Hu's Cosmic Spacetime Origin Theory (HCSOT): A Unified Modified Gravity Framework for Dark Matter, Dark Energy, the Hubble Tension, and Cosmic Tensions — V8.6 with Pre-Registered Euclid DR1 Weak-Lensing Prediction (+5.5% to +8.0% at k=0.1 h/Mpc)

Hu's Cosmic Spacetime Origin Theory (HCSOT) is a minimal modified gravity framework based on a single scalar-tensor field. Dark matter and dark energy are unified through density-dependent effective gravitational coupling with one additional free parameter (α ≈ 0.087). The theory addresses the Hubble tension, S₈ tension, DESI DR2 dynamical dark energy, JWST early galaxies, SPARC galaxy rotation curves, cosmic void dynamics, and H0LiCOW strong-lensing time delays. Pre-registered prediction for Euclid DR1 (October 2026): +5.5% to +8.0% enhancement in the weak-lensing matter power spectrum at k = 0.1 h/Mpc relative to ΛCDM (fiducial: +6.4%). The Limber approximation is used to convert P(k) to the angular power spectrum C_ℓ. Detection threshold: 4%–5%. Signal-to-noise ratio: 5.3 (statistical). Monte Carlo validation: 10,000 realisations, 97.7% exceed 5% threshold, 95.3% within [5.5%, 8.0%]. Cosmic variance contribution (~5%–8%) is discussed. Key features of V8.6: · Complete linear scalar-tensor perturbation equations with explicit anisotropic stress σ_φ · Nonlinear saturation model honestly disclosed as empirical parametrisation; rigorous nonlinear solution remains an open problem · Observational evidence hierarchically classified: core prediction / consistency checks / auxiliary cross-checks · Five explicit falsification criteria and three physical prohibitions (no singularities, no heat death, no unbounded gravitational binding) · α = 0.087 independently constrained by local H₀ (SH0ES + H0DN) and Big Bang nucleosynthesis (BBN: α ≥ 0.069, S = 1.044) · 14 companion papers; 19 analysis scripts archived in separate code repository (DOI: 10.5281/zenodo.20104919) · Bayesian evidence: ln B ≈ 4.8 (strong preference over ΛCDM) Version history: The original theoretical framework was first publicly archived as Version 1 on 10 April 2026. This V8.6 (30 May 2026) is the final pre-Euclid-DR1 manuscript. No further revisions are planned unless factual errors are identified. Corrected manuscript PDF to V8.6 Licence: CC BY 4.0