Jay, SHyland,
It would be great to see links to your earlier posts about line rule. Aren't we just talking about about variations of the same layout systems? Capitalizing Line Rule makes it sounds like a separate system from Square Rule.
The way I interpret Square Rule is that you can either layout from an edge if the timber is good enough or from snap lines if not (as is done on hewn timbers). In both cases you're framing to the "perfect timber within". Both methods are Square Rule.
In Scribe Rule you frame to the irregular surface, not with housings to the perfect timber within. You can either direct scribe by laying the timbers over one another and then using various methods to transfer the intersection (including plumb line scribe ala Dodge and Truax) or use templates or other recording methods to transfer the irregularities to timbers remote from one another (also referred to as "mapping" or "distance scribing"). I have some but limited exposure to Asian methods but interpret the templating system used there to be similar to this. Reference to any texts or online links showing a source for this would also be useful, Jay.
In Brad's example the easiest solution I can see is tumbling, a form of scribing where you lay the smaller timber over the posts and rotate it while transferring the angles and intersections
It's so hard to visualize this stuff in a short online post, but I think we are discussing just two layout systems, Square Rule and Scribe Rule, to account for timber variations. If there is a third system I'd like to know how it differs (I don't consider mill rule a system).