Sovereign Scaling Resonance (SSR): an Oscillatory Dark Energy Extension of ΛCDM with Cosmological Constraints and Laboratory Falsifiability

We present the Sovereign Scaling Resonance (SSR) model — a pseudo-scalar dark energy field Ξ governed by a cosine potential whose vacuum scale is anchored to the Planck–proton mass-ratio hierarchy: pₛₛᵣ = Mₚ⁴/ζ⁶, where ζ = Mₚ/mₚ ≈ 1.29 × 10¹⁹. The exponent n = 6 is the unique integer placing pₛₛᵣ within a factor of three of the observed dark energy density; it is an empirical anchor, not a derived prediction. We derive the equation of state analytically from the field action via a WKB treatment of the linearised scalar equation in e-fold time, obtaining w(z) ≈ −1 + A sin[ω ln(1+z) + φ]. The shift symmetry of the cosine potential requires, by standard effective field theory, an axion-photon coupling ℒ = −(gᵐˠʳ/4fᴹ)Ξ FμνḜᴵμ, which we derive without additional assumptions and which connects the cosmological model to near-future laboratory experiments. We confirm ghost-free and tachyon-free stability analytically, and derive an oscillatory correction to the effective gravitational coupling Gₑⁱ(z) that provides a coherent weak-lensing target for Stage-IV surveys. Bayesian inference using Cobaya against Pantheon+ supernovae, DESI 2024 BAO (DR1), and fσ₈ growth-rate data, with four parallel Metropolis–Hastings chains (59,444 accepted steps, R−1 = 0.029), yields H₀ = 70.75⁺⁰·‸⁸₋⁰·‸⁴ km s⁻¹ Mpc⁻¹ (1.7σ from SH0ES), Ωₘ = 0.2714⁺⁰·⁰⁰‸⁷₋⁰·⁰⁰⁷‹, A = 0.033⁺⁰·⁰²⁰₋⁰·⁰‸⁰, ω = 5.43⁺⁰·⁷³₋⁰·⁵⁰, and axion decay constant fᴹ = 0.504⁺⁰·³¹₋⁰·³² (68% CI). The SSR model improves the growth-rate fit by Δχ² = −21.7 relative to a matched-pipeline ΛCDM reference (ΔBIC = +33.8). The SSR field mass mᴲ ≈ 5 × 10⁻³ eV places it directly in the target range of ALPS II, PVLAS-FIN, and CAST-IAXO, providing an independent laboratory falsifiability channel.