Capacity-Fixed Trace-Free Gravity and Non-Perturbative Edge-Partition Boundary Selection

Abstract

This work reframes the cosmological-constant problem by separating what gravity determines locally from what must be selected globally. The exact trace-free field equation Rμν − ¼Rgμν = 8πG(Tμν − ¼Tgμν) places every constant vacuum-stress shift in the kernel of the source projector, preventing vacuum energy from acting as a conventional local gravitational source. The Bianchi identity nevertheless restores a global integration mode, so trace-free gravity alone does not determine its amplitude. The central proposal is to fix this mode through the finite information capacity of the de Sitter horizon: Λcap = 3π/(ℓP²N∂). In this formulation, Λ is neither a bare coupling nor a fitted dark-energy fluid; it becomes an eigenvalue associated with an admissible boundary Hilbert-space sector. The microscopic selector is constructed from a non-perturbative horizon edge theory whose Hamiltonian combines a common physical-kernel constraint, a running sector, and an exact de Sitter edge partition function. Three independent theorem gates determine the required data: a Hopf–Bradlow–APS–Harish-Chandra recursion fixes the Fibonacci/valuation registry rank at Nφ = 292; GLSM and modular stringy-edge matching give b g∂²(ℓP⁻¹) = 0.559754586… and Ξedge ≃ 0.99916928; and the determinant-line calculation yields −log Zedge(q) = ½ln q + Θ∂(q) + SHC(q) + o(1). These ingredients define the free-energy functional Γ∂(q) = q[ln(q/q⋆) − 1] − log Zedge(q) and generate a unique stable terminal scale q⋆ = Ξedge exp[16π²/(b g∂²)] = 3.307251460713979 × 10¹²², without inserting Λobs, qobs, or the observed de Sitter radius as inputs. Projection onto the nearest admissible integer then gives Λ⋆ = 3π/(ℓP²qphys). The resulting invariant sieve connects this amplitude mechanism to anomaly-free quantum constraints, a protected dark-matter charge sector, finite S³ valuation closure, and a hierarchy of observational null tests. Its physical logic is therefore sharply compressed: vacuum shift → trace-free kernel → integration mode → horizon-capacity sector → edge-partition minimizer. Observation is assigned a falsifying rather than calibrating role: BAO, CMB, supernovae, growth, lensing, curvature splitting, free-spectrum reconstruction, and the condition cT = c must all test the same selected edge-character branch. The central research claim is that the celebrated 10¹²² hierarchy need not be placed into the local gravitational action—it can emerge as the non-perturbatively selected information capacity of the physical de Sitter horizon.