The Infrared-Cutoff Census: No Premise Selects the Cutoff, for the Whole Class the Holographic Cluster Actually Uses
*2026-11-03 — draft — not deposited* I proved for one member of the holographic dark-energy family — the Granda–Oliveros cutoff, L⁻² = αH² + βḢ — that no premise selects the point: the Cohen–Kaplan–Nelson bound is an inequality and cannot entail its own saturation, and the premises plus today's data leave a whole curve of the (α, β) plane standing (paper #331, gated digit-for-digit in §2). The holographic cluster in the world's literature does not use one cutoff; it uses a class. This paper censuses that class — Hubble, future event horizon, Granda–Oliveros, Ricci — on the census pattern of papers #8 and #423, against the Total Science Index store, where 518 records in the gr-qc lane name holographic dark energy. The four censused cutoffs are named — in a record's title or abstract, which is what was counted; naming, not usage in the record's model — in 190 records (Hubble), 71 (Ricci), 50 (future event horizon) and 50 (Granda–Oliveros); a record may name several, so the counts overlap, and no four-cutoff union or usage majority is claimed from them. (The only union computed is for six cutoffs: 303 of the 518 records name at least one, §3.) The verdict is uniform, and it is an obstruction, not a complaint about practice. The saturation lemma is member-blind: for every L in the class, every density ρ = s·3c²M_p²L⁻² with 0 < s ≤ 1 satisfies the bound, so saturation is assumed at every address in the class, not derived at any. The selection lemma is likewise class-wide: the premise set held in this paper, in the abstract and in §4 alike — the bound, the dimensional form ρ ~ M_p²L⁻², and FRW kinematics — is satisfied by all four cutoffs, and a premise set satisfied by four distinct points of cutoff space entails none of them. (Locality is not among the premises: the future
Authors
- William Alexander Aldred
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-03
- DOI
- https://doi.org/10.5281/zenodo.23925740
- Primary Topic
- Cosmology and Gravitation Theories
- Type
- preprint