Brandon,

Your argument is very well made (as usual!), but could I also offer an alternative interpretation.

It starts with the important assumption that a 4-Pt Roll (from upright to upright say), commences the instant the aeroplane starts to rotate (deviate) from upright level flight.

The 4-Pt Roll then comprises:
# 4 ‘Rolling Transitions’ (From upright to knife edge, from knife edge to inverted, from inverted to knife edge and from knife edge back to upright)
and,
4 ‘Periods of non-Rolling Flight’ (knife edge, inverted, knife edge and upright).

For the purposes of illustration let us also assume that:
# The ‘Rolling Transitions’ take T1 seconds (or cover D1 distance)
# The ‘Periods of ‘Non Rolling Flight’ take T2 seconds (or cover D2 distance)

Then:
# The first half of the 4-Pt Roll happens after time (2xT1 + 2xT2) or after a distance (2xD1 + 2xD2) has been covered
# The second half of the 4-Pt Roll commences with the start of the 3rd ‘Rolling Transition’ from inverted to knife edge flight (i.e. not ½ way through the 3rd transition)
# The second half of the 4-Pt Roll also happens after time (2xT1 + 2xT2) or after a distance (2xD1 + 2xD2) has been covered

With this interpretation, we have:
# An equal number of ‘Rolling Transitions’ and ‘Periods of non-Rolling Flight’ (4 of each)
# An equal period of time before and after the centre point (2 x T1 + 2 xT2)
# An equal distance covered before and after the centre point ( 2xD1 + 2xD2)

In other words, perfect symmetry! Easier to fly and easier to judge.

Clearly the same argument could be applied to any number of point rolls. With the 2 of 4 Roll up (PO 9 Manoeuve No 4), the centre of the line would be defined as the start of the second ‘Rolling Transition’ from edge on to belly on.

As you say, it all comes back to the question of how a Pt Roll is interpreted. Whatever the answer, my main argument is not with other pilots. As I said in Post #16:
# The fact that Manoeuvre No 1 is still being debated 6 months in the new season is testament to the fact that the original FAI description was ambiguous
# The ambiguity could easily be removed by the addition of a few more words

Having said all of the above, if you’re in the Judges Chair at the 3rd Centralised tomorrow, I will do my very best to fly the manoeuvres exactly how you want. With a gale force wind predicted, I think that any minor differences in interpretation will be the least of all my worries!!!

Kind regards

Bob

PS:
Single rolls or a 2 of 2 Pt Roll are different to Point Rolls in that there is no way of defining the 'Period of non Rolling Flight'. For that reason, I would define the centre of a 2 of 2 or a single roll in the same way as you do i.e. half way through the 'Rolling Transition'. This way of looking at things - coupled with the traditional interpretation of Immelmans - would also make it slightly easier for me to accept the need to push down immediately after the top 1/2 roll in Manoeuvre No 1!!!