a surprisingly simple ratio: 118 / (12π²) = 0.9963.

The number 118 is just counting, how many distinct particle states the Standard Model has. The number 12π² = 118.435 is pure geometry. The fact that these nearly match is either a deep connection between particle physics and cosmology, or the most remarkable coincidence involving π and the Standard Model that anyone has found.

What makes this hard to dismiss as numerology: the Hubble constant (the expansion rate of the universe) cancels out of the formula completely. This isn't fitted to any measurement, it's an algebraic identity that falls out of the Planck unit definitions. The only thing that matters is how many particle species exist.