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Variational Backbone and Regime Closures XXI (Dark-Energy Scale): The Holographic Emergence of the Dark-Energy Scale from Partial Observation Why Λ is horizon-set and tiny; why its numerical value is a clock, not a constant
The cosmological-constant problem has two faces, usually conflated. The scale problem asks why the dark-energy curvature is ∼ 10−122 in Planck units rather than of order unity; the coincidence problem asks why its present fractional value is ΩΛ ≃ 0.685. This Part answers the first and argues that the second is not a derivation target. Reading the cosmic horizon as the Part I virtual boundary, we treat its unread exterior as information summarized onto a holographic screen of Nsur = A/ℓ2 P surface degrees at the Part XIV first-law temperature. Under the horizon-screen instance, Jaynes energy placement, Komar bulk dictionary, inherited vacuum-tail equation of state, and compression-saturation gate, the background curvature readout is Λ = 3/R2 ; this relation is not inserted as an input, and the smallness Λℓ 2 P ∼ (ℓP /R) 2 is simply the horizon-to-Planck length ratio squared. Three results make the derivation self-contained within the series. (i) The undetermined Bekenstein– Hawking coefficient cancels in Λ, so the scale survives the open Part XIV normalization. (ii) Neither the equipartition nor the balance is an extra postulate: equipartition is the Jaynes reading of the counted degrees, and the balance is the horizon-screen form of the Internal Invisibility bound Nsur ≥ Nbulk. (iii) That bound is saturated only after the imbalance– compression dictionary gate identifies the holographic imbalance with the Part II compression residual; the closing identity—holographic imbalance proportional to compression residual— then follows from the Komar algebra and the matter-as-summary-footprint reading. The dark-energy scale thus rests on one axiom (Internal Invisibility), one inference principle (Jaynes), and one holographic form (the area law). The value ΩΛ is, by construction, the read fraction of the present epoch—a clock, not a constant—and is left as an explicit non-claim.
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