TLY Methodology v0.1

Principle: every published figure must be reproducible by anyone, from keyless public endpoints, by running open code. The script tly_v0_calc.py is the methodology; this document explains it. No number without a source URL and a runnable path.

1. Definition

S(t) = sum over age bands a of N(a, t) x e(a, t)

where N is world population in the band and e is remaining life expectancy at the band's mean exact age. v0 is a single global aggregate; v1 (see SPEC.md) computes it per country and week.

2. Data sources (all keyless, all public)

3. Estimator

Band mean age: uniform-within-band (0-4 -> 2.5, ..., 80-84 -> 82.5; open 100+ band -> 101). e at the mean age: piecewise-linear interpolation on the WHO exact-age anchors {0, 1, 5, 10, ..., 85}; flat at e(85) beyond 85.

Life-table vintage: WHO's latest global table is 2021, a COVID-anomaly year (e0 = 71.37). WPP 2024 reports world e0 recovered to 73.3 by 2024 - almost exactly the 2019 table (e0 = 73.12). The 2019 table is therefore primary and the 2021 table is reported as a lower bound.

Result (population 2023, table 2019):

4. The issuance identity

With age density N(a, t), force of mortality mu(a), births B, and a fixed life table, two standard identities -

de/da = mu(a) e(a) - 1 (remaining expectancy along age) dN/dt + dN/da = -mu N (population transport)

dS/dt = B e(0) - N

The mu terms cancel exactly: expected deaths do not change S because they are already priced into e(x). The full accounting is therefore

dS/dt = B e(0) - N + N dEbar/dt - (excess deaths) x e(age at death) [mint] [spend] [table-revision drift] [shocks only]

Correction log: an earlier working estimate of +2.9%/yr was wrong twice over - it omitted the spend term and subtracted GBD YLL (which uses an aspirational reference table and double-counts against our own e). The open recomputation caught it. This is the point of the openness rule.

Trajectory: g decays with fertility. WPP 2024 medium variant has population peaking around 10.3 billion in the mid-2080s; S peaks earlier (the aging of the pyramid drags E-bar down before headcount turns), then declines - a built-in demographic halving-and-reversal schedule. Exact peak year is a v1 computation from the WPP projection variants.

5. Shock scenarios

Only excess deaths versus the table burn stock. WHO estimates 14.83 million excess deaths associated with COVID-19 across 2020-2021 (https://www.who.int/news/item/05-05-2022-14.9-million-excess-deaths-were-associated-with-the-covid-19-pandemic-in-2020-and-2021). Burn = excess x mean e at age of death:

A century-scale pandemic moves supply by less than a tenth of a percent. Supply is glacially smooth; essentially all price variance will be demand-side.

6. Wealth-neutrality of rebases (proof)

Let wallet i hold share s_i of supply M(t), so balance b_i = s_i M(t). A rebase multiplies M by k and every balance by the same k; s_i is unchanged. Market value of the wallet = s_i x (market capitalization), which contains no M term. Therefore rebases transfer nothing and create nothing; all holder returns come from the market price of the share. Deaths never enrich a holder (mortality neutrality) and longevity gains never dilute one.

7. Vision-consistent asymptote

Burger = 15 minutes at $6.00 implies $24.0000/hour, x 8,766 h/yr = $210,384.00 per life-year. Across S that is a $76.2458 quadrillion capitalization. Anchor for scale: UBS Global Wealth Report base of USD 454.4T (end-2022) grown by UBS's published rates (+4.2%, +4.6%, +10.8%) gives ~USD 549T of global personal wealth - the asymptote is ~138.9x all personal wealth on Earth. The Mirror token requires no particular price to function; the v4 Ledger only pays people more than dust near the asymptote. This is why Mirror ships first.

8. Known limitations (v0), in order of size

1. Period vs cohort expectancy: period tables ignore future mortality improvement, understating true cohort remaining years - plausibly +3-8% for young cohorts. Scheduled as a v1.x methodology factor (projected cohort tables), per the versioned-expansion rule. 2. Population vintage: bands are 2023; at ~+0.9%/yr headcount growth the 2026 stock is roughly 2-3% above the stated S. 3. Global aggregation: no country split in v0; aggregation error order +-1-2%. v1 computes per country. 4. Flat e beyond 85 overstates the 90+ bands' e; those bands are 0.288% of population; bias on S < +0.05%. 5. Uniform-within-band mean ages; drift window is pre-COVID by construction; shock age-profile is parameterized (three-point sensitivity shown), not observed.

9. Versioning

10. Extension ladder: v0 to the ceiling

v0 is the minimal defensible estimator. Each rung below is a strict upgrade, ordered by impact; estimated level effects are working figures, to be computed when each rung lands.

11. Hard ceilings no math removes

1. Registration coverage: a large share of world deaths (very roughly 4 in 10) are never registered; below that floor, "data" is imputation. More coverage means more model, not more measurement. 2. Cohort truth is unknowable in real time: any e beyond the period table is a forecast and will be revised. Handled by first-print settlement and forward-only corrections, never by pretending otherwise. 3. State-published statistics are manipulable. Mitigation is triangulation (WPP vs IHME GBD vs national vs HMD) and capped epoch adjustments; elimination is impossible.

12. Prior art

JPMorgan's LifeMetrics (2007) was an open-methodology longevity index later transferred to the Life & Longevity Markets Association; the index worked, the derivatives market died of one-sided demand and basis risk. Lesson encoded here: the index layer must be self-sustaining as a data product (v1), and the Mirror token supplies a permissionless second side that swap markets never had. Academic base: Lee-Carter (1992), Cairns-Blake-Dowd, UN probabilistic projections, Human Mortality Database.