A First-Principles Derivation of the Cosmological Constant from an Eleven-Dimensional Covariant Master Action

The normalized cosmic inventory and the cosmological constant are distinct observables of one gravitational solution. The first compares the response carried by different physical sectors, whereas the second is the dimensionful coefficient of the homogeneous metric term in the field equation. We derive both from a stationary reduction of a single eleven-dimensional covariant master action. Information projection supplies the generative structure of the higher-dimensional theory; its cosmological realization is developed through covariant variation, dimensional reduction, the physical constraint quotient, and finite-region gravity. On a regular 4+7 branch, a transported observer coframe and a stationary 1+6 internal splitting decompose the 66-dimensional symmetric response space into sectors of ranks 3, 18, and 45. The seven action terms are assembled before their shared auxiliary variables are eliminated. Unit-normalized sources, complete trace readout, and a common boundary-energy conversion then give Ω_b : Ω_cdm : Ω_bg = 3 : 18 : 45, with (Ω_b, Ω_cdm, Ω_bg) = (1/22, 3/11, 15/22) on the universal response branch. The absolute background coefficient is the first derivative of the reduced on-shell background action along the physical four-volume family, a_Λ = −dΓ_bg,on/dV₄⁽ᵗ⁾, and Λ_geom = (8πG_cos/c⁴) a_Λ. The dimensional realization combines the microscopic formation ruler with a positive finite-source lapse, spatial coframe, York momentum, and source-determined free boundary. The composition trace and proper-time clock determine the homogeneous curvature normalization. Its surface work is realized by the coupled ADM equations, and the finite-volume and Iyer–Wald expressions recover the same coefficient. The positive genus-zero solution gives Λ_bg = 1.0890639698897008 × 10⁻⁵² m⁻²;R_Λ = 1.659716579066454 × 10²⁶ m;H_prop = 67.499884050046 km s⁻¹ Mpc⁻¹. The relative difference from the representative curvature formed from the Planck 2018 base-ΛCDM central parameters is 1.392567232 × 10⁻⁴, with that comparison performed after the stationary solution is determined. The nonlinear source–boundary system has eighty-one stationary event realizations with positive physical Hessians. Complete constrained derivatives give the vacuum susceptibility, nearby dynamical response, and propagation of source and clock uncertainty. An accompanying finite event–boundary calculation exhibits delayed feedback, an attracting periodic orbit, and geometric bifurcations. Its time-dependent information metric, phase response, energy balance, and boundary quantum backreaction are developed together with the full-angular spectral matching. An explicit volume and proper-time map connects these internal dynamical quantities to their spacetime interpretation. Version 2.0: Revision and Expansion Version 2.0 substantially expands the first-principles derivation of cosmic composition and the cosmological constant presented in Version 1.0. The manuscript grows from 430 to 523 pages while retaining its ten-part, thirty-five-chapter structure; the technical appendices now extend from A to P. The principal cosmological results and the central physical interpretation are preserved. The theoretical foundations are connected to the cosmological calculation through precise chapter, section, equation, and page references to the parent eleven-dimensional unified-field theory and the intermediate studies of physical time and absolute scale. New Appendix O provides a bidirectional correspondence between these foundations and the definitions and proofs in the present paper. New Appendix P brings together the finite background and event–boundary realizations, their defining equations, and their numerical data. The derivation is strengthened by fuller proofs connecting source normalization, physical response traces, complete readout, and the common boundary-energy conversion that yields the composition ratio. The constrained stationary response is developed for moving constraint surfaces and for the induced variation of the background partial action along the physical four-volume family. The finite-source lapse receives an explicit positivity, existence, and uniqueness proof on the stated function domain. The nonlinear source–boundary treatment is expanded through exact volume compensation, the explicit volume-multiplier formulation, and the corresponding physical Hessian. The volume-conjugate response, Brown–York surface stress, coupled ADM equations, and Iyer–Wald boundary work are connected more explicitly on the same stationary family. The vacuum analysis incorporates mixed vacuum–volume derivatives. The numerical analysis adds adjoint sensitivities, residual-based estimates of observable errors, and covariance propagation that retains correlations between the common source, clock, and geometric quantities. The existing event–boundary chapter is expanded with the time-dependent information metric, phase fluctuations, full-angular spectral matching, and boundary quantum backreaction. The physical-test chapters also incorporate subsequent reaction-network, recombination-transfer, and conserved-stress growth and lensing calculations, with each numerical realization connected to its own equations and source data. The numerical supplement now goes beyond algebraic checks of tabulated values: it includes executable recalculation of the finite-source lapse, surface normalization and coupled ADM solution, all eighty-one nonlinear source–shape stationary states, the explicit volume-constraint equations, and selected adjoint sensitivities from the supplied upstream arrays. Notation, cross-references, the bibliography, and the abstract have been unified across the complete manuscript.