Crossover — where it appears
Named by 4 essays across one field — each of them below, with the objects they name alongside it.
What the halving is a function of
A move is answered while the board is cooler than the follow-up's temperature — or half of it, depending which of two classes the position is in, and the classes were stated in terms of forms. They are a feature of one wall: whether the follow-up's right wall rises straight up before it leans. Fifty-five positions, no exception, and the crossover becomes something a reader can see.
A subtraction, not a factor
The crossover factor was a half on fights whose answer starts another fight, measured on a pool with two three-deep positions in it. A pool built to be deep gives twenty, and the factor does not survive them: the crossover is the follow-up's temperature less a half on eighteen of the twenty, and a factor of a half agrees with that only where the temperature is one — which nearly every position in the earlier pool had.
Half of the smaller temperature
The correction to the sente crossover has been priced twice — first as a factor of a half, then as a subtraction of a half — each time on a pool whose answers were all about the same size. Over 128 fights with answers from a number up to a temperature of six, the correction is half the answer's temperature, saturating at half the fight's own. Both earlier readings are regions of that one law.
The premises an induction would need
The rung below settled by a grouping test that a position's crossover depends on its own temperature and its answer's and on nothing below them, and asked for the induction. The four paragraphs are not written here; the checking they would rest on is. The law holds at five levels, survives translation, heating and cooling — and none of that is the step.
Named alongside it
The objects these essays reach for when they reach for this one.
EnumerationFollow-upSenteTemperatureThermographAmbientCounterexampleSwitchCoupon stackInvariantStrategyAmbient temperature