Education around immediate changes to improve diet quality and barriers to dietary behaviour change. Participants will consume a whole-food diet focused on improving diet quality based on the NOVA classifications of unprocessed or minimally processed foods/ingredients (removal of NOVA category 4 foods from diet). This diet is high carbohydrate (45-65% of total energy coming from carbohydrate, 20-35% from fat and 15-25% from protein) based on the Australian dietary guidelines focusing on the consumption of low-energy, nutrient dense whole foods. The higher carbohydrate diet reflects current contemporary 'standard care' dietary recommendations as outlined by the National Health and Medical Research Council's Australian Dietary Guidelines, and therefore represents the most appropriate control diet to compare to the effects of the proposed intervention.

Markers of sleep micro-architecture during PSG including sleep onset latency, REM onset latency, sleep duration, sleep efficiency measured at 12 weeks compared with baseline.

Change in Narcolepsy Severity Scale measured at 12 weeks compared with baseline and 3 weeks.

The Narcolepsy Severity Scale is a 15-item self-reported outcome measure validated for use in NT1 patients. It evaluates the severity, frequency, and impact of the 5 main narcolepsy symptoms (EDS, cataplexy, hallucinations, sleep paralysis, and disrupted night-time sleep). Total score ranges from 0 to 57, with higher scores indicating more severe symptoms. Except for cataplexy, these narcolepsy symptoms are also relevant for some NT2 patients, and thus, we will use the Narcolepsy Severity Scale in both NT1 and NT2 patients.

Change in Idiopathic Hypersomnia Severity Scale measured at 12 weeks compared with baseline and 3 weeks.

The Idiopathic Hypersomnia Severity Scale is a self-reported measure validated in patients with IH. It is a 14-item questionnaire that measures aspects of night-time and daytime sleep symptoms and the sleep inertia related to each, as well as impaired daytime functioning due to hypersomnolence. Symptom frequency, intensity, and consequences are rated using a 3- or 4-point scale. Total score ranges from 0 to 50, with higher scores indicating more severe and frequent symptoms.

Weekly cataplexy rate (in patients with NT1 only): patients will be asked the number of cataplectic events each day (and description if full or partial events) alongside the sleep diary in week 12 (prior to the final visit), compared to the week prior to baseline, and during week 3 (the week prior to randomisation).

Karolinska Sleepiness Scale (KSS): Participants will be asked to rate their sleepiness before each MWT trial using the KSS, a 9-point Likert scale designed to assess their state of sleepiness at any given time measured at 12 weeks compared to baseline. A higher KSS score indicates a higher level of subjective sleepiness.

Change in Epworth Sleepiness Scale: Participants will be asked to rate on a 4-point scale (0-3), their usual chances of dozing off or falling asleep while engaged in eight different activities to provide an indication of their daytime sleepiness measured at 12 weeks compared to baseline and 3 weeks. Higher scores suggest higher levels of excessive daytime sleepiness.

The PVT will be used to assess sustained attention via a simple reaction time task. The device is a hand-held box with a red-light emitting diode display of a three-digit millisecond counter (PVT-192, Ambulatory Monitoring Inc, Ardsley, NY, USA). Participants are instructed to respond as fast as possible when they first see a visual stimulus appear. The time taken to respond to the stimulus is displayed in milliseconds (ms). During each 10-minute PVT session, visual stimuli appear at variable intervals between 2 to 10 seconds. The PVT response variables to be analysed are: a) mean reciprocal reaction time (RT); b) mean of the fastest 10% of RTs; c) mean reciprocal of slowest 10% of RTs; and, d) number of lapses (response time >500ms). Tests will take place after each MWT trial.

Quantitative analysis of the EEG from PSG data for assessment of sleep microarchitecture including power spectral analysis across all frequencies throughout the entire sleep period and separately in REM and non-REM sleep, K-complexes, and sleep spindles. These will be measured at 12 weeks compared to baseline.

The key metabolic efficacy outcome is the blood pathology-based measure of high sensitivity C-reactive protein (hs-CRP) at 12 weeks compared with baseline.

The key quality of life efficacy outcome is the 36-Item Short Form Survey (SF-36) summary scores (Physical Component Summary score and the Mental Component Summary) at 12 weeks compared with baseline.

