κ(A) and κ of the row-equilibrated matrix, along both families, n = 8

At its defaults it draws κ(a) and κ of the row-equilibrated matrix, along both families, n = 8. Write A = D·X with D diagonal and every row of X of unit norm. Every theorem about relative accuracy is a hypothesis on κ(X), and κ(A) appears in none of them — which is easy to read past and is the whole difference between the two families here. Along the graded family κ(A) climbs from 271 to 7.04·10⁵⁰ and κ(X) is 4.892 at every one of the six matrices — the grading is exactly what the diagonal factor absorbs. Along the uniform family κ(X) climbs to 3.87·10²⁵. That is the number that says which question has an answer, and it is not the number anybody prints.

scaled-classifier is one function in lib/figures/relacc.js — relative accuracy — small compared to what, against an exact rational answer. Everything below came out of it during this build, at arguments taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Write A = D·X with D diagonal and every row of X of unit norm. Every theorem about relative accuracy is a hypothesis on κ(X), and κ(A) appears in none of them — which is easy to read past and is the whole difference between the two families here. Along the graded family κ(A) climbs from 271 to 7.04·10⁵⁰ and κ(X) is 4.892 at every one of the six matrices — the grading is exactly what the diagonal factor absorbs. Along the uniform family κ(X) climbs to 3.87·10²⁵. That is the number that says which question has an answer, and it is not the number anybody prints.

Write A = D·X with D diagonal and every row of X of unit norm. Every theorem about relative accuracy is a hypothesis on κ(X), and κ(A) appears in none of them — which is easy to read past and is the whole difference between the two families here. Along the graded family κ(A) climbs from 117 to 8.38·10⁴⁹ and κ(X) is 3.372 at every one of the six matrices — the grading is exactly what the diagonal factor absorbs. Along the uniform family κ(X) climbs to 1.37·10¹¹. That is the number that says which question has an answer, and it is not the number anybody prints.

Write A = D·X with D diagonal and every row of X of unit norm. Every theorem about relative accuracy is a hypothesis on κ(X), and κ(A) appears in none of them — which is easy to read past and is the whole difference between the two families here. Along the graded family κ(A) climbs from 4350 to 8.83·10⁴⁹ and κ(X) is 5.653 at every one of the six matrices — the grading is exactly what the diagonal factor absorbs. Along the uniform family κ(X) climbs to 1.45·10³¹. That is the number that says which question has an answer, and it is not the number anybody prints.

Write A = D·X with D diagonal and every row of X of unit norm. Every theorem about relative accuracy is a hypothesis on κ(X), and κ(A) appears in none of them — which is easy to read past and is the whole difference between the two families here. Along the graded family κ(A) climbs from 271 to 7.04·10⁵⁰ and κ(X) is 4.892 at every one of the six matrices — the grading is exactly what the diagonal factor absorbs. Along the uniform family κ(X) climbs to 3.87·10²⁵. That is the number that says which question has an answer, and it is not the number anybody prints.

Every figure above checked its own claims on the way to being drawn, and a claim that failed would have stopped the picture rather than shipped a wrong one. Those checks used to leave no trace at all: a passing one returned true and the only evidence the figure had checked anything was that nothing crashed. The list below is what they actually said, collected by running this generator with an observer installed — not a description of what it is believed to check.

5 distinct claims across 4 sets of arguments, grouped below by shape — because most of them are one sentence with a different number in it, and how many separate times that sentence was put to the test is the informative part.

It draws a decomposition and prints its residual. It calls scaledCond, and every figure above carries the badge — which residualcheck verifies by looking for it in the emitted SVG rather than by finding the call that builds one. A badge that is constructed and then left out of the body is the failure that check exists for.

Across the library: the rule bites on 217 of 397 generators — 199 print a residual and 18 are exempt with a published reason; 180 factorise nothing. Read from lib/residual-rule.js, which is the same body the gate enforces from, and the gate's last check fails the build if this page and it disagree about any generator.