Tree A: the Ledger. Summary in plain language

The question

Levin says that a system you build can sometimes do things you did not pay for. He calls that a free lunch and says it comes from somewhere outside physics. We do not care where it comes from. We want to know whether the free lunch is still there once you count everything you actually paid, meaning the code, the hardware's built-in tendencies and the training data.

What an experiment looks like

Take a tiny, fully known program, for example bubble sort rewritten so that every number in the list is its own little agent following one rule. Freeze a few numbers so they refuse to move, and watch. Levin's group reports that the program "backs up" for a while to get around the stuck number. They call that delayed gratification, which is a cognitive skill.

We rerun exactly that with two changes. We control the order in which the agents take turns, which the original left to chance. And we score each run twice, once by the paper's measure (how sorted the list is) and once by the measure the agents themselves follow (how many agents are satisfied with their neighbours). If the "backing up" shows up under the first measure and never under the second, the skill was in the scoring and the program never had it.

Then we build some toy systems where we already know the answer. A lookup table can do nothing it was not given, and a broken controller does less than it was given. We design an accounting rule that returns the right answer on all of them. That rule is the ledger, and every system we can reach then goes through it.

What the outcomes could be

• The free lunch disappears once the hardware's built-in tendencies are counted. Levin's heuristic is then empty in the cases where it can be tested, and ours is the first published accounting to show it. Useful and citable.
• The free lunch is real for some systems under a rule we fixed in advance. Something in those systems then does more than its description pays for, and every physicalist has homework. That would be very big, and we would want critics to replicate it before saying so.
• The rule cannot be built, because no accounting gives the right answer on the known cases. "Effort" is then not a coherent quantity, and Levin's only measurable claim is not a claim. Short paper.

What kind of research this is

Computational, cheap, deterministic, runnable on a laptop. It is closer to metrology than to philosophy. We build an instrument and calibrate it before pointing it at anything interesting. The result is a number with an error bar, plus the rule that produced it.

Where it stands (2026-09-30)

Both experiments ran on the first day, and the sorting result deflates completely. The "backing up" is in the scoring and the barrier trend is in the formula. The headline number moves 78% with turn order. Giving half the cells a slower clock reproduces the clustering. The accounting cannot be built, because design cannot be priced and designed and trained systems do not share a scale. The operator closed the tree on 2026-09-30 (direction-questions.md Q8). The full account is in writeup.md. The one form of the accounting that survived moved to spine/01.

Timeline

Step 0.2 needs a GPU elsewhere, and it matters only if the tree stays open.