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

This paper addresses the scale side of the cosmological-constant problem within VBRC. The problem has two faces that are often conflated: the scale problem, which asks why the dark-energy curvature is extremely small in Planck units, and the coincidence problem, which asks why the present fractional value of dark energy is near its observed epoch-dependent value. Part XXI treats the first as the derivation target and explicitly leaves the second as a clock/readout question rather than a constant to be derived. The construction reads the cosmic horizon as the Part I virtual boundary. The unread exterior of the finite cosmological protocol is summarized onto a holographic screen with area-counted surface degrees of freedom, and the horizon-screen instance uses the Part XIV first-law temperature. With Jaynes energy placement, the Komar bulk dictionary, the inherited vacuum-tail equation of state, and the compression-saturation gate, the background curvature readout becomes Lambda proportional to the inverse square of the horizon radius. The smallness of Lambda in Planck units is then the square of the horizon-to-Planck length ratio, not the result of inserting a raw zero-point vacuum sum. Three structural checks make the scale result internal to the series. First, the undetermined Bekenstein-Hawking normalization coefficient cancels from the curvature readout, so the scale survives the open Part XIV surface-density normalization. Second, the equipartition and balance inputs are not treated as unrelated postulates: equipartition is read as the Jaynes placement of energy over the counted horizon degrees, while the balance is the horizon-screen form of the Internal Invisibility bound between surface and bulk readability. Third, saturation is licensed only after the imbalance-compression dictionary identifies the holographic imbalance with the Part II compression residual. The resulting dark-energy scale rests on one structural principle, one inference principle, and one holographic form: Internal Invisibility, Jaynes inference, and the area law. The present value of the fractional dark-energy density is not derived here; it is interpreted as the read fraction of the current epoch. Part XXI therefore addresses the smallness of the cosmological-constant scale, while keeping the coincidence problem as an explicit non-claim.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-26
DOI
https://doi.org/10.5281/zenodo.20920196
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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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

Yi
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

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

Yi
preprint en

Abstract

This paper addresses the scale side of the cosmological-constant problem within VBRC. The problem has two faces that are often conflated: the scale problem, which asks why the dark-energy curvature is extremely small in Planck units, and the coincidence problem, which asks why the present fractional value of dark energy is near its observed epoch-dependent value. Part XXI treats the first as the derivation target and explicitly leaves the second as a clock/readout question rather than a constant to be derived. The construction reads the cosmic horizon as the Part I virtual boundary. The unread exterior of the finite cosmological protocol is summarized onto a holographic screen with area-counted surface degrees of freedom, and the horizon-screen instance uses the Part XIV first-law temperature. With Jaynes energy placement, the Komar bulk dictionary, the inherited vacuum-tail equation of state, and the compression-saturation gate, the background curvature readout becomes Lambda proportional to the inverse square of the horizon radius. The smallness of Lambda in Planck units is then the square of the horizon-to-Planck length ratio, not the result of inserting a raw zero-point vacuum sum. Three structural checks make the scale result internal to the series. First, the undetermined Bekenstein-Hawking normalization coefficient cancels from the curvature readout, so the scale survives the open Part XIV surface-density normalization. Second, the equipartition and balance inputs are not treated as unrelated postulates: equipartition is read as the Jaynes placement of energy over the counted horizon degrees, while the balance is the horizon-screen form of the Internal Invisibility bound between surface and bulk readability. Third, saturation is licensed only after the imbalance-compression dictionary identifies the holographic imbalance with the Part II compression residual. The resulting dark-energy scale rests on one structural principle, one inference principle, and one holographic form: Internal Invisibility, Jaynes inference, and the area law. The present value of the fractional dark-energy density is not derived here; it is interpreted as the read fraction of the current epoch. Part XXI therefore addresses the smallness of the cosmological-constant scale, while keeping the coincidence problem as an explicit non-claim.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Cosmology and Gravitation Theories
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