window-drift

At its defaults it draws how far a carried triangular factor drifts from the data, over 2976 steps of a sliding window. A window of 24 rows on 6 columns, moved one row at a time: each step folds a row in with Givens rotations and removes one with hyperbolic rotations, and the factor is never rebuilt from the rows. The rows are integers times powers of two, so AᵀA is exact in a double and the vertical axis is a distance from the answer. No single step amplifies by more than 2.72, no downdate fails, and after 2976 steps the factor is 3.87·10⁻¹⁴ from the matrix it is supposed to factor — a fitted slope of 0.554 in the step count, against a bound whose slope is 1.

window-drift is one function in lib/figures/seqstab.js — accumulation — what a carried factor collects, and why it is a walk rather than a sum. 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 window of 24 rows on 6 columns, moved one row at a time: each step folds a row in with Givens rotations and removes one with hyperbolic rotations, and the factor is never rebuilt from the rows. The rows are integers times powers of two, so AᵀA is exact in a double and the vertical axis is a distance from the answer. No single step amplifies by more than 2.72, no downdate fails, and after 2976 steps the factor is 3.87·10⁻¹⁴ from the matrix it is supposed to factor — a fitted slope of 0.554 in the step count, against a bound whose slope is 1.

A window of 24 rows on 6 columns, moved one row at a time: each step folds a row in with Givens rotations and removes one with hyperbolic rotations, and the factor is never rebuilt from the rows. The rows are integers times powers of two, so AᵀA is exact in a double and the vertical axis is a distance from the answer. No single step amplifies by more than 2.72, no downdate fails, and after 2976 steps the factor is 3.87·10⁻¹⁴ from the matrix it is supposed to factor — a fitted slope of 0.554 in the step count, against a bound whose slope is 1.

A window of 24 rows on 6 columns, moved one row at a time: each step folds a row in with Givens rotations and removes one with hyperbolic rotations, and the factor is never rebuilt from the rows except every 500 steps. The rows are integers times powers of two, so AᵀA is exact in a double and the vertical axis is a distance from the answer. No single step amplifies by more than 2.72, no downdate fails, and after 2976 steps the factor is 1.27·10⁻¹⁴ from the matrix it is supposed to factor, against 3.87·10⁻¹⁴ with no refresh at all.

A window of 24 rows on 6 columns, moved one row at a time: each step folds a row in with Givens rotations and removes one with hyperbolic rotations, and the factor is never rebuilt from the rows except every 100 steps. The rows are integers times powers of two, so AᵀA is exact in a double and the vertical axis is a distance from the answer. No single step amplifies by more than 2.72, no downdate fails, and after 2976 steps the factor is 2.48·10⁻¹⁵ from the matrix it is supposed to factor, against 3.87·10⁻¹⁴ with no refresh at all.

A window of 24 rows on 6 columns, moved one row at a time: each step folds a row in with Givens rotations and removes one with hyperbolic rotations, and the factor is never rebuilt from the rows except every 25 steps. The rows are integers times powers of two, so AᵀA is exact in a double and the vertical axis is a distance from the answer. No single step amplifies by more than 2.72, no downdate fails, and after 2976 steps the factor is 8.72·10⁻¹⁹ from the matrix it is supposed to factor, against 3.87·10⁻¹⁴ with no refresh at all.

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.

9 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 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 113 of 238 generators — 98 print a residual and 15 are exempt with a published reason; 125 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.