One exponential law
Theorem.One exponential law — tissue gas washout, RC charging, radioactive decay, Newton cooling and animation easing are ONE equation dy/dt = λ(y∞ − y).
Proof.tissue gas washout, RC charging, radioactive decay, Newton cooling and animation easing are ONE equation dy/dt = λ(y∞ − y) — closed form matches the integrated ODE in all five costumes; Bühlmann's 16 halftimes reconstruct from the ledgered He table via Graham and form an OCTAVE ladder (middle rung ratio 1.417 ≈ √2, 1.99 compartments per doubling) whose ends drift 2.000 → 1.275, a 1.57× spread proving he fitted a law he never derived; the same kernel eases every animation, so 16 compartments are 16 rates.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/6/4/index.ts#oneExponentialLaw
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
"One exponential law" 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 oneExponentialLaw.
- 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 (oneExponentialLaw @ src/6/4) 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 oneExponentialLaw (src/6/4/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.