The SF-36 is a 36-item, patient-reported measure of health status consisting of eight scaled scores, which are the weighted sums of the questions in their section. Each scale is directly transformed into a 0-100 scale on the assumption that each question carries equal weight. The lower the score the more disability. The higher the score the less disability.

Laboratory Analyses for metabolic risk, inflammatory markers and hormones: A 25mL fasted blood sample will be collected by a trained professional at a commercial laboratory at baseline and at 3 months to assess cardio-metabolic risk and inflammatory status at baseline, end of week 3 and week 12. Outcome measures will include hs-CRP, erythrocyte sedimentation rate (ESR), fasting glucose and insulin [HOMA-IR for insulin resistance], blood lipids and lipoproteins and liver function.

Anthropometry and vitals data: weight, waist circumference, neck circumference, heart rate and blood pressure will be measured at baseline and 12 weeks.

Assessment of mood and quality of life will be assessed at baseline, 3 weeks and 12 weeks using the SF-36: The 36-Item Short Form Survey (SF-36) is a 36-item, patient-reported survey of patient health. The SF-36 is a measure of health status consisting of eight scaled scores, which are the weighted sums of the questions in their section. Each scale is directly transformed into a 0-100 scale on the assumption that each question carries equal weight. The lower the score the more disability. The higher the score the less disability.

Assessment of mood and quality of life will be assessed at baseline, 3 weeks and 12 weeks using the Hospital Anxiety and Depression Scale (HADS): The HADS is a self-report rating scale of 14 items on a 4-point Likert scale (range 0-3). It is designed to measure anxiety and depression (7 items for each subscale). The total score is the sum of the 14 items, and for each subscale the score is the sum of the respective seven items (ranging from 0-21). Higher scores indicate higher levels of anxiety or depression.

Assessment of mood and quality of life will be assessed at baseline, 3 weeks and 12 weeks using the EQ-5D-5L: The EQ-5D questionnaire comprises two parts. The first is the EQ-5D descriptive system, respondents are asked to tick boxes to indicate the level of problem respondents experience on each of the five dimensions. The combination of these ticks under each dimension describes that person's EQ-5D self-reported health state. The second part of the questionnaire is the EQ VAS, so called because it incorporates a Visual Analogue Scale. This captures the respondent's overall assessment of their health on a scale from 0 (worst health imaginable) to 100 (best health imaginable).

Assessment of mood and quality of life will be assessed at 12 weeks only using the Clinical Global Impression Instrument: rating scales are measures of symptom severity, treatment response and the efficacy of treatments. It is a brief 3-item observer-rated scale undertaken by the clinician at the end of an intervention period. It consists of a severity scale, an improvement scale and an efficacy index. Severity of illness is rated on a 7-point scale, ranging from 1 (normal) through to 7 (amongst the most severely ill patients). Global improvement is rated on a 7-point scale, ranging from 1 (very much improved) to 7 (very much worse). Efficacy index describes both therapeutic efficacy and treatment-related adverse events and range from 0 (marked improvement and no side-effects) to 16 (unchanged or worse and side-effects outweigh the therapeutic effects).

Each component of the CGI is rated separately; the instrument does not yield a global score.

The following information will be collected via a survey at the time of enrolment: age, sex, health status, evidence of diagnosis as per inclusion criteria, time since diagnosis and medications relating to participant HS condition.

The following demographics will be measured at the baseline and 12 week visits: height (baseline only), weight, waist circumference, office blood pressure.

Aim to characterise participant behaviour and lived experience through surveys including diet satisfaction: convenience, flexibility and enjoyment. The 45-item Dietary Satisfaction Questionnaire (DSat-45) uses seven scales to assess characteristics that influence diet satisfaction: Healthy Lifestyle, Convenience, Cost, Family Dynamics, Preoccupation with Food, Negative Aspects, and Planning and Preparation. The items are assessed using five responses ranging from 'Disagree Strongly' to 'Agree Strongly', which are scored from 1 to 5. Items are reverse-scored if necessary, so that higher scores indicate greater diet satisfaction, and scale scores are created by averaging scores across items. A Total Diet Satisfaction score is also calculated by averaging all item scores. This will be measured at the end of 3 and 12 weeks only.

