The Deepest GLIMPSE of a dense gas cocoon enshrouding a Little Red Dot The detection of strong Balmer breaks and absorption features in Little Red Dots (LRDs) suggests they host active galactic nuclei embedded within dense gas envelopes, potentially powered by super-Eddington accretion. We present GLIMPSE-17775, a luminous (Lbol ∼ 1045 erg s−1) LRD at z = 3.501 behind Abell S1063 (μ ∼ 2), observed with deep JWST/NIRCam and a ∼20 hr (80 hr delensed) NIRSpec G395M spectrum. The data reveal over 40 emission and absorption features, including a rich forest of low-ionization Fe ii lines and numerous broad hydrogen recombination transitions. We use this depth to test the dense-gas interpretation through five independent diagnostics. Nearly all permitted lines show exponential wings with consistent FWHM, a signature of Thomson scattering requiring ne ≳ 108 cm−3. Adopting this width yields MBH ∼ 106.7M⊙, a factor of 10 lower than Gaussian fits, and λEdd ∼ 1.8. Additional diagnostics support the same picture: a pronounced Balmer break (fν,4050/fν,3670 = 2.0 ± 0.1), enhanced He i λ7065 and λ10830 with P-Cygni absorption, Bowen-fluorescent O i λ8446–λ11290 emission requiring Lyβ pumping, and 16 Fe ii lines matching fluorescence models. These features indicate a dense (n ∼ 108 cm−3), partially ionized cocoon where scattering and fluorescence dominate line formation, providing strong evidence that at least some LRDs are powered by super-Eddington black hole growth in the early Universe. 1004 2 IOP Publishing application/pdf