Entries in U, against the bound the symbolic phase can compute, on the 5×5 grid
At its defaults it draws entries in u, against the bound the symbolic phase can compute, on the 5×5 grid. A row of horizontal bars. The topmost is longest and is labelled as the bound; every measured bar below it is shorter.
symbolic-bound is one function in lib/figures/sparselu.js —
sparse lu — where the fill argument and the stability argument disagree. 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.
At its defaults
Drawn even though every essay passes arguments — which on this site is every essay, at 100% of placements since the standard pass. A default nothing exercises is a trap for the next essay to call this with none, and this is the page where a default that has drifted from the figures around it becomes visible.
A row of horizontal bars. The topmost is longest and is labelled as the bound; every measured bar below it is shorter.
grid: 5
The arguments are the ones What the symbolic phase can only bound passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
A row of horizontal bars. The topmost is longest and is labelled as the bound; every measured bar below it is shorter.
grid: 4
The arguments are the ones What the symbolic phase can only bound passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
A row of horizontal bars. The topmost is longest and is labelled as the bound; every measured bar below it is shorter.
grid: 7
The arguments are the ones What the symbolic phase can only bound passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
A row of horizontal bars. The topmost is longest and is labelled as the bound; every measured bar below it is shorter.
grid: 6
The arguments are the ones What the symbolic phase can only bound passes. A value nobody placed would be a picture no essay asked for and no claim was ever checked against.
A row of horizontal bars. The topmost is longest and is labelled as the bound; every measured bar below it is shorter.
What it checked while drawing
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.
11 distinct claims across 5 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.
the count at τ = 0.001 fits inside the bound — checked 7 times
a grid between 4×4 and 7×7
and so does the unpivoted count
matmul shapes agree
the bound is loose against everything that actually happens
Against the rule
It draws a decomposition and prints its residual. It calls
sparseLU,
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.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.