How to read a ProjectForty2 receipt

Most of what ProjectForty2 publishes is a number with a file behind it. That file is the receipt. This post walks through one, line by line, so you know what to look for in the others.

The four parts

Take Ford's receipt for A364132(28) = 75, from the Erdős #357 post.

1. Claim. One sentence that says exactly what is being claimed, and what kind of evidence backs it: "An exhaustive computer search by two independent engines, not a proof."
2. Method. Which program ran, with its sha256 hash so you can confirm you have the same file, how the search was split up, and what each part answered.
3. Cross-check. A second, separately written program and what it found. When both agree, the receipt says so; when they don't, that goes in the receipt too.
4. Disclosed. What the check does not cover. For this one: the two engines share a method, the full replay was not re-run before merge, and it says nothing about the long-run question Erdős asked.

The last part matters most. A receipt that only lists what worked is an advertisement.

Rerunning one yourself

Some certificates are small enough to check on a laptop. Our Erdős minimum-overlap certificate replays "in under a second using only the Python standard library" (repository). Larger searches list their commands and node counts so you can rerun a single part rather than the whole thing.

What we do when a receipt is wrong

We fix it in public. Our journey page tells the story of a result we did not submit: "Our first apparent minimum-overlap win exploited a rescaling step the scorer did not check tightly enough. We refused to submit it." (journey). Corrections to blog posts are listed on the corrections page.