Our rebuild of the collapse model.

We rebuilt the collapse study’s model from the equations in its paper, then checked our results against every number the paper states in its text. It’s our own version—not the authors’ code—and it never replaces their results.

Side by side with the paper.

“Time active” is the share of the 1,000 years a civilization spends running rather than collapsed; the paper calls it the duty cycle. Where the paper only shows a chart, there’s no exact number to compare.

Averages from our 20,000 runs of each future, next to the paper’s numbers.
Future	Time active, ours	Time active, paper	Collapses, ours	Collapses, paper	Match
S1	63.1%	Chart only	9.7	10.0	Yes
S2	61.0%	Chart only	5.9	Chart only	Yes
S3	100.0%	100.0%	0.0	0.0	Yes
S4	38.2%	38.1%	6.6	6.6	Yes
S5	99.0%	99.0%	0.5	Chart only	Yes
S6	79.4%	Chart only	4.3	4.5	Yes
S7	58.0%	57.0%	7.4	7.5	Yes
S8	87.3%	87.0%	1.9	2.0	Yes
S9	91.1%	91.0%	1.5	1.5	Yes
S10	100.0%	100.0%	0.0	0.0	Yes

From the paper

Settings and results

We copy the model’s settings from the paper’s Table 4, and its results from the numbers it states in its text. Results it only shows in charts stay blank.

Our own

The rebuilt model

We coded the paper’s three equations ourselves. Where the paper leaves details open—how ties break, exactly when recovery starts—we made our own documented choices.

Limits to keep in mind

This is our own version of the published equations, not the authors’ code.
Where the paper leaves the timing of each yearly step open, our choices may differ from theirs.
We only check numbers the paper states in its text; we never guess from charts.
The authors’ code and summary data are linked, not copied, because they have no license.

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