Spacetime is shown to possess a finite capacity for mutually distinguishable relational configurations. This work formalizes that capacity as a structural boundary condition—Finite Adjacency Closure—imposed as a global consistency requirement on physical law. The requirement is expressed as the Adjacency Network Theorem (ANT): any physically consistent description of spacetime admits only finitely many distinguishable relational configurations. This single boundary condition is sufficient to resolve both the cosmological constant hierarchy and the normalization of gravity without modifying quantum mechanics or general relativity and without introducing new observables. From holographic consistency, trace normalization, and infrared saturation alone, admissible adjacency growth is forced to follow Fibonacci recursion and to terminate at a unique closure depth of N⋆= 287. At this depth, adjacency growth saturates into a finite, strongly connected relational structure—the Finite Junction Web (FJW) —which contains the complete set of mutually distinguishable configurations permitted by physical consistency. The FJW defines a single dimensionless invariant, the Latent Entanglement Number (LEN) capacity ℒcap ≈ 6. 64×10⁵9, representing the total admissible inventory of relational configurations, distinct from trace-based history counts. Local matter–energy restricts accessible configurations on the FJW through the Matter–Entanglement Link (MEL), producing curvature as a macroscopic response of a finite relational substrate rather than as a fundamental interaction. Vacuum energy suppression follows directly from bounded configuration counting and correlation redundancy on the saturated FJW, yielding the Emergent Network Zero-point Organization (ENZO) dual hierarchy in which the vacuum-to-Planck energy density ratio scales as the inverse square of ℒcap, with a fixed dimensionless spectral coefficient — the Eigenvalue–Spectral Trace Invariant Functional (ESTIFA) —determined by closure alone. Unity-trace normalization at the saturation boundary of the FJW produces a finite limit–derivative residue, a length scale emerging solely from closure. Combining ENZO scaling with trace normalization yields a finite infrared gravitational normalization fixed entirely by fundamental constants and the single invariant ℒcap. No independent cosmological or gravitational observables are introduced; quantities such as the Hubble parameter or dark energy fraction, where referenced, appear only as reparameterizations of standard measurements and are not required for internal closure. Quantum mechanics remains intact as amplitude accounting over a finite admissible configuration space, while General Relativity remains intact as the continuum description of large-scale adjacency deformation of the FJW. Their apparent tension is resolved by recognizing that both operate on a finite relational substrate subject to global closure. The framework introduces one invariant, zero tunable parameters, and no modified dynamics, while yielding falsifiable late-time cosmological consequences. Finite adjacency closure, as formalized by ANT, is identified as an underlying consistency condition of physical law: closure through finite distinguishability.
Rommel Milan Wong (Thu,) studied this question.