The Lugon Framework: Informational Foundations of Physical Law; Part V — The Unified Equilibrium: Binding the Invariants

Part V of the Lugon Framework completes the passage from “informational bookkeeping” to a single dynamical law for geometry, energy, and record. Parts I–III established that a sequestered informational domain (ℚ-domain) and the realized geometric domain (ℝ-domain) share a finite horizon capacity and obey a global balance law, while Part IV showed that gravity can be read as curvature feedback to informational exchange. The present paper fuses those ingredients into the Unified Equilibrium: a local constraint in which curvature, stress–energy, and informational flux appear as different faces of one conserved ledger. The resulting equilibrium equation reproduces General Relativity, Quantum Field Theory, and familiar thermodynamics in the appropriate limits, so that standard conservation laws appear as localized projections of a deeper invariance of informational capacity. The construction starts by extending the Part III balance law with the curvature–feedback law of Part IV into a balanced action whose variation yields both the field equations and a conserved Noether “ledger current”. The equilibrium law enforces that any change in realized record within a causal domain must be paid for by a compensating change in curvature and exchange tensor, subject to a finite capacity bound implied by horizons. In the low-entropy early universe, the informational stress is negligible and the unified field equation reduces, to excellent approximation, to GR+ΛCDM with a constant residual curvature baseline Λ0. This recovers standard cosmology as the young-universe limit of the equilibrium and explains why a constant Λ works so well at CMB scales. As entropy and realized record grow, the capacity margin shrinks and the informational stress term µv can no longer be ignored. The effective cosmological term becomes Λeff(t) = Λ0 + δΛ ( S(t) / Scap ) with δΛ→0 as S→0 and | δΛ | ≪ Λ0 over the redshift range probed so far. In this regime, cosmic acceleration is reinterpreted as entropy-compatible expansion: the universe enlarges and redistributes its accessible horizon capacity to keep the ledger within bounds, rather than being driven by a perfectly rigid vacuum fluid. The equilibrium equation then links three classes of observables to the same underlying mechanism: (i) a finite gravitational-wave memory floor set by the minimal permanent ledger update in curvature, (ii) an entropy-linked, nearly constant residual curvature baseline Λ0 with small, late-time drift in Λeff(t) that can surface as early/late H0 tension, and (iii) coherence plateaus in precision clock networks set by the minimum flux of ledger current through the coherence operator. Together, these define an experimental envelope for testing the Unified Equilibrium. Finally, the coercive structure of the equilibrium law explains the arrow of time without inserting it by hand: informational corrections can relax but not fully reverse without violating boundedness, so entropy increases as the universe uses geometric adjustment to preserve capacity while writing new record. In this view, the universe is not sustained by external forces or hidden variables but by continuous self-correction: reality functions as a closed informational ledger, with geometry, energy, and entropy as three accounting languages of one perpetual equilibrium that began in a nearly perfect ΛCDM limit and slowly deforms as the ledger fills.