seed-against-machine

At its defaults it draws the draw moves the answer by a third; the machine moves it by a rounding. A randomised rank-8 approximation of a 120 × 60 matrix, at five rates of spectral decay. The upper curve is the relative spread of the error over eight seeds; the lower is its spread over seven partitionings of one seed's reduction. The first runs from 0.0626 to 0.31 and the second from 9.82·10⁻¹⁶ to 2.83·10⁻¹⁵: at least 4.4·10¹³ between them. The machine's contribution is not zero — four to seven of the seven partitionings return distinct values at every rate — it is simply inside the width of a line the method draws for a reason it announces. This is the one field on the site where the fifth author is already dominated, and it is dominated by the one source of variation that comes with a seed attached.

seed-against-machine is one function in lib/figures/race.js — what a reduction decides when the decision is discrete — a step count, a rank, and a test's tolerance. 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.

A randomised rank-8 approximation of a 120 × 60 matrix, at five rates of spectral decay. The upper curve is the relative spread of the error over eight seeds; the lower is its spread over seven partitionings of one seed's reduction. The first runs from 0.0626 to 0.31 and the second from 9.82·10⁻¹⁶ to 2.83·10⁻¹⁵: at least 4.4·10¹³ between them. The machine's contribution is not zero — four to seven of the seven partitionings return distinct values at every rate — it is simply inside the width of a line the method draws for a reason it announces. This is the one field on the site where the fifth author is already dominated, and it is dominated by the one source of variation that comes with a seed attached.

A randomised rank-8 approximation of a 120 × 60 matrix, at five rates of spectral decay. The upper curve is the relative spread of the error over eight seeds; the lower is its spread over seven partitionings of one seed's reduction. The first runs from 0.0626 to 0.31 and the second from 9.82·10⁻¹⁶ to 2.83·10⁻¹⁵: at least 4.4·10¹³ between them. The machine's contribution is not zero — four to seven of the seven partitionings return distinct values at every rate — it is simply inside the width of a line the method draws for a reason it announces. This is the one field on the site where the fifth author is already dominated, and it is dominated by the one source of variation that comes with a seed attached.

A randomised rank-4 approximation of a 120 × 60 matrix, at five rates of spectral decay. The upper curve is the relative spread of the error over eight seeds; the lower is its spread over seven partitionings of one seed's reduction. The first runs from 0.0278 to 0.121 and the second from 7.32·10⁻¹⁶ to 2.51·10⁻¹⁵: at least 1.8·10¹³ between them. The machine's contribution is not zero — four to seven of the seven partitionings return distinct values at every rate — it is simply inside the width of a line the method draws for a reason it announces. This is the one field on the site where the fifth author is already dominated, and it is dominated by the one source of variation that comes with a seed attached.

A randomised rank-16 approximation of a 120 × 60 matrix, at five rates of spectral decay. The upper curve is the relative spread of the error over eight seeds; the lower is its spread over seven partitionings of one seed's reduction. The first runs from 0.0566 to 0.484 and the second from 1.49·10⁻¹⁵ to 4.94·10⁻¹⁵: at least 1.1·10¹³ between them. The machine's contribution is not zero — four to seven of the seven partitionings return distinct values at every rate — it is simply inside the width of a line the method draws for a reason it announces. This is the one field on the site where the fifth author is already dominated, and it is dominated by the one source of variation that comes with a seed attached.

Every figure above asserted its own claims on the way to being drawn, and a claim that failed would have failed the build rather than drawn a wrong picture. Those assertions 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.

4 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.

The rule does not apply to it. It factorises nothing, so there is no residual it could be withholding. That is worth stating rather than leaving blank: a site that reported the rule as satisfied by every generator would be counting mostly generators the rule never reached.

Across the library: the rule bites on 197 of 363 generators — 179 print a residual and 18 are exempt with a published reason; 166 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.