The Computational Lagrangian: How an 8D→4D Information Projection Framework Recovers Standard Lagrangian Dynamics, Derives the Cosmological Constant, and Resolves Open Pathologies of Quantum Field Theory

he Lagrangian formulation has been the foundation of theoretical physics since Euler and Lagrange, surviving every paradigm shift from classical mechanics through general relativity to quantum field theory. We demonstrate that the standard Lagrangians of physics---including the Einstein--Hilbert action with cosmological constant, the Standard Model Lagrangian density, and the principle of least action itself---emerge as projected special cases of a more fundamental object: the Computational Lagrangian = -, defined on a discrete octonionic substrate whose structure is forced by triadic closure and computability constraints. The kinetic term measures the information flux through associative (Fano-line) channels; the potential term measures the accumulated non-associative residue sequestered by the total function requirement. The action integral is taken over discrete computational succession, not continuous time. We show that restriction to the 4D projection surface recovers the classical variational framework, with SC = 0 reducing to S = 0. The projection decomposes into two information channels: an eigenvector (coupling) channel of capacity C = 137 and an eigenvalue (mass) channel of capacity M = 125. The framework derives the inverse fine-structure constant ^-1 = 137. 035999143 (Earth observer frame, 1. 62 from CODATA 2022) with zero free parameters, and computes the vacuum energy density _ 6. 1 10^-10~J/m³, matching the observed value 5. 96 10^-10~J/m³ to within 2\%. The cosmological constant emerges as the per-unit bandwidth cost of manufacturing locality---the loco-genesis overhead of the projection channel itself. The 123-order-of-magnitude vacuum energy discrepancy between quantum field theory and observation is not a failure of physics; it is the quantitative measure of the locality assumption's invalidity. We show how six open pathologies of the classical Lagrangian framework---the vacuum energy catastrophe, renormalization, the measurement problem, the 26 free parameters, the hierarchy problem, and QM--GR incompatibility---arise as artifacts of the locality assumption and how the Computational Lagrangian framework addresses each. The framework contains no free parameters at the axiomatic level; specific projections introduce calculable corrections whose full decomposition (particularly the gravitational holonomy () ) remains an open problem. An executable companion code environment implementing the computational framework accompanies this paper. Six falsifiable predictions are specified. All core computations are reproducible. Keywords Computational Lagrangian, variational principle, locality, cosmological constant, vacuum energy catastrophe, octonionic projection, information theory, channel capacity, fine structure constant, Bell's theorem, loco-genesis, emergent spacetime, Fano plane, non-associativity, Standard Model, parameter-free derivation, falsifiable predictions