Here I present a minimal statistical estimate for the free-neutron mean life by modeling the neutron as a geometric lock between a ℤ₃-stabilized three-loop proton junction and a single-loop lepton in the Relator framework. Using the kinematic lock R·ω = c, the Euclidean phase-budget split ω² = ω_ℂ² + ω_ℝ³², a maximum-entropy Gaussian collar on the generator space ℂ, and the Relator mapping (ω_ℂ/ω) ² = (2/|g|) ², I obtain a closed-form decay rate in an invariant “attempt × gate” form: Γₙ = (ωₙ/π²) · 𝒢ₙ where 𝒢ₙ ≡ q⁴ · γᵣel · J · PQ Here q and γᵣel are explicitly invariant under exchanging the electron and proton inputs (e ↔ p), while PQ enforces the energy-release requirement Q = (mₙ − mₚ − mₑ) ·c² through the neutron channel ratio ω_ℝ³, n/ωₙ inferred from the measured gₙ. Evaluated with PDG/CODATA inputs, the model yields τₙ (model) = 877. 8277819 s and t₁/₂ (model) = 608. 4638520 s, consistent with the most precise recent bottle value and highlighting the tension with proton-counting beam determinations.
Mehrdad Pajuhaan (Sat,) studied this question.