SSEE Cosmological Framework: A Zero-Free-Parameter Derivation of Dark Energy and the CMB Background (The Complete 7-Paper Suite)

We present the complete suite of seven research preprints defining the Structural Self-Energy Expansion (SSEE-V3.6), a deterministic, zero-free-parameter ($k=0$) cosmological model. The framework derives the expansion history of the Universe, CMB observables, and perturbation scale limits exclusively from the golden ratio (φ) and π, without invoking scalar-field fine-tuning or exotic particle phenomenologies. Version V3.6 constitutes the definitive, peer-review-hardened release. Following extensive internal and external cross-reference audits, all 7 manuscripts are numerically consistent. Major updates in this version include a phenomenological two-sector proposal for the fσ₈ tension (φ-DM), a working Effective Field Theory (EFT) derivation of the dark energy kineticity, and a unified Cobaya MCMC pipeline demonstrating statistical preference for the SSEE background over ΛCDM in specific domains. The Seven-Paper Suite Paper 1 — Theoretical Framework & Predictive Register: Establishes the axiomatic foundation of SSEE. Derives a dynamic dark energy equation of state (w₀ -0.840, wₐ -0.670) directly from geometric symmetries. The native prediction aligns within 0.05σ of DESI DR2 BAO measurements. Paper 2 — Bayesian MCMC Validation (BAO & Clusters): Confronts the theoretical parameters against DESI DR2, Planck 2018 priors, and galaxy cluster data. Key results: H₀ = 66.75 ± 0.44 km/s/Mpc (low-z fit). The =-5.55 physically validates the dynamic dark energy sector over ΛCDM. Paper 3 — CMB Confrontation (MCMC & Canonical Bounds): Tests the theoretical background against Planck 2018 PR4 via a full Cobaya MCMC pipeline. Scanning the parameter space yields H₀ = 67.08 ± 0.03 km/s/Mpc. The resulting = -23.6 (full MCMC) and = -31.3 (diagonal scan) constitute statistical evidence in favour of the SSEE background under this specific model comparison. Paper 4 — Algebraic Derivation of Cosmological Parameters: Formalises the "Nine Sovereignties" theorem: a closed algebraic system predicting the primordial spectral index (nₛ = 1 - φ⁻⁷ ≈ 0.96556), the Hubble constant (H₀ ≈ 67.96), and the matter density (Ωₘ ≈ 0.3201). All predictions are pure algebraic consequences of φ and π. Paper 5 — Israel-Stewart Causal Perturbations: Performs an Israel-Stewart causal viscous perturbation analysis. Proves analytically that the macroscopic effective sound speed vanishes (c²s,eff = 0), causally stabilising the fluid. Evaluates the IS growth index γIS = 0.554, documenting an initial 2.56σ fσ₈ tension due to the single-sector approximation. Paper 6 — The φ-DM Two-Sector Resolution (NEW): Introduces the geometrically required second dark matter sector. The framework algebraically defines a particle mass scale m_φ = 5.71 eV and a free-streaming scale kfs = 0.493\,h/Mpc. The two-sector dynamics phenomenologically reduce the structure growth tension, bringing the fσ₈ mean tension across 6 independent surveys from 2.56σ down to 0.50σ at the linear-growth level. Paper 7 — Effective Field Theory (EFT) of SSEE (NEW): Bridges the geometric macroscopic fluid to a fundamental K-essence scalar field. Derives the bare kineticity αK(0) 0.073 from pure geometry. Proves the existence of a bare physical sound speed cₛ² ∈ [0.60, 0.95] free of gradient instabilities, formally completing the framework's perturbation viability. Key Updates in V3.6 Expanded to 7 Papers: Added formal resolutions for structure growth (Paper 6) and quantum-field kineticity (Paper 7). Tension Reduced: The fσ₈ structure growth tension was phenomenologically reduced down to 0.50σ via the algebraic φ-DM sector. Rigorous Auditing: All cross-references, equations, nomenclature (e.g., c²s,bare vs cₛ²), and MCMC values were mathematically stress-tested and cross-validated across all 7 manuscripts. Full Reproducibility: Includes completely unified Python scripts (ssee_paper6_verification.py, Cobaya MCMC pipelines) required to replicate all figures and findings.