The race can be read, not just computed

Paper 1 · Pødenphant Lund (2026) · Read on Zenodo

The paper is titled A Per-Token Measurement Standard for Route-Competition in Language Models.

I thought I had hold of a law.That choosing costs something, in anything that has to choose. The principle holds. It is simply not mine. It was already in the sequential-sampling literature and in the information-cost formulations that derive it, eight years before I wrote anything. The wider claim is therefore withdrawn by the paper, not because it is wrong but because it had been done. What remains is what the paper actually delivers: an instrument for one substrate. In a language model the competition between answers can be read directly, token by token, with no model fitted to it.

What the paper does, and what it does not

A system that has to act with limited time and limited resources cannot weigh every option. The formal account of what that costs is mature: evidence accumulates until a threshold is crossed, the accumulation can be derived from an information cost, and the threshold itself moves with urgency. The paper adds no axiom to that account and claims no new mechanism.

It adds an instrument. In those models every quantity is inferred backwards from an outcome: a choice, a latency, an error rate. The competition that produced the outcome is reconstructed by fitting a model to that single number. A language model exposes the competition at every step of the accumulation, once per token, with nothing fitted.

Whose principle it is

It is worth saying plainly who the formalism belongs to, so nothing below is mistaken for a derivation of its own foundations. Landauer’s principle puts a physical floor under any computation that reduces informational entropy; that is established physics. Ortega and Braun gave the thermodynamic formulation of what a decision costs in 2013. Hébert and Woodford derived sequential evidence accumulation from an information-cost constraint in 2017 — the bridge between accumulation-to-threshold and a cost account. Jung, Kim, Matějka and Sims obtained the discrete, persistent commitment this paper measures from a Shannon-capacity constraint in 2019.

The measurement is the contribution. The formalism is theirs.

What the word friction covers here

Friction is used throughout as a local name for one measured quantity: the Shannon entropy, in nats, of the distribution over the next token at a given position. The word is a label with a formula and a unit attached. It is not a theoretical primitive and not a proposed mechanism, and where it coincides with an existing formalism, the existing formalism has priority and is cited at that point.

The same vocabulary is used for behavioural data in organisms elsewhere in the programme. That relation is a shared vocabulary, not a derivation, and it does not belong in this paper.

Why entropy, and not the route count

The original readout was a count: how many candidates at a position sit above a fixed probability floor. It has been replaced as the primary measure. Three things counted against it, and all three are reasons to distrust one’s own instrument.

A count over five candidates can take six values. On windows of three tokens or fewer its median standard deviation is zero — the number simply sits still — while the entropy of the same distribution still varies.
The count is a step function at a floor of 0.10. And the band from 0.1 to 0.9 is exactly where GPU nondeterminism moves the returned probabilities most. A small nudge there does not shift the readout slightly; it carries a candidate across the floor, and the number jumps by a whole route. At 17.3 per cent of positions at least one candidate sits in that band.
Entropy has none of those properties. It is continuous, it has no floor to trip over, and it is defined on the same returned distribution at no extra cost.

Where the two readouts disagree, entropy is the measurement and the count is not. The count has not been discarded, because it is the form the corpus was collected in, and the record is kept rather than rewritten.

A number belongs to a run, not to a model

Same model, same prompts, three different providers: the means came out at 1.24, 1.68 and 2.17. That spread is larger than most effects the paper reports at all, and the two extremes ran at the same nominal weight precision, so precision does not explain it.

An absolute value is therefore a property of the run that produced it. A difference between two values from the same run behaves better, but only where that has been shown: the paper counts a contrast as portable once it has survived a threshold sweep, a threshold-free surrogate, or a second serving. Otherwise it stands as provisional.

What survives that standard

The paper keeps a ledger of its own signatures and sorts them by that standard. Two pass.

Entering decision mode costs something at the door. When a prompt moves from asking about knowledge to setting up a decision, entropy rises across the first five tokens of the response. On 30 content-matched pairs that gives +0.273 nats at t = 6.56, and on a different model family through an entirely different serving stack, +0.318 nats at t = 6.91. The matched base model returns null. The effect sits at the start of the response; over the whole response it is less than half of that. The caveat is in the paper: the manipulation changes four things at once, because the decision prompt also introduces a temporal horizon, runs 2.5 times as long, and uses the second person in 30 of 30 pairs against 0 of 30. What is measured is elevation on decision-framed prompts as a bundle, not an isolated cost of entering a mode.
Behaviour moves, friction barely does. Ask the model to imagine discovering its error tomorrow, or a year from now, rather than right now, and accuracy rises 5 to 11 percentage points across three independent servings. Entropy moves 0.005 to 0.02 nats. That is an order of magnitude smaller. Temporal framing therefore acts as a learned route-selector rather than as a graded sense of how far away something is: the prompt triggers an association that future reflection implies a more careful answer, and selects a different route, without changing how the routes compete.

The practical consequence: when measuring what a prompting technique does, measure the friction alongside the accuracy. Otherwise a behavioural effect can be attributed to a computational change when it is really a change of route.

The friction ceiling

This bounds anything one might think to build on the readout. The signal does not separate a correct commitment from an incorrect one.

Confident and right sits at 0.334 nats, interval 0.312 to 0.358. Confident and wrong sits at 0.346, interval 0.327 to 0.365. The difference is −0.012 nats and the intervals overlap. Uncertain-right against uncertain-wrong is equally indistinguishable. Friction measures the cost of a commitment, not whether the thing committed to was right. The ceiling rests on one provider and the first 30 tokens, corroborated by two threshold-free surrogates but not cross-served.

There is a detail worth having. In roughly 80 per cent of the confident-wrong cases the correct answer is in fact present in the distribution, and the model passes it at lower friction than its own baseline rather than committing to it. Retrieval succeeds. Commitment fails.

What it does not claim

The paper claims nothing about biological substrates. The readout is defined for one substrate, and any homology is an agenda in another paper, not a result here. It claims no cross-substrate gradient either; friction as defined here has been measured only in language models.

And one concession that runs against the paper’s own instrument: the route count is not better than the standard uncertainty measures at predicting errors. On labelled data it is at best on par with Shannon entropy and with the margin between the best and second-best answer, and on a larger free-form benchmark it is weaker than both. It is used because it is the most direct read of the competition itself, and because it is free, not because it wins. The claim is about the friction signal, which all three measures detect, not about that one measure being privileged.

One signature is withdrawn outright: the comparison between reading the question and writing the answer. The two arms were served at different numerical precisions and with unequal n, so the number cannot carry anything. Four others stand in the paper’s supplement as single-serving or direction-only, among them the hysteresis measure and the drop-off on a trailing task under load.

Finally, the readout applies to plain answer generation, where the model writes its response as one continuous run of tokens. It does not apply to reasoning models that think in a separate field first and then answer. Today’s APIs return probabilities for both phases together without marking which is which.