Multi-Source Theory 3.0: Informational Projections, Gaussian Correlation Bounds, and Cosmological Tests

Multi-Source Theory (MST) investigates whether observable physical states can be described as projections of correlated underlying informational domains. This revision replaces broad emergence claims with a hierarchy of explicit assumptions, conditional mathematical results and a restricted cosmological model. We establish the Bell-locality limitation of classical product projection channels and formulate a separate quantum extension using completely positive, trace-preserving maps. For jointly Gaussian sources and a normalized linear projection Z=X+GY, a Schur-complement argument gives det Cov(Z)/det Cov(X) >= exp[-2I(X;Y)], with a stated equality condition. Its scalar form constrains the source correlation required for variance suppression. We then define MST-G1: two correlated Gaussian primordial fields projected into one adiabatic curvature field, with spectrum P_zeta=P_0(1+2ru f+u^2 f^2) and a fixed localized profile f. This construction enforces positivity and ties two spectral response coefficients. We derive its feature morphology, prove its observational degeneracy with an appropriately chosen single Gaussian field, and compute illustrative CMB spectra with CAMB. Exact linear response statements are restricted to fixed-background, unlensed spectra. A prospective inference protocol addresses null-model non-identifiability, prior dependence and correlated polarization validation. Causal geometry is retained as an open existence and stability problem; the gravitational reduction is restated with the correct Lovelock hypotheses. Reproducible algebraic checks and forward calculations accompany the paper. No observational fit, empirical confirmation, derivation of quantum mechanics or derivation of spacetime is claimed. What changed in version 3.0This is a substantive scientific revision of MST 2.0. It replaces the former primordial feature template with the explicit MST-G1 Gaussian source law and projection, corrects the Bell and Lovelock interpretations, restricts causal reconstruction to its valid conditional setting, and retires the unspecified memory generator. It adds a Gaussian covariance bound, a conditional auxiliary-tracer consistency relation, numerical verification and reproducible CAMB predictions. Files and reproducibilityThe deposit package comprises a main manuscript, technical supplement and source archive containing LaTeX, Python code, exact direct dependency versions, scientific figures, JSON/CSV numerical outputs, a prospective validation protocol and a SHA-256 manifest. CMB outputs are fiducial forward calculations with CAMB 2.0.4, not fits to observed data. Scientific status and assistanceThe work is a research preprint. The mathematical claims depend on their explicit assumptions; the source interpretation is not identified by a single Gaussian power spectrum. No empirical confirmation or independent peer review is asserted. An OpenAI AI assistant contributed substantially to analysis, mathematical reformulation, English drafting, code generation and numerical execution. The human author is responsible for the submitted text and claims. Version and licenseVersion 3.0, prepared 7 September 2026. Original text, code and figures: Creative Commons Attribution 4.0 International (CC BY 4.0). External software and observational data retain their own terms.