Horizon-Maintenance Dark Energy and Horizon Ledger Occupancy: Pre-Euclid Registration, the Minimal w(a) Relation, and Reconstruction Protocols in Finite Distinction Systems

This paper(FDS-X1) is a conditional physical bridge claim connecting finite observer boundaries to the darkenergy scale. The original pre-Euclid note registered the claim before major Euclid dark-energy data products: if a cosmological horizon is treated as a finite distinguishability boundary, the relevant dark-energy scale should be horizon-like, of order M2 PlH2 0 , rather than a Planck-volume vacuum density. The present version integrates both roles: pre-registration and technical model, sharpening the claim into a horizon-ledger occupancy model. Using the standard horizon entropy and temperature as bridge inputs, a spherical horizon of radius Rh has ledger density ρh = ThSh Vh = 3M2 Pl,redR −2 h in natural units. The dark-energy-like horizon-maintenance component is written ρHM(a) = 3M2 Pl,redµh(a)R −2 h (a), where µh(a) is a bounded horizon-ledger occupancy or response factor. If this component obeys an effective continuity equation, its physical equation of state satisfies wHM(a) = −1 − 1 3 d ln µh d ln a + 2 3 d ln Rh d ln a . The strict non-phantom version is equivalent to the ledger-growth condition d ln µh/d ln a ≤ 2d ln Rh/d ln a. The paper gives an event-horizon specialization, a reconstruction protocol for µh(a), pre-registered outcome and demotion conditions, and normal-form numerical code. It does not derive general relativity, quantum gravity, the Bekenstein-Hawking coefficient, perturbations, or a likelihood-ready replacement for ΛCDM.