Five app marginals. One unique-person union. Thirty-one possible cohorts.
Count people, not memberships.
The source lists 10.770B app memberships and almost 4B unique people. Solve what overlap is forced, what remains possible, and which claim the totals cannot support.
Source census ledger
All values in millions
The post’s audience figures are treated as supplied assumptions. This tool does not query Meta, identify people, verify monthly activity, or decide whether the stock is cheap.
Audience Overlap Bounds Lab / completed feasible-range proof
At least — people must use 2+ apps.
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The arithmetic before the Venn diagram
10.770B memberships − 4.000B people = 6.770B repeat memberships
That subtraction proves duplication exists, but not how people are distributed across apps. The LP supplies the missing discipline: one variable for every exact nonempty app combination, with all five marginals and the union held fixed.
A person active on WhatsApp, Facebook, and Instagram contributes three memberships but one person to the union.
Each endpoint is feasible under the supplied totals; neither endpoint is claimed as Meta’s actual audience structure.
Endpoint witness
- Solve the source snapshot to inspect a nonzero cohort allocation.31 cohorts
A witness is one complete allocation that attains the lower 2+ bound while reproducing every supplied total.
What the aggregate data can honestly say.
For cohort x[S], S is one of the 31 nonempty combinations of five apps. The solver enforces sum x[S] = unique people and, for each app, sum x[S containing app] = its audience. It then changes only the objective to find each rigorous endpoint.
These constraints do not measure retention, geography, bots, account duplication, daily use, advertising yield, or economic value. Use the output to qualify a reach claim, then replace the source snapshot with verified inputs and separate evidence before making a valuation decision.