Emergent Spacetime from Multi-Source Informational Projection: Coupled Projection Kernels, Causal Reconstruction, and Observational Constraints

This update paper consolidates and extends the Multi Source Theory (MST), an informational-emergent framework in which observable spacetime, fields and quantum states are modeled as the image of pre-geometric informational domains (Sources) under information-losing Markov projection kernels. Version 1.0 defined the single-source architecture, the push-forward measure, an effective projection stress tensor and falsifiability criteria. Version 2.0 makes four substantive additions: Multi-source formalism. A family of sources with a Gibbs-type inter-source coupling, a composite projection kernel, and a multi-source data-processing theorem implying a quantitative correlation budget: any observable covariance between projected sectors is bounded by sqrt(2 I(S_i;S_j)), where I is the mutual information between sources. Non-local quantum correlations thereby become a constrained consequence of source coupling rather than an independent postulate. A consistency check against the CHSH setting is included. Causal reconstruction. The pre-geometric-to-Lorentzian transition is reduced, via the Malament-Hawking-King-McCarthy reconstruction theorem, to explicit hypotheses on projected causal order and volume data, together with a measurable emergence order parameter (geometricity, via the Myrheim-Meyer dimension estimator). Lovelock reduction. Any local, second-order, covariant projection term merely renormalizes the cosmological constant and Newton's constant; the observable content of MST is therefore necessarily non-local, higher-derivative or matter-coupled. Constraints and a priority sub-model. A unified notation, a table of quantitative observational constraints (PPN, gravitational-wave speed, Lorentz violation, dark-energy equation of state, primordial features, non-Gaussianity, tensor modes, collapse-model bounds) and a single priority sub-model, MST-1, with a parameter-free cross-prediction in CMB polarization. The framework remains a research program: no empirical confirmation is claimed, and explicit rejection criteria are stated. Results previously presented as novel (the data-processing inequality, entropy contraction) are now cited as standard lemmas.