a population's growth rate is a bond's yield and its generation time is Macaulay duration
Theorem.a population's growth rate is a bond's yield and its generation time is Macaulay duration — Σφ(a)e^(−ra)=1 ∧ ΣCF_a(1+y)^(−a)=P, CF:=φ, P:=1 ⇒ r = ln(1+y) ∧ T_Lotka = D_Macaulay.
Proof.the Euler-Lotka equation Σ φ(a)e^(−ra) = 1 and bond pricing Σ CF_a(1+y)^(−a) = P are the same root-find on the same discounted sum: set CF := φ and P := 1 and r = ln(1+y), verified to 2.1e-16 over a 35-period schedule. The mean length of a generation, Σ a φ(a)e^(−ra) / Σ φ(a)e^(−ra), is then character-for-character Macaulay duration, agreeing to 2.8e-14. Demography and fixed income call one solver on one array and rename the output.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/stats/index.ts#growthRateIsAYield
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
"a population's growth rate is a bond's yield and its generation time is Macaulay duration" 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 growthRateIsAYield.
- 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 (growthRateIsAYield @ 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 growthRateIsAYield (src/stats/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.