Little's law is an accounting identity rather than a statistical one
Theorem.Little's law is an accounting identity rather than a statistical one — Σ_i X_i = ∫_{T₀}^{T₁} N(t) dt (Fubini on 1{a_i ≤ t < d_i}) ⇒ L = λW pathwise.
Proof.Σ sojourn times = ∫ N(t) dt is Fubini applied to the indicator of being present, so L = λW holds PATHWISE for any cohort wholly inside the window — no stationarity, no distribution, no independence, no equilibrium. Verified to 1.7e-13 over 60 jobs with nothing assumed. What breaks it is not a violated statistical assumption but a violated cohort: clipping the same jobs at a window boundary moves the total from 806 to 466, which is the error every dashboard makes when it divides a truncated total by a rate.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/stats/index.ts#littlesLawIsAccounting
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Little's law is an accounting identity rather than a statistical one" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation littlesLawIsAccounting.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (littlesLawIsAccounting @ src/stats) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes littlesLawIsAccounting (src/stats/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.