ADX-629 Therapy for Sjogren-Larsson Syndrome

Inclusion Criteria: * Patricipant or participant's guardian is willing to provide written informed consent prior to the initiation of any study procedures. Assent will be solicited from participant intellectually capable of providing assent. * Participant is willing to comply with all study procedures and availability for the duration of the study. * Participant is 5-50 years of age at the time of enrollment. * Participant has a genetically-confirmed diagnosis of SLS with two pathogenic sequence variants in ALDH3A2. * Participant has active ichthyosis and neurologic symptoms of spasticity. * Participant is able to swallow oral tablet medication and is willing to adhere to the study regimen. * Participant is willing to suspend use of all topical creams 7 days before initial baseline evaluation and before the 12-week center visit. * Participant has not been treated with any experimental drug for 1 month before baseline visit and during ADX-629 treatment. * Participant who is sexually active agrees to use adequate contraception throughout the duration of the study, as follows: * For females of child-bearing potential: Negative pregnancy test at Baseline and compliant with a medically approved contraceptive regimen during the study or documented to be surgically sterile or postmenopausal. * For sexually-active men: Compliant with a barrier contraceptive regimen during the study. Exclusion Criteria: * History of any malignancy within 5 years of screening except for basal cell or squamous cell in situ skin carcinomas or carcinoma in situ of the cervix that has been treated with no evidence of recurrence. * Participant is known to be human immunodeficiency virus (HIV) positive or has other known immunodeficiency. * Participant has evidence of an active systemic or skin infection, including severe acute respiratory syndrome (SARS-CoV-2). * History of significant tachycardia, bradycardia, acute or chronic cardiovascular disease, or any clinically significant abnormalities in rhythm or conduction detected on electrocardiogram (ECG), or QT interval corrected for heart rate using Fridericia's formula (QTcF) of \>440 ms or \<340 ms during screening. * History or presence of gastrointestinal, hepatic disease, moderate or severe hepatic impairment (defined as Child-Pugh Class B and Class C) or any other condition known to interfere with absorption, distribution, metabolism, or excretion of drug. * Acute or chronic renal disease, moderate or severe renal impairment, history of renal disease, or estimated glomerular filtration rate (eGFR) \<60 mL/min/1.73 m2 calculated by Chronic Kidney Disease Epidemiology (CKD-EPI) equation. * History of any other condition that, in the opinion of the Investigator, would compromise the participant's ability to comply with the protocol or that might compromise the participant's safety or the interpretation of the study results. * Participant is currently receiving immunosuppressive therapy, including intermittent or low-dose corticosteroids and is not able or willing to suspend its use for a period from 2 weeks before and throughout the study. * Participant is currently receiving and refuses to interrupt any systemic or topical medication that is excluded. * Participant received an investigational systemic or topically administered prescription drug within 30 days before enrollment. * Participant has received botulinum toxin (Botox) injections within 6 months of enrollment. * Participant has a known allergic reaction to any ingredients of study drug formulation. * Participant is currently participating in any other therapeutic clinical study. * Participant is pregnant, intending to become pregnant, or breastfeeding.