A charger siting plan, and a proof that almost nothing beats it

THE PLAN. 500 new fast-charging sites in the United States bring 14,959,825 more people within 10 km of one, lifting coverage from 83.22% to 87.73%. The same budget in Mexico brings 24,965,167 people into range, lifting coverage from 66.04% to 85.85%. The sites are chosen, not described: each is a census tract or locality centre, and the full selection is reproducible from the published code.

AND A PROOF THAT ALMOST NOTHING BEATS IT. No arrangement of 500 sites anywhere in either country covers more than 0.63% more people than this plan does. That is not a solver's claim — the bound is the Lagrangian of the relaxed problem, valid for any non-negative multipliers, so three lines of numpy verify it independently of whether the solver converged. Maximum coverage is NP-hard and a tool asserting optimality at this size would be wrong; a certificate is what can honestly be offered instead. At 2,000 sites the Mexican plan is proven optimal outright, with a gap of exactly zero.

A WIDELY REPRODUCIBLE STATISTIC ABOUT THE MEXICAN REGISTRY IS WRONG. Measuring a station's coordinate against the median coordinate of its own state suggests 27% are badly placed — but that measures how large a state is, not how wrong a coordinate is, and a state with ten stations spread across it scores 100%. Judged against the nearest INEGI locality instead, 186 of 2,046 stations (9.09%) fall in a different state than the one they claim.

AND MOST OF WHAT LOOKS LIKE ERROR IS VOCABULARY. Comparing the two registries' state names directly gives 23.95%. Four pairs differ by wording rather than by place — one registry writes the state of Mexico, Veracruz, Michoacan and Coahuila in their short forms and the other in their constitutional ones. Crosswalking those four takes the measured error to 9.09%. Without that step this project would have published an error rate about itself that was seventy per cent too high.

THE FILTER COSTS ALMOST NO COVERAGE AND NO GEOGRAPHY. Dropping the wrong-state stations and the 12 carrying the country's geographic centroid as a placeholder keeps 1,859 of 2,046 stations (90.9%), retains all 32 states, and shifts which states are represented by only 2.54 percentage points. The data supports siting, once it is cleaned in a way that can be checked.

CANADA'S CHARGER REGISTRY IS AN AMERICAN SYSTEM THAT EXCLUDES CANADA. Canada's demand side is complete and verified here — 56,686 dissemination areas totalling 36,991,981 people, with 0 missing coordinates. What is missing is the stations. The only registry obtainable without a key is the US Department of Transportation's mirror, and it contains 0 Canadian rows. Canada's own national locator is the same American service embedded in a Canadian page. So Canada gets a demand layer and no plan, and the reason is registry access rather than Canadian statistics.

SOME PEOPLE CANNOT BE REACHED BY ANY BUDGET. 4,247,037 people in the United States and 8,429,625 in Mexico live more than 10 km from any settlement of 2,500 or more. No number of new sites reaches them under this model, because the constraint is where settlements are rather than where chargers are. That is a fact about population geography, and it bounds what any siting exercise can promise.

THE SAME BUDGET BUYS FAR MORE IN MEXICO. 500 sites move Mexican coverage by 19.81 percentage points against 4.51 in the United States, because Mexico starts from 66.04% against 83.22%. The two figures are computed by one method but they are not a league table: a US tract and a Mexican locality are different objects, and a locality can be a single household.