The Primeon Wavefunction as the Rosetta Stone of Physics

We construct an analytic “primeon wavefunction” in prime-exponent space (p-space) and show
that it simultaneously encodes thermodynamics, quantum phase structure, particle families, chirality,
degeneracy, dark matter, and the cosmic microwave background (CMB). Each prime number 𝑝 defines an
axis in an infinite-dimensional lattice of occupation numbers 𝑛𝑝, with energy 𝐸({𝑛𝑝}) = ∑𝑝 𝑛𝑝 ln 𝑝. The
canonical partition function of this ensemble is the Riemann zeta function 𝑍 (𝜎) = 𝜁 (𝜎) for 𝜎 = ℜ(𝑠) > 1. We define a normalized p-space state

Ψ(n, 𝜃0; 𝑠, m) = 1√𝜁 (𝜎) ∏𝑝[𝑝− 𝜎2 𝑛𝑝 𝑒𝑖𝑛𝑝(𝜏 ln 𝑝+𝑚𝑝𝜃𝑝)] ,

with 𝑠 = 𝜎 + 𝑖𝜏, integer occupations 𝑛𝑝 ≥ 0, eigenphases 𝜃𝑝 ∈ [0, 2𝜋), and curl/winding numbers𝑚𝑝 ∈ ℤ. The normalization by 𝜁 (𝜎) makes the squared modulus equal to a Gibbs distribution on
the arithmetic lattice, in line with earlier number-theoretic statistical models. The factorization over primes is exactly the Euler product, so the self-similarity of number theory becomes a self-similarity of physics. We show how different regimes of 𝜎 (𝑍 (2), 𝑍 (3.5),𝑍 (7), and 𝜎 → ∞) reproduce the long-range forces, weak interactions, nuclear physics, and cosmological heat death. We argue—as a conjecture—that this p-space wavefunction acts as a “Rosetta Stone” translating between number theory and physical phenomena, in the same spirit that zeta-regularized partition functions already appear in quantum field theory and spectral geometry .