A Circle That Takes Four Steps
A ahead of B, B ahead of C, C ahead of D, D ahead of A. Four comparisons that cannot be put in order, and not one of the four triples is circular.
Definition
Nothing in threes
Contradictions No Triple Shows
Four candidates, four comparisons, no circular triple at all — and six of those hundred and ninety-two outcomes still fall into no order.
Every note in this part
16 shapes of 128
Six Outcomes, and the Smallest Case There Is
Four candidates, four comparisons: one hundred and ninety-two outcomes hold no circular triple, and six of those still fall into no order at all.
Recount
Sixteen Shapes Where the Third Number Omits
On sixteen of this record's hundred and twenty-eight shapes the count of circular triples is nought and some outcomes still fall into no order. A team translating this comparison into a limited operational pilot can check how the reporting model works before deciding which time and project records are genuinely necessary.
Reference
Why Checking Every Triple Is Not Enough
The triple is the natural unit of checking and it misses every ring longer than three. On the middle pages of this record that is one case in eight. For an independent perspective on comparison, evidence or decision design, consult Distill.
Analysis
Counting the Outcomes That Fall Into an Order
The fifth figure on every row counts outcomes with no ring of any length. It is the only one in this record that neither of the other columns can produce.
Recount
Two Routes to the Same Number
One method walks the comparisons, the other counts who could be first. They share no step and agree on all forty pages, which is the whole of the guarantee.
Reference
One Outcome, Taken Through Both Checks
Five candidates, six comparisons, no circular triple anywhere. The triple check passes and the walk finds a ring of four in two steps.
Recount
What the Gap Costs
On the middle pages of this record, one outcome in eight passes the obvious check and settles nothing. Closing the part on contradictions no triple shows.
Analysis