Cost and incidence
Two bills. A skip counted twice is not a measurement.
A key is free. Anyone can make another. If a seat is going to stay scarce, the cost cannot sit on the key. It has to sit on making the object. One key can cover many objects. Each object is still another bill. How do you make a digital thing scarce?
The maker pays to produce an object. Once, per object.
The checker pays to examine a file claiming to be one. Once, per file looked at.
They are separate accounts. Neither is the other's mirror. The holes those bills can fall into are Threat model. This page is who pays.
The production bill
If the key is free, the next seat is free unless making the object is not. That making-cost is the floor.
How a construction spends that bill is an instance choice. How high the floor sits is also a choice. Raise it and the same budget buys fewer objects. Lower it and the same budget buys more. That is the whole of what it decides.
It does not count people. It does not forecast a population, say what share of a room is fabricated, or guarantee that every producer paid the same. And it is not a dollar figure. Those are other accounts. Why the cost does not divide across a second object is What kind of cost refuses to divide?
The checking bill
A broken file, a file under the wrong key, or a file carrying no marks at all can be thrown out from the bytes alone, without redoing the production work. That is the cheap side, and bulk junk should die there.
A file that already looks finished is the other side. Confirming means doing enough of the work again that a miss would have shown. That look costs more than the cheap refusal. It does not cost the production bill. Why is the check always cheaper than the making?
The split is the design rather than an accident. If the cheap side cost the making, there would be no defence against volume, and the door would close on its own.
Two things this bill does not buy. A sample that mismatches is enough for a gate to refuse this file. A sample that matches does not accept it. And a match says the file matched what it bound itself to, not what was spent making it.
Why the two bills do not divide
A cheap rejection is not proof that anyone paid the floor.
The check was cheap because it skipped the expensive work. A fabricated file can skip that same work while being made. Both parties saved on the same omitted thing, so counting one as the defender's advantage and the other as the attacker's cost is counting a single skip twice.
State both costs where both are known. Do not divide a production bill by a skipped check and call the result a measurement.
The split does not fall between an attacker and a defender. It falls between paying the production work and not paying it. The fabricated file and the cheap refusal are siblings on the same side of that line. A number taken from one of them is therefore not a fact about the other.
A saving quoted from the check is still not a fact about the maker, and the reverse is the same mistake. This page does not invent a ratio of fill time to leg time.
Who was paying before
Screening at a door has an incidence.
The honest visitor pays in time and irritation, and pays again at the next service, because nothing they did carries.
The service pays to run the screening.
The bulk operator pays too, and pays least. The apparatus is defeated once and the defeat is reused across every account afterwards, so the cost per account approaches nothing.
The heaviest share falls on the party the door was never aimed at, and the lightest on the party it was built for.
Who pays now
The maker pays at production, once per object. Someone making one pays for one. Someone making ten thousand pays the occupancy ten thousand times, because nothing built for the first object's room reduces the ten-thousandth. Whether that holds against a well-funded party trying hard to break it has not been established.
Whoever checks still pays to look, and can still throw junk away cheaply. Looking did not become free. Starting stopped being free, and stopped getting cheaper with volume.
Whether that trade is worth making for a given room is a decision about that room. It is not a theorem. Why a finished file is still worth carrying is Why carry the cost forward?
What is still open
More machines still make more objects at once. A higher floor means fewer objects per budget, and that is all. It does not by itself change what fraction of a population is fabricated. That depends on who turns up and what they would otherwise be doing.
One object, one seat is a rule a checker has to name. The floor does not name it, and recognition can still change.
Measured numbers, where a record has them, are timings and sizes for a named construction on named machines. They are not a price list for this argument.