Aim to characterise participant behaviour and lived experience through diaries including macronutrient/micronutrient change: Measurement of increased nutrient density or changes in macronutrient distribution assessed using 24-hour food recalls. Participants will use the ASA24 (2016, Australian version) developed by the National Cancer Institute (USA) and adapted to the Australian context by Australian researchers. It is a self-administered 24-hour dietary recall tool that enables a multiple, automatically coded food diary. It provides food choices based on the Australian Food, Supplement and Nutrient database (AUSNUT) 2011-13. Data will be collected prior to each telehealth consultation. This will be measured at baseline 3, 4, 6, 8, 10 and 12 weeks only.

Aim to characterise participant behaviour and lived experience through objective measures of compliance including dietary adherence measured by ketosis level: The level of ketones achieved and duration of ketone levels within the nutritional ketosis range (0.5-3mmol/L) as ascertained by a finger-prick test using an Abbott Freestyle Optium Neo (https://www.youtube.com/watch?v=X819\_lhKpw0) and urinary dipsticks. All participants will measure morning and evening capillary ketones two days per week.

Aim to characterise participant behaviour and lived experience through objective measures of compliance including dietary adherence measured by ketosis level: The level of ketones achieved and duration of ketone levels within the nutritional ketosis range (0.5-3mmol/L) as ascertained by urinary dipsticks. All participants will measure afternoon/evening urinary ketone levels four times per week.

Aim to characterise participant behaviour and lived experience through objective measures of compliance including habitual sleep-wake data: will be collected to describe temporal patterns of sleep and activity. This will be measured using 7-day actigraphy monitors (GeneActiv wrist watch) in the week prior to baseline visit, the end of week 3 and during week 12.

Aim to characterise participant behaviour and lived experience through diaries including habitual sleep-wake data: will be collected to describe temporal patterns of sleep and activity. This will be measured using a modified Karolinska sleep diary in the week prior to baseline visit, the end of week 3 and during week 12.

Aim to characterise participant behaviour and lived experience through surveys including Patient Reported Experience Measures: collect information about the experience of health services, and the outcomes of health services, as described by patients. At baseline, the Longitudinal PREM will be collected. This survey collects information related to adults receiving care that extends over a long period of time and is seen as a longitudinal capture of a person's experience.

Aim to characterise participant behaviour and lived experience through surveys including Patient Reported Experience Measures: collect information about the experience of health services, and the outcomes of health services, as described by patients. At baseline, the Patient Assessment of Chronic Illness Care (PACIC) will be collected. This survey collects information related to adults receiving care that extends over a long period of time and is seen as a longitudinal capture of a person's experience.

Aim to characterise participant behaviour and lived experience through surveys including Patient Reported Experience Measures: collect information about the experience of health services, and the outcomes of health services, as described by patients. At 12 weeks, the Outpatient PREM question set will be collected. This survey collects data capturing the patients' experiences of outpatient clinics and services.

Qualitative data will be collected through semi-structured interviews related to the patient experience.

Thematic analysis of these qualitative interviews will be conducted at three key timepoints during the intervention. These will align with:

• The commencement of intervention (to characterise the patient lived experiences and expectations),
• The end of the three-week whole food run in period (dietary change evaluation),
• The end of the twelve-week intervention (process evaluation).

Overall project evaluation will be assessed using the implementation plan using the RE-AIM Framework and the CFIR framework.

The implementation plan will evaluate the randomized controlled trial in synchrony with thematic analysis of a series of qualitative interviews conducted at three key timepoints during the intervention. These will align with the commencement of intervention (to characterise the patient lived experiences and expectations), at the end of the three-week whole food run in period (dietary change evaluation), and at the end of the twelve-week intervention (process evaluation). These interviews will provide a platform to better understand the patient experience during the intervention and will guide future iterations of the program.

The evaluation methodology will use a combination of the RE-AIM (Reach, Effectiveness, Adoption, Implementation, Maintenance) and CFIR (Consolidated Framework for Implementation Research) dissemination and implementation frameworks.