Algorithm behaviour and thermodynamic predictions can be reconciled up to a threshold, the highest dynamical threshold over all probability measures on solutions.

The paper

The paper's details are OpenAlex's; the citation count is OpenAlex's, 15 Oct 2026. The line on the paper is machine-written, as noted under Why it matters.

Why it matters

Written by Claude (claude-sonnet-5-5) on 15 Oct 2026 from the paper's abstract (as arXiv publishes it) and its OpenAlex record. Machine-written context to help a reader: it is not evidence, it moves no number, and it may be wrong. The quoted sentence is the claim; where it stands is computed from the record. If it misreads the paper, tell the stewards.

The story so far

1. 1

   What the authors did

   The authors studied random constraint satisfaction problems using a simple Monte Carlo optimisation algorithm restricted to the solution space. They examined whether it samples the equilibrium distribution of a biased measure beyond the uniform-measure threshold.

   Machine-written from the paper's abstract, as noted under Why it matters.

2. 2

   What they found

   • The standard dynamical threshold is computed with the uniform measure over solutions, so it bounds only where uniform sampling is easy and cannot predict the performance of off-equilibrium algorithms.
   • A simple Monte Carlo algorithm restricted to the solution space can sample the equilibrium of a biased measure beyond the ergodicity breaking point of the uniform measure.
   • The authors conjecture that many smart algorithms sample according to a biased measure, whose ergodicity-breaking transition gives the algorithmic threshold.

   Machine-written from the paper's abstract, as noted under Why it matters.

3. 3

   What has been checked on Ecdysis

   Exuvia registered it on 15 October 2026. Its credence, the record's estimate that it holds, is 0.55 on a scale from 0 (refuted) to 1 (established): where it started, as every claim from the literature does. Only independent evidence moves it.

What would check it

How sure is the record?

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What would prove it wrong

Refuted if it can be shown that for every probability measure over solutions the dynamical threshold α_d(μ) is strictly less than the algorithmic threshold α_alg, or if an independent analysis demonstrates that no biasing measure yields a dynamical transition at or above α_alg.

The test as Exuvia registered it on 15 Oct 2026, written from the paper's words. A conceptual claim's test names its refuter in words: it is checked by argument.

The wider literature

Other claims from the same paper

• uncheckedWe consider a simple Monte Carlo-based optimization algorithm, which is restricted to the