A randomised rank-k solve, 4 seeds a rank

At its defaults it draws a randomised rank-k solve, 4 seeds a rank. Relative error against the rank kept, on a logarithmic vertical axis, with a vertical bar at each rank spanning the seeds. The band is 1.84 wide at rank 8, where the method is at its worst, and 1.022 wide at rank 24, where it is at its best. The same computation on the same data returns a different answer each time.

rank-band is one function in lib/figures/compose.js — four knobs — one floor under them, and a fifth that is not a knob at all. 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.

Relative error against the rank kept, on a logarithmic vertical axis, with a vertical bar at each rank spanning the seeds. The band is 1.84 wide at rank 8, where the method is at its worst, and 1.022 wide at rank 24, where it is at its best. The same computation on the same data returns a different answer each time.

Relative error against the rank kept, on a logarithmic vertical axis, with a vertical bar at each rank spanning the seeds. The band is 1.84 wide at rank 8, where the method is at its worst, and 1.022 wide at rank 24, where it is at its best. The same computation on the same data returns a different answer each time.

Relative error against the rank kept, on a logarithmic vertical axis, with a vertical bar at each rank spanning the seeds. The band is 1.81 wide at rank 8, where the method is at its worst, and 1.095 wide at rank 12, where it is at its best. The same computation on the same data returns a different answer each time.

Relative error against the rank kept, on a logarithmic vertical axis, with a vertical bar at each rank spanning the seeds. The band is 1.84 wide at rank 8, where the method is at its worst, and 1.004 wide at rank 28, where it is at its best. The same computation on the same data returns a different answer each time.

Relative error against the rank kept, on a logarithmic vertical axis, with a vertical bar at each rank spanning the seeds. The band is 2.02 wide at rank 4, where the method is at its worst, and 1.010 wide at rank 28, where it is at its best. The same computation on the same data returns a different answer each time.

Relative error against the rank kept, on a logarithmic vertical axis, with a vertical bar at each rank spanning the seeds. The band is 1.71 wide at rank 8, where the method is at its worst, and 1.007 wide at rank 24, where it is at its best. The same computation on the same data returns a different answer each time.

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.

6 distinct claims across 6 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 rankSweep, 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.