The Repair After a Failed Parent

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

The Repair After a Failed Parent

In this worked DODAG, node B starts at Rank 256 and directly parents E and F, both at Rank 512. When B becomes unavailable, the chapter recalculates the affected descendants: E switches to parent A and lands at Rank 640, F switches to C at Rank 768, and H and I follow their repaired parents to Rank 896 and 1024. This audit asks the question that repair invites: do those recalculated Ranks still increase monotonically toward the root so the tree stays loop-free, or does the repair only prove the upward path while leaving downward DAO evidence unrefreshed?

Companion to the chapter Worked Example: Rank and Parent Choice — every number here comes from that chapter.

Ada: The forward pass in this chapter is clean, so let me audit the harder claim: after parent B fails, the recalculated Ranks are E = 640, F = 768, H = 896, I = 1024, and the repaired tree is “worse but still loop-avoiding.” Every value uses candidate_rank = parent_rank + round(256 x link_cost), and here all link costs are multiples of 0.5, so the rounding is exact – no precision is lost.

Recomputing the affected descendants:

• E drops B and takes A (link cost 1.5): 256 + round(256 x 1.5) = 256 + 384 = 640.
• F drops B and takes C (cost 1.5): 384 + round(256 x 1.5) = 384 + 384 = 768.
• H keeps E (cost 1.0), now through E’s new Rank 640: 640 + round(256 x 1.0) = 640 + 256 = 896.
• I keeps F (cost 1.0), now through F’s new Rank 768: 768 + round(256 x 1.0) = 768 + 256 = 1024.

Loop-avoidance check – each child’s Rank must strictly exceed its parent’s: 640 > 256 (E over A), 768 > 384 (F over C), 896 > 640 (H over E), 1024 > 768 (I over F). All four increase toward the root, so no child can select one of its own descendants as parent.

The audit confirms the separation the chapter keeps: these repaired Ranks prove the upward tree is still loop-free and monotonic, but every one of them is an upward number – none refreshes the DAO route state a root-to-leaf command would still need.

Every number above is taken from the chapter’s own material and re-derived step by step.