The One Convention Everything Rests On
Each item on a list is counted as a separate coin. That is a unit of measurement, not a claim about anybody, and every figure on this site depends on it.
Reference
Halving
Every item halves what is left
A list whose items must all be met halves its own intake with each one added.
Part one
9 notes in this part
What The First Compulsory Item Costs
The first item on a list throws away half the possibility space. It is the largest single cut any item will ever make, and it is the one nobody thinks about.
Analysis
One In Two, Four, Eight, Sixteen
The full table of compulsory-only lists, from one item to eight. Nine shapes, nine powers of two, and no exceptions anywhere in the sequence.
Reference
The Eighth Item And Where It Leaves You
Eight compulsory items admit one profile in two hundred and fifty-six. The eighth line is the one that gets argued about and the one that changes least.
Analysis
Why The Halving Is Exact And Not Approximate
The halving law holds precisely, for every compulsory item, with no exceptions anywhere in the record. The proof fits in a paragraph and is worth having.
Reference
The Item Added Last Is The Item Added First
Compulsory items commute. The order they were written in leaves no trace in the result — obvious in arithmetic, and persistently untrue in how lists get read.
Analysis
Why Lists Get Longer And Never Shorter
Adding a line costs the author nothing and costs the filter half of everything. The asymmetry is structural, and it explains how lists reach eight items.
Analysis
Why This Record Stops At Eight
Eight compulsory and eight optional items is where the enumeration ends. The bound is a choice, it is stated rather than implied, and nothing new lies past it.
Reference
Reading A List You Did Not Write
What the arithmetic lets a reader work out about a list in front of them, and the much longer list of things it does not.
Analysis