STRUGGL LIVING SCIENCE · ZERO-LLM-MATH ENGINE 1,104 PEER-REVIEWED STUDIES · 8 DETERMINISTIC PILLARS

Living Science & Interactive Calculators

Every Struggl coaching decision is governed by deterministic sports-science equations backed by 1,104 peer-reviewed studies and empirical finisher datasets. Explore the 8 interactive calculators and verifiable reference tables below:

Pillar	Deterministic Subsystem	Primary Equation / Guardrail	Foundational DOI
01 · Wathan 1RM & RPE	`Prescriptive Load Subsystem`	Piecewise Wathan + Zourdos RPE (-2.5%/RIR) + Total BW System Load	`10.1519/00124278-199711000-00001`
02 · Implicit RPE	`Implicit RPE & Capacity Subsystem`	Wathan Curve Inversion & Hard-Set Filter (RPE >= 6.0 / <= 4 RIR)	`10.1007/s40279-024-02069-2`
03 · Fractional Volume	`Fractional Volume Matrix Subsystem`	1.0x Primary / 0.5x Secondary across 17 Muscles vs MEV/MAV/MRV	`10.1080/02640414.2016.1210197`
04 · Hybrid EWMA ACWR	`Hybrid EWMA Workload Subsystem`	0.82^d Acute / 0.96^d Chronic Decay + Foster Monotony	`10.1136/bjsports-2016-096589`
05 · Interference Tax	`Concurrent Interference Subsystem`	6h/3h AMPK-mTOR Clock + 36h Glycogen + 48h Hinge Recovery	`10.1519/JSC.0b013e31823a3e2d`
06 · Hyrox Compromised Run	`Hyrox Pace Decay Subsystem`	200k-Finisher Speed-Tier Decay (+17.2% to +24.0%) & Lap 1-8 Multipliers	`10.3389/fphys.2025.1519240`
07 · Tanaka + Karvonen Zone 2	`Autonomic HRR Zone Subsystem`	HRmax = 208 - 0.7*Age + Karvonen HRR vs 220-Age Error	`10.1016/S0735-1097(00)01054-8`
08 · 4-Rule Plan Gate	`4-Rule Plan Gate Subsystem`	Adherence Ledger + Capacity + ACWR > 1.5 + Pain >= 7/10 Gate	`10.1007/s40279-017-0795-y`

PILLAR 01 · Prescriptive Load Subsystem

Prescriptive Load Engine (Piecewise Wathan 1RM, RPE Discount & Bodyweight Calisthenics)

wathan_factor(reps) = 1.0 if reps==1 else 0.4880 + 0.538 * exp(-0.075 * reps); rpe_discount = (10.0 - target_rpe) * 0.025; intensity_pct = max(0.30, wathan_factor - rpe_discount); For weighted calisthenics (is_bw=True): target_total = e1rm * intensity_pct, prescribed_added_kg = target_total - bodyweight_kg.

Primary DOI: ISBN:978-0873226998 · Open Interactive Calculator →

PILLAR 02 · Implicit RPE & Capacity Subsystem

Implicit RPE & Hard-Set Filter (Zero-Input RIR Deduction & Capacity Envelope)

Given athlete e1RM and logged (weight, reps): max_reps = max_reps_at(e1rm, total_load); rir = max(0.0, max_reps - reps); inferred_rpe = clamp(10.0 - rir, 5.0, 10.0).

Primary DOI: 10.1007/s40279-024-02069-2 · Open Interactive Calculator →

PILLAR 03 · Fractional Volume Matrix Subsystem

Fractional Hypertrophy Volume Matrix (1.0x Primary / 0.5x Secondary across 17 Muscles vs MEV/MAV/MRV)

Iterates over 17 fine muscle groups (17-muscle anatomical taxonomy). Each hard set (RPE >= 6) credits +1.0 set to `muscles_primary` and +0.5 set to `muscles_secondary`.

Primary DOI: 10.51224/SRXIV.460 · Open Interactive Calculator →

PILLAR 04 · Hybrid EWMA Workload Subsystem

Unified Hybrid Load & EWMA ACWR (0.82^d Acute / 0.96^d Chronic Decay + Foster Monotony)

Exponentially weighted daily load: ACUTE_DECAY = 0.82 (7d window, yesterday = 82% of today), CHRONIC_DECAY = 0.96 (28d window). Solves the 7-day rolling average boxcar lag.

Primary DOI: 10.1136/bjsports-2016-096589 · Open Interactive Calculator →

PILLAR 05 · Concurrent Interference Subsystem

Concurrent Training & Interference Tax Engine (6h/3h AMPK-mTOR Clock, Glycogen & 48h Hinge Window)

5 deterministic rules: (1) Same-day gap < 3.0h = high severity, < 6.0h = moderate; (2) Glycogen-depleting run (>= 15km or >= 90min) within 36h before heavy legs; (3) Quality run within 48h after heavy hinge/squat; (4) Back-to-back quality runs <= 24h; (5) Hard run share > 20% (Seiler 80/20 rule).

Primary DOI: 10.1519/JSC.0b013e31823a3e2d · Open Interactive Calculator →

PILLAR 06 · Hyrox Pace Decay Subsystem

Hyrox Compromised Running & Station Variance Engine (200k-Finisher Speed-Tier Decay & Lap 1-8 Multipliers)

Piecewise linear interpolation of compromised running slowdown based on standalone 5K time: (<=17:00 -> 1.172x, 20:00 -> 1.180x, 22:30 -> 1.192x, 25:00 -> 1.205x, 30:00 -> 1.225x, >=35:00 -> 1.240x).

Primary DOI: 10.3389/fphys.2025.1519240 · Open Interactive Calculator →

PILLAR 07 · Autonomic HRR Zone Subsystem

Dual Tanaka + Karvonen Heart Rate Reserve (HRR) Zone 2 Calculator vs 220-Age Error

max_hr = max_hr or round(208 - 0.7 * age) [Tanaka 2001]; If rest_hr is known: Karvonen HRR = round(rest_hr + pct * (max_hr - rest_hr)); Zone 2 = 60% to 70% HRR.

Primary DOI: 10.1016/S0735-1097(00)01054-8 · Open Interactive Calculator →

PILLAR 08 · 4-Rule Plan Gate Subsystem

4-Rule Plan Gate & Missed-Workout Rescheduler (Adherence Ledger, Capacity Gate, ACWR Gate, Pain Gate)

4-Rule Deterministic Plan Gate: (1) capacity_findings (blocks loads > e1RM * 1.05 or > max_reps + 2), (2) load_findings (blocks RPE >= 8 when ACWR > 1.5), (3) pain_findings (blocks exercises hitting body_area with pain >= 7/10), (4) interference_findings (blocks concurrent training violations).

Primary DOI: 10.1007/s40279-019-01236-0 · Open Interactive Calculator →