Generator-offset property: Difference between revisions
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=== Conjecture 5 === | === Conjecture 5 === | ||
An SGA scale is always pairwise-well-formed (PWF). That is, the result of identifying any two step sizes of an SGA scale is always a non-multiperiod mos. | An SGA scale is always pairwise-well-formed (PWF). That is, the result of identifying any two step sizes of an SGA scale is always a non-multiperiod mos. | ||
==== Proof ==== | |||
Suppose the scale is aX bY bZ. We know SGA scales are MV3. We know that MV3s project to mosses when one removes all instances of one step size, in particular s. Thus it suffices to prove that the result of equating any two step sizes is a mos. Equating Y and Z equates the swung alternants, resulting in the mos aX 2bW (this is a known fact). | |||
The only new claim is: Equating X and Z equates the generator with the difference between the start of the 2nd chain with the end of the 1st one or vice versa; similarly for equating X and Y. | |||
== Falsified conjectures == | == Falsified conjectures == | ||