verification-band

At its defaults it draws the widths a proof is available at, against the precision. Two boundaries against the number of significand bits, on a logarithmic vertical axis, with the band between them shaded. The narrow boundary runs from 0.00162 at 12 bits to 3.33·10⁻¹⁶ at 53, a small multiple of u at each. The wide boundary is 1.414214 at every precision — which is √2, the half-width at which the box first touches the line where the Jacobian is singular.

verification-band is one function in lib/figures/krawczyk.js — verdicts — exactly one root in this box, or none, or nothing can be said. 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.

Two boundaries against the number of significand bits, on a logarithmic vertical axis, with the band between them shaded. The narrow boundary runs from 0.00162 at 12 bits to 3.33·10⁻¹⁶ at 53, a small multiple of u at each. The wide boundary is 1.414214 at every precision — which is √2, the half-width at which the box first touches the line where the Jacobian is singular.

Two boundaries against the number of significand bits, on a logarithmic vertical axis, with the band between them shaded. The narrow boundary runs from 0.00162 at 12 bits to 3.33·10⁻¹⁶ at 53, a small multiple of u at each. The wide boundary is 1.414214 at every precision — which is √2, the half-width at which the box first touches the line where the Jacobian is singular.

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.

16 distinct claims across 2 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 66 of 131 generators — 51 print a residual and 15 are exempt with a published reason; 65 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.