Same filter

Different lists, one filter

Twenty-one shapes admit exactly one profile in two hundred and fifty-six.

Part five

8 notes in this part

Twenty-One Lists, One Filter

Twenty-one shapes in this record admit exactly one profile in two hundred and fifty-six. They run from eight items to sixteen and they are the same filter.

Reference

The Ladder Of Classes

Forty-six values here are shared by more than one shape, and the largest classes form a descending ladder: twenty-one, twenty, nineteen, eighteen.

Reference

Eight Items And Sixteen, The Same Filter

The extreme case: a list of eight and a list of sixteen that admit identically. What the extra eight lines are doing, and why nobody can tell.

Analysis

Why They Agree, And Why It Is Not A Coincidence

Shapes that admit identically do so for a reason that can be stated in one line, and the reason explains the whole ladder of classes.

Reference

The Shapes That Admit Exactly One Profile

Eighty-one of the four hundred and five shapes admit a single profile. They span seventeen values, from the empty list to a sixteen-item conjunction.

Reference

Two Hundred And Three Distinct Answers

Four hundred and five shapes produce two hundred and three different intakes. Exactly half the variety in how lists are built does nothing to what they admit.

Reference

Length Cannot Be Read As Rigour

The conclusion this section has been building to, stated plainly, with the three specific errors it rules out.

Analysis

Comparing Two Lists Honestly

The method, in four steps, and the one assumption it rests on. It works even for a reader who rejects the coin convention entirely.

Analysis