STRUGGL LIVING SCIENCE · PILLAR 02 / 08
VERIFIED DETERMINISTIC CODE + CROSSREF DOIs
Implicit RPE & Hard-Set Filter (Zero-Input RIR Deduction & Capacity Envelope)
Direct Citation Summary (TL;DR for Athletes & AI Retrieval Engines):
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).
Validated against Robinson, Z. P., Pelland, J. C., Remmert, J. F., Refalo, M. C., Jukic, I., Steele, J., & Zourdos, M. C. (2024). Exploring the Dose-Response Relationship Between Estimated Resistance Training Proximity to Failure, Strength Gain, and Muscle Hypertrophy: A Series of Meta-Regressions. Sports Medicine, 54, 2209-2231. (
10.1007/s40279-024-02069-2)
and executed deterministically in the Struggl Implicit RPE & Capacity Subsystem.
1. Interactive Deterministic Calculator
2. Verifiable Reference Benchmark Table
Pre-computed directly from the Struggl Implicit RPE & Capacity Subsystem (infer_rpe):
| Logged Set (% of e1RM × Reps) | Wathan Max Reps at Load (`max_reps_at`) | Deduced RIR (`max_reps - reps`) | Implicit RPE (`infer_rpe`) | Hypertrophy Gate (`_HARD_SET_RPE_MIN = 6`) | Single-Set Load AU (`row_load`) |
|---|---|---|---|---|---|
| 60 kg × 8 reps (e1RM = 100 kg) | 12.0 reps | 4.0 RIR | RPE 6.0 | COUNTS (1.0 Primary / 0.5 Secondary) | 5.3 AU |
| 70 kg × 6 reps (e1RM = 100 kg) | 12.0 reps | 6.0 RIR | RPE 5.0 | EXCLUDED (Warm-Up / >4 RIR) | 2.4 AU |
| 75 kg × 6 reps (e1RM = 100 kg) | 9.6 reps | 3.6 RIR | RPE 6.4 | COUNTS (1.0 Primary / 0.5 Secondary) | 4.8 AU |
| 75 kg × 8 reps (e1RM = 100 kg) | 9.6 reps | 1.6 RIR | RPE 8.4 | COUNTS (1.0 Primary / 0.5 Secondary) | 11.7 AU |
| 80 kg × 5 reps (e1RM = 100 kg) | 7.3 reps | 2.3 RIR | RPE 7.7 | COUNTS (1.0 Primary / 0.5 Secondary) | 6.2 AU |
| 80 kg × 7 reps (e1RM = 100 kg) | 7.3 reps | 0.3 RIR | RPE 9.7 | COUNTS (1.0 Primary / 0.5 Secondary) | 13.3 AU |
| 85 kg × 5 reps (e1RM = 100 kg) | 5.3 reps | 0.3 RIR | RPE 9.7 | COUNTS (1.0 Primary / 0.5 Secondary) | 9.5 AU |
| 90 kg × 3 reps (e1RM = 100 kg) | 3.6 reps | 0.6 RIR | RPE 9.4 | COUNTS (1.0 Primary / 0.5 Secondary) | 5.4 AU |
3. Exact Deterministic Equations (Zero-LLM-Math Architecture)
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).
Three-tier RPE resolution for every logged set: (1) explicit logged RPE, (2) implicit RPE via Wathan inverse against 90-day e1RM envelope, (3) fallback default RPE 7.5.
_HARD_SET_RPE_MIN = 6 (<= 4 RIR). Sets with explicit or inferred RPE < 6 are excluded from hypertrophy volume matrices as warm-up/junk sets.
Anti-hallucination validator scanning AI coach prescriptions against the athlete's measured 90-day capacity envelope (+5% ceiling).
