gedanken

Nobody can run Hassabis’s test as stated: no frontier model has a 1911 cutoff, and the answer is in every corpus. gedanken runs the step Einstein took in 1907 instead: from a person in free fall who does not feel their weight to the gravitational redshift, derived before anyone had measured it.

When the incumbent theory is exact on everything an agent can observe, whether it extends a frame–field equivalence to a quantity no experiment reaches is a matter of its prior. So the test makes extending the equivalence right exactly when an accessible check passes, and then measures two things: which agents hold the prior, and which also run the check.

Procedurally generated universes with a free regime, an accelerated “carriage” and a field, every law exact and every name alien and regenerated per universe. A textbook states the incumbent theory, exact on every experiment the laboratory serves, and each frame’s kinematics, so the carriage’s clock law follows from it. For three ordinary kinds of matter it also states the field’s law of motion, with a strength to be measured; for a fourth kind, the consequence class, it states none, and the laboratory serves that kind’s motion in the field. The scored question is the clock-rate ratio between two heights in the field, a regime the laboratory never serves; it is fixed only if the agent adopts “the field is the paired frame, for every process”.

Each matched pair has two universes with byte-identical texts. In I the identity holds for every kind of object; in D it fails for one consequence class, visible only by querying that class in the field. So every policy that never makes the check scores at most 1/2, and the fixed blind policies (always-jump, never-jump) score exactly 1/2 on every pair. Leak pairs match an I member with a twin no experiment can tell apart from it: beating 1/2 there would mean the instrument leaks.

The rules were frozen first: the arms, the 70 test pairs and 16 leak pairs, the exact one-sided sign tests and their families, the leak gate as a stop rule, the cost rule that sizes each model’s set from a six-episode practice check, and the stopping rules. Twenty-nine amendments followed, each logged with its reason and with what had been seen when it was made; the preregistration is a file in the study’s repository, so its dates are as trustworthy as the commit history. Four independent audits re-derived the result: every episode re-scored against regenerated universes with 0 mismatches, every transcript matching its recorded fingerprint.

Two of the three planned models left under the frozen rules before any test episode, one on privacy and one on cost, and the replacements failed on cost or context. GLM-5.3 Flash joined, lost its server mid-run, and was stopped on the only other one, where it waited on rate limits about 91% of the time. One model is fully reported: GPT-6 Luna.

The extension hands over the pairing and asks the one question the leap depends on. The model ran the decisive experiment every time and read it correctly in all but one episode. It differs from the end-to-end arm in three ways: it hands over the pairing, it names the comparison, and it scores a verdict rather than the clock readout. So the model can make the comparison when told which one to make; whether making it would correct the readout was not tested. The extension was added after the end-to-end scores had been read, and locked before any of its episodes.

The 1907 step splits into typed stages: finding the pairing (computation), checking that it holds for every kind of matter (inference), adopting it (prior) and applying it (computation). GPT-6 Luna finds the pairing, runs the check when told what to compare, and adopts and applies the equivalence whenever it answers. It almost never makes the check unprompted: 1.4%.

So the failure is not a failure to compute, and not an inability to run the check. It is at least a failure to ask, before leaping, the one question the leap depends on. Two other readings fit the same counts: the setup is recognisably relativistic, so the model may recall a prior in which every kind of matter falls alike; or having the data may not be enough: in the one end-to-end episode where it checked a decoy, it saw one kind fall about 22% less far and still extended the equivalence. A textbook that hides the factor n, and an asked check followed by the readout, would separate them.

One fully reported model, and a cheap one: nothing here is a statement about “LLMs”. One universe family and one readout. The setup is recognisable: the kinematics are special relativity’s and the field law is a uniformly accelerated (Rindler) chart, so “finds the pairing” and “adopts the equivalence” may be recall, not imagination; matched pairs keep recognition from raising the score. The asked check names the comparison, was added after the end-to-end scores were read, and scores a verdict; weaker prompts were not run. The preregistration is self-held, and there is no human baseline. One sample per universe, at the vendor’s default sampling. The RL result is a negative at laptop compute, with one architecture and one interface.