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Splitting U(0,1)F
 U(0,1)F Primus splitvalues Secundus splitvalues Tertius splitvalues Quartus splitvalues [1] 2 0 1 1 [2] F 1 F+1 F-1 [3] 0 0 -1 1 [4] -1 1 0 0

 Splitting U(0,1)Fthe primus Primusdoubled Secundusdoubled Secundusdoubled Primusdoubled Tertiusdoubled Quartusdoubled Quartusdoubled Tertiusdoubled U-5 -F4+3F2-1 = -F * F3-3F + -1 = F2-2 * -F2+1 + 1 = F2-F-1 * -F2-F+1 + 0 = -F2-F+1 * F2-F-1 + 0 U-4 -F3+2F = -F * F2-2 + 0 = F2-2 * -F + 0 = F2-F-1 * -F-1 + -1 = -F2-F+1 * F-1 + 1 U-3 -F2+1 = -1 * F2-2 + -1 = F * -F + 1 = F-1 * -F-1 + 0 = -F-1 * F-1 + 0 U-2 -F = -1 * F + 0 = F * -1 + 0 = F-1 * -1 + -1 = -F-1 * 1 + 1 U-1 -1 = 0 * F + -1 = 2 * -1 + 1 = 1 * -1 + 0 = -1 * 1 + 0 U0 0 = 0 * 2 + 0 = 2 * 0 + 0 = 1 * 1 + -1 = -1 * 1 + 1 U1 1 = 1 * 2 + -1 = F * 0 + 1 = 1 * 1 + 0 = 1 * 1 + 0 U2 F = 1 * F + 0 = F * 1 + 0 = 1 * F+1 + -1 = 1 * F-1 + 1 U3 F2-1 = F * F + -1 = F2-2 * 1 + 1 = F-1 * F+1 + 0 = F+1 * F-1 + 0 U4 F3-2F = F * F2-2 + 0 = F2-2 * F + 0 = F-1 * F2+F-1 + -1 = F+1 * F2-F-1 + 1 U5 F4-3F2+1 = F2-1 * F2-2 + -1 = F3-3F * F + 1 = F2-F-1 * F2+F-1 + 0 = F2+F-1 * F2-F-1 + 0

Note that the secundus-based split of a zero-series is neutral: what goes in comes out - in this case the primus.
Note also that a series operating on itself - in this case the primus-based split - renders the secundus as its output series.