4. Peer-Reviewed Scientific Evidence & CrossRef DOIs (1,104-Paper Corpus)
| Study / Citation | DOI / Identifier | Mechanistic Role in Struggl Engine |
|---|---|---|
| Robinson, Z. P., Pelland, J. C., Remmert, J. F., Refalo, M. C., Jukic, I., Steele, J., & Zourdos, M. C. (2024). Exploring the Dose-Response Relationship Between Estimated Resistance Training Proximity to Failure, Strength Gain, and Muscle Hypertrophy: A Series of Meta-Regressions. Sports Medicine, 54, 2209-2231. | 10.1007/s40279-024-02069-2 |
Definitive meta-regression justifying proximity-to-failure gating (sets within 0-4 RIR / RPE >= 6 drive hypertrophy). |
| Refalo, M. C., Helms, E. R., Trexler, E. T., Hamilton, D. L., & Fyfe, J. J. (2023). Influence of Resistance Training Proximity-to-Failure on Skeletal Muscle Hypertrophy: A Systematic Review with Meta-Analysis. Sports Medicine, 53, 649-665. | 10.1007/s40279-022-01784-y |
Demonstrates that sets terminated far from failure (>4 RIR / RPE < 6) produce markedly inferior hypertrophy. |
| Halperin, I., Malleron, T., Har-Nir, I., Androulakis-Korakakis, P., Wolf, M., Fisher, J., & Steele, J. (2022). Accuracy in Predicting Repetitions to Task Failure in Resistance Exercise: A Scoping Review and Exploratory Meta-Analysis. Sports Medicine, 52(2), 377-390. | 10.1007/s40279-021-01559-x |
Shows lifters under-predict RIR by 2-5 reps on average — motivating Struggl's deterministic implicit RPE derivation from e1RM curves. |
| Hermann et al. (2025) — Without Fail: Muscular Adaptations in Single-Set Resistance Training Performed to Failure or with Repetitions-in-Reserve. (Medicine and science in sports and exercise) | 10.1249/mss.0000000000003728 |
Cited in 1 Nippard audit video(s) |
| Robinson et al. (2024) — Exploring the Dose-Response Relationship Between Estimated Resistance Training Proximity to Failure, Strength Gain, and Muscle Hypertrophy: A Series of Meta-Regressions. (Sports medicine (Auckland, N.Z.)) | 10.1007/s40279-024-02069-2 |
Cited in 1 Nippard audit video(s) |
| Refalo et al. (2022) — Influence of Resistance Training Proximity-to-Failure on Skeletal Muscle Hypertrophy: A Systematic Review with Meta-analysis (Sports Medicine) | 10.1007/s40279-022-01784-y |
Cited in 1 Nippard audit video(s) |
| Lacerda et al. (2020) — Is Performing Repetitions to Failure Less Important Than Volume for Muscle Hypertrophy and Strength? (Journal of strength and conditioning research) | 10.1519/jsc.0000000000003438 |
Cited in 1 Nippard audit video(s) |
| Martorelli et al. (2017) — Strength Training with Repetitions to Failure does not Provide Additional Strength and Muscle Hypertrophy Gains in Young Women. (European journal of translational myology) | 10.4081/ejtm.2017.6339 |
Cited in 1 Nippard audit video(s) |
| Morán-Navarro et al. (2017) — Time course of recovery following resistance training leading or not to failure. (European journal of applied physiology) | 10.1007/s00421-017-3725-7 |
Cited in 1 Nippard audit video(s) |
5. Frequently Asked Questions
What counts as a 'hard set' for muscle hypertrophy?
Based on Robinson et al. (2024, DOI: 10.1007/s40279-024-02069-2) and Refalo et al. (2023, DOI: 10.1007/s40279-022-01784-y), hypertrophy is driven by sets performed within 0 to 4 Repetitions in Reserve (RIR), corresponding to RPE >= 6.0. In the Struggl Hard-Set Filter (RPE >= 6 threshold), sets below RPE 6 are automatically filtered out as warm-up volume.
How does Struggl calculate RPE if I only log weight and reps?
In the Implicit RPE Subsystem, Struggl inverts the Wathan curve against your 90-day e1RM for that exercise to determine the maximum reps possible at that weight, subtracts your performed reps to obtain implied RIR, and computes Implicit RPE = 10 - RIR.