endurance-coach-proof-and-analysis-toolkitlisted

Load when you need to PROVE a statistical method in this repo's insight engine is correct, not just invoke it — deriving or checking any estimator in src/insights/stats.ts, correlations.ts, monitoring.ts, metrics.ts, efficiency.ts, or powerCurve.ts. Triggers: "prove it don't just install it", "derive the CI", "why effective-N / effN", "why Fisher-z", "why Bonferroni-before-BH", "how does the permutation null work", "why circular-shift not plain shuffle", "is this estimator right", "is corrWithCi correct", "what's the variance-inflation factor / VIF", "why q=0.1", "why K=400", "why seed 0x9e3779b1", "why the mulberry32 PRNG", "derive CTL/ATL/TSB", "why τ=42/7 not 2/(τ+1)", "why EF~CTL+time not residualise-then-trend", "Frisch–Waugh–Lovell", "what does the power-curve collapse bug teach", "why mean-max power", reviewing a PR that changes a formula, or reproducing a correlation/monitoring/economy number by hand. This is the MATH home: it gives each estimator's derivation, exact code location, a worked example, a
maxeskell/personal-training-app · ★ 0 · AI & Automation · score 70

Install: claude install-skill maxeskell/personal-training-app

# Proof & analysis toolkit — first-principles statistics of the insight engine **Use this when** you must convince yourself (or a reviewer) that a statistical method in `src/insights/` is *correct* — derive a confidence interval, justify a multiple-comparisons correction, re-derive the load model, or reproduce a reported number by hand. **Don't use this when** you want the *decision procedure* for whether a finding ships confirmed vs exploratory (that is the executable campaign in sibling `endurance-coach-n1-validation-campaign`), or the *domain meaning* of CTL/EF/decoupling (sibling `endurance-domain-reference`), or you are triaging a live "this correlation looks too good" symptom (sibling `endurance-coach-debugging-playbook`). Everything here is *deterministic and makes zero LLM calls* — these are pure functions with fixture tests. You can reproduce every number in a Node REPL or a `node:test` file. Verify claims against the repo before trusting them; exact line citations are given so you can `sed -n` the source. ## Why this toolkit exists (the one failure mode it fights) The named enemy, stated in the header comment of `src/insights/stats.ts:1`: **"impressive-looking nonsense."** Fitness (CTL), fatigue (ATL), HRV, RHR and weight are all heavily *autocorrelated* (today looks like yesterday) and *trending*. Run a naive Pearson correlation on two such series and you get a big r with a tiny p-value that means nothing — the effective information is a fraction of the point c