A foundational framework for epistemic objectivity based on transversal convergence across metalogically independent regimes of validation. Introduces the Metalogical Convergence Theorem, demonstrating that structures attain objective status not through correspondence or consensus, but through inevitability under constraint across all adequate modes of representation. Provides a principled resolution of intra-regime incompleteness within the proposed framework and foundations for validation in multi-model science. Overview. This work addresses a foundational problem in contemporary epistemology and philosophy of science: when does convergence within a representational system become epistemically binding, rather than merely regime-relative? The paper develops a second-order extension of projective epistemology by introducing metalogical convergence—the requirement that epistemic objectivity arises only when structural invariance emerges across metalogically independent validation regimes, each governed by distinct failure conditions (e.g., deterministic, stochastic, and inductive validation logics). Within the proposed projective-operator framework, knowledge is formalized as constrained projection from a non-axiomatic source of constraint (“reality”) into representational domains; truth is treated as the limit of refinement under constraint within a regime; and objectivity is identified with invariance enforced by transversal failure across independent validation logics. The Metalogical Validation Principle distinguishes local (regime-level) truth from metalogical (trans-regime) truth. The Metalogical Convergence Theorem characterizes when a candidate structure is unavoidable under independent refinement, explaining why certain structural relations persist across theoretical change while others remain artifacts of a single regime. The paper also provides a failure-mode analysis that separates genuine metalogical independence from pseudo-independence driven by hidden shared assumptions, clarifying when apparent convergence is epistemically non-binding. The resulting framework offers general foundations for validation under model pluralism and multi-model science, with implications for robustness, confirmation, and theory change. Version & Access Note. Current version: working manuscript (restricted access). This Zenodo deposit serves as a versioned repository during ongoing refinement.