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.
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.
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):
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.
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.
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.
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.
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.
tly_v0_calc.py + results_v0.json. First-print discipline applies from v1.0 onward (see SPEC.md capabilities 3 and 7).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.
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.
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.