14 of 14 places survive the arithmetic and 3 survive one missing link

At its defaults it draws 14 of 14 places survive the arithmetic and 3 survive one missing link. The top 15 of a PageRank ranking on an eighty-page link graph, and how many of its 14 adjacent comparisons keep their order under three kinds of doubt. Perturbing the teleport vector at the rounding level moves every entry by at most 4.05·10⁻¹¹ and settles 14 of them. Moving α across the range everybody uses moves entries by 0.00123 and settles 11. Removing a single arc — one link that might or might not have been crawled — moves entries by 0.00443 and settles 3. The gaps between consecutive entries run from 6.28·10⁻⁵ to 0.00241, so the ordering is decided by the data at a scale ten orders above anything the arithmetic does. This is the one field on the site where the computation is not the weakest part of the answer.

order-stability is one function in lib/figures/graphwalk.js — the walk and the ranking — a rate that is not the published one, a positivity the arithmetic loses, and places nothing settles. 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.

The top 15 of a PageRank ranking on an eighty-page link graph, and how many of its 14 adjacent comparisons keep their order under three kinds of doubt. Perturbing the teleport vector at the rounding level moves every entry by at most 4.05·10⁻¹¹ and settles 14 of them. Moving α across the range everybody uses moves entries by 0.00123 and settles 11. Removing a single arc — one link that might or might not have been crawled — moves entries by 0.00443 and settles 3. The gaps between consecutive entries run from 6.28·10⁻⁵ to 0.00241, so the ordering is decided by the data at a scale ten orders above anything the arithmetic does. This is the one field on the site where the computation is not the weakest part of the answer.

The top 15 of a PageRank ranking on an eighty-page link graph, and how many of its 14 adjacent comparisons keep their order under three kinds of doubt. Perturbing the teleport vector at the rounding level moves every entry by at most 4.05·10⁻¹¹ and settles 14 of them. Moving α across the range everybody uses moves entries by 0.00123 and settles 11. Removing a single arc — one link that might or might not have been crawled — moves entries by 0.00443 and settles 3. The gaps between consecutive entries run from 6.28·10⁻⁵ to 0.00241, so the ordering is decided by the data at a scale ten orders above anything the arithmetic does. This is the one field on the site where the computation is not the weakest part of the answer.

The top 24 of a PageRank ranking on an eighty-page link graph, and how many of its 23 adjacent comparisons keep their order under three kinds of doubt. Perturbing the teleport vector at the rounding level moves every entry by at most 4.05·10⁻¹¹ and settles 23 of them. Moving α across the range everybody uses moves entries by 0.00123 and settles 15. Removing a single arc — one link that might or might not have been crawled — moves entries by 0.00443 and settles 4. The gaps between consecutive entries run from 3.78·10⁻⁶ to 0.00241, so the ordering is decided by the data at a scale ten orders above anything the arithmetic does. This is the one field on the site where the computation is not the weakest part of the answer.

The top 6 of a PageRank ranking on an eighty-page link graph, and how many of its 5 adjacent comparisons keep their order under three kinds of doubt. Perturbing the teleport vector at the rounding level moves every entry by at most 4.05·10⁻¹¹ and settles 5 of them. Moving α across the range everybody uses moves entries by 0.00123 and settles 4. Removing a single arc — one link that might or might not have been crawled — moves entries by 0.00443 and settles 2. The gaps between consecutive entries run from 1.21·10⁻⁴ to 0.00241, so the ordering is decided by the data at a scale ten orders above anything the arithmetic does. This is the one field on the site where the computation is not the weakest part of the answer.

The top 10 of a PageRank ranking on an eighty-page link graph, and how many of its 9 adjacent comparisons keep their order under three kinds of doubt. Perturbing the teleport vector at the rounding level moves every entry by at most 4.05·10⁻¹¹ and settles 9 of them. Moving α across the range everybody uses moves entries by 0.00123 and settles 8. Removing a single arc — one link that might or might not have been crawled — moves entries by 0.00443 and settles 3. The gaps between consecutive entries run from 1.21·10⁻⁴ to 0.00241, so the ordering is decided by the data at a scale ten orders above anything the arithmetic does. This is the one field on the site where the computation is not the weakest part of the answer.

The top 20 of a PageRank ranking on an eighty-page link graph, and how many of its 19 adjacent comparisons keep their order under three kinds of doubt. Perturbing the teleport vector at the rounding level moves every entry by at most 4.05·10⁻¹¹ and settles 19 of them. Moving α across the range everybody uses moves entries by 0.00123 and settles 13. Removing a single arc — one link that might or might not have been crawled — moves entries by 0.00443 and settles 3. The gaps between consecutive entries run from 3.78·10⁻⁶ to 0.00241, so the ordering is decided by the data at a scale ten orders above anything the arithmetic does. This is the one field on the site where the computation is not the weakest part of the answer.

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.

7 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.

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 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.