FA-75208 / CRDT convergence / Member archive

Fractional position allocation: a gap of one digit is treated as room · case 03

Two neighbours one digit apart receive a new position equal to the lower neighbour.

Member previewVariant 3 · 3 implementations · 10 checks per implementation

Case contract

Starting from the given sorted positions, positions are digit lists in base 10 compared lexicographically and never ending in 0. Inserting at list index i allocates between the neighbours p (or [] at the start) and q (or [] at the end): walking depth d, lower digit a is p[d] or 0, upper digit b is q[d] while q still constrains (else 10); if b - a > 1 append (a+b)//2 and stop, else append a, and q stops constraining once a < b. Return positions as dotted strings in list order.

Why this case matters

Sequence CRDTs such as Logoot and LSEQ assign dense identifiers so that concurrent inserts never need renumbering.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
append repeatedly	`["5", "7", "8", "9", "9", "9", "9"]`	`["5", "7", "8", "9", "9.5", "9.7", "9.8"]`	Failed

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