Back on the topic of PCA Identify, there's still a handful of patterns for which I'd probably expect that a mod value lower than the period should be reported, but is ultimately not. Here's a simple example:
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x = 5, y = 3, rule = 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15
.G$3.G!
This oscillator's initial phase is two knightwise NES cells. When we Identify this, a period of 16 and a mod of 16 are reported. If we manually go to generation 8 (16/2), however, we see that the pattern is composed of two NSW cells, and that selecting the entire configuration and rotating it 180 degrees (or flipping it on both axes) returns us to the initial T=0 configuration of two knightwise NES cells. The evolution from T=8 to T=15 is also identical to that of T=0 to T=7, rotated 180 degrees. As such, it seems fair to conclude that this pattern's mod should be one half of its period.
I've gathered several more PCA oscillators which I believe should have lower mod values below, for testing and documentation purposes:
reported 204, expected 102
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x = 3, y = 4, rule = 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15
L2$C.B$.H!
reported 310, expected 155
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x = 5, y = 3, rule = 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15
A.A2$H.I.D!
reported 8332, expected 4166
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x = 5, y = 6, rule = 2PCA4,0,2,4,12,8,5,9,7,1,6,10,11,3,13,14,15
3.A$A.H2$2.H2$4.L!
reported 10216, expected 5108
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x = 4, y = 3, rule = PCA_8
B.J$.B.D$2.D!
reported 16226, expected 8113
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x = 31, y = 4, rule = PCA_4
A$.D23.H$24.I5.B$25.H3.H!
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Mods also aren't reported anymore for some higher-range Generations oscillators:
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x = 8, y = 5, rule = R2,C3,S2-3,7,B4,8,N*
2.2A$.A2.A$2A.3A$.A2.A$2.2A!
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x = 10, y = 6, rule = R2,C5,S2-3,B3,8,NB
.A6.A$.2AC2.C2A$B2D.2A.2DB$B2D.2A.2DB$.2AC2.C2A$.A6.A!