ESD Framework: Linear-Cosmology and Galactic-Dynamics Closure of the Zero-Parameter Golden-Ratio Cosmology

We present the linear-cosmology and galactic-dynamics closure of the zero-parameter golden-ratio cosmology introduced in Gravity, Electromagnetism, and the Dark Sector from a Sin-gle Displacement Action with Zero Free Parameters [1], in which a single closure constantc = (4 ln φ − 1)/φ ≈ 0.5715870660 (φ = (1 + √5)/2) fixes the ΛCDM background throughtwo topological-reflection identities (A: ΩΛ = 2πc2/3; B: 3ΩDM + Ωb = 8πc4Ωm). Followingthe ESD framework synthesis [2] we report two readings side by side. Primary (boundary-input): Ωb = 0.0493 is matched to Planck 2018 as boundary data and Identity B then predictsΩDM = 0.2659 (+0.53%); the framework reproduces every linear cosmological observable insideΛCDM error bars with zero standing tension on ωbh2. Secondary (closure-pool): if Identity B isadditionally closed against matter closure and driven from c alone, the framework emits the falsi-fiable zero-parameter prediction Ωb = 0.0501 (+1.61%), ωbh2 = 0.02273 (+2.40σ vs Planck 2018,+0.94σ vs ACT DR4+WMAP, +1.11σ vs BBN-Yeh), with targeted resolution at CMB-S4. Atthe headline cosmology the framework is operationally ΛCDM in every linear channel we test:solver-independent P (k) residual vs Planck ΛCDM that is dominated by the framework’s lockedns = 1 − 2/N ⋆e = 0.9611 tilt prediction (CLASS lock-vs-Planck RMS 3.10% primary / 3.62%secondary; after stripping the analytic (k/kpivot)∆ns tilt the residual collapses to max 0.41%primary / 1.00% secondary across seven decades in k, confirming sub-percent Ω-closure con-sistency with Planck); RSD χ2/dof = 0.44; µeff = 1; sub-cosmic-variance Yukawa screening(λD ≈ 17 RH ); DESI Y1+BOSS BAO χ2/dof = 1.21; KiDS-bin-3 ξ+ shape residual ≤ 1.9%peak (closure-pool benchmark; collapses further under headline); (S8, Ωm) = (0.830, 0.316) sitsat Planck and inherits the standard Planck-vs-cosmic-shear tension at ∼ 2–3σ. The framework’sgauge-cascade inflationary closure additionally predicts ns = 0.9611 (N totale = F12 ln φ = 69.295locked, ∆reh = 17.82 from the parent-action conformal decay width Γχ = m3χ/(24πM 2Pl) asdetailed in Ch. 15 of [2]), sitting at −0.31σ from the Camspec PR4 reanalysis and inside thePlanck collaboration’s own pipeline-systematic envelope. The framework’s distinctive signaturesare nonlinear: disformal lensing Mlens/Mdyn ∈ [1.38, 2.18] at SPARC transition, [1.06, 1.20] inclusters, [5.18, 13.9] in deep MOND (Cassini-safe by more than four orders of magnitude at theactual Cassini geometry u ≈ 2.8 × 106, consistent with [1] §7); structural deep-MOND satu-ration 1 + s/c = 48 replacing MOND’s pa0/gN divergence; and the full SPARC validation∆χ2 = −843 vs MOND across 171 late-type galaxies, already published in [1].