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Context. Lyman α (Ly α ) emission is highly sensitive to dust and neutral hydrogen and is believed to be suppressed in dusty or hydrogen-rich galaxies – especially during the epoch of reionization (EoR). Yet, moderately dusty Ly α emitters (LAEs) are observed at this epoch, suggesting that complex interstellar medium (ISM) geometries and feedback-driven outflows facilitate Ly α escape. Aims. We investigated the dust, gas, and stellar properties of the gravitationally lensed LAE HCM 6A at z = 6.5676 to characterize its multiphase ISM structure and the physical conditions that regulate Ly α escape. Methods. We combined JWST/NIRISS slitless spectroscopy, HST+JWST/NIRCam imaging, and JWST/NIRSpec slit spectra from the CANUCS program. Using a customized BAGPIPES spectral-energy-distribution-fitting framework with a flexible attenuation law, we derived spatially resolved stellar, nebular, and dust properties on integrated (≈1 kpc), slit-level (≈0.1 kpc), and pixel-level (≈25 pc) measurements, thanks to strong lensing with a magnification of μ ≈ 8.3 − 9.1. A high-quality Ly α map from SLEUTH , a tool for extracting spatially resolved emission-line maps from slitless spectroscopy, traces the spatial distribution of Ly α emission. Results. We measure an unlensed stellar mass of log M * = 8.3 − 8.4 and an intrinsic UV magnitude of M UV = −19.8 ± 0.1. Slit-level measurements show that the oldest, most massive region (S1) is moderately dusty with consistent stellar ( A V , β ) and nebular ( A V B , line-emission) indicators, implying a uniform ISM geometry, while the dust tracers of the youngest region (S3) are highly mismatched, revealing a complex, feedback-shaped multiphase ISM. Ly α emission arises primarily from S3. Pixel-level maps reveal a dust-cleared central clump (C3) where Ly α emerges, encircled by dustier outskirts, consistent with a very recent (≲10 Myr) starburst that created Ly α escape channels. Next, slit-level maps show Calzetti-like attenuation curves with a UV bump that increases with stellar age and decreases with V -band attenuation ( A V ), with a tentative detection of a UV bump in S1 at ∼25% of the Milky Way amplitude. Pixel-level maps reveal that both the curve slope ( S ) and the UV bump ( B ) peak in the region between two clumps (C1 and C2), indicating dust-grain processing in a merger-driven starburst. Conclusions. Our observations provide a uniquely detailed, spatially resolved view of a moderately dusty LAE at the EoR, demonstrating how the interplay between multiphase ISM geometry and feedback governs Ly α escape. Constraining some key quantities requires fully resolved spectroscopy, which future JWST/NIRSpec integral field unit observations will provide.
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