What question did this study set out to answer?

The study aims to predict the photometric masses of the Little Red Dot population at high redshifts using permutohedron geometry.

May 22, 2026Open Access

Paper CLI of the One-Octonion Brane-Bulk Series Little Red Dots as Self-Lensed Sources in a G2-Permutohedron The Universal a0/(Aperm/4) G Surface Density and a

Key Points

The study aims to predict the photometric masses of the Little Red Dot population at high redshifts using permutohedron geometry.
Applies sump formalism alongside G2 permutohedron geometry.
Analyzes JWST-selected Little Red Dot (LRD) population at z ≳6.
Derives mass predictions without free parameters.
Mean projected surface density of a sump is 279 M⊙/pc2, higher than naive estimates.
Systematic SED-fit mass overestimate of ∼5.7% for the LRD population due to lensing.
No resolved arcs expected at typical LRD Einstein radius of θE ≈3 mas.

Abstract

We apply the sump formalism (Papers XXVI–XXVIII) together with the G2 permutohedron geometry established in Paper CLV (vacuum fluctuations as G2 permuto- hedron bubbles, A = (12 √ 3 + 6)(4/10)R2) to the JWST-selected Little Red Dot (LRD) population at z ≳6, and derive a parameter-free prediction for a systematic overesti- mate of their photometric masses. The central result is that the mean projected surface density of a sump with permutohedron geometry is universal and larger than the naive 2D disk value: Σperm sump = a0/(Aperm/4) G = a0/(2.68 G) = 0.583 kg/m2 = 279 M⊙/pc2, independent of the central black hole mass. This is the disk value a0/(πG) = 238 M⊙/pc2 multiplied by the permutohedron-Cauchy factor π/(Aperm/4) = 1.17. For a source at zS = 10 lensed by a sump at zL = 6, this produces a uniform convergence ∆κperm sump ≈0.027 and a magnification µ ≈1.057 (a 5.7% flux enhancement). Since LRD masses are inferred from fluxes under the implicit assumption µ = 1, the population exhibits a ∼5.7% sys- tematic SED-fit mass overestimate, modulated by DLDLS/DS. The Einstein radius of a typical LRD (MBH ∼107 M⊙) is θE ≈3 mas, far below the Roman Space Telescope PSF, so no resolved arcs are expected. Three formal predictions (CLI-1, CLI-2, CLI-3), zero free parameters. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

Read Full Paperexternally

Ask AI

Mark Helpful

Bookmark

Relay

View Full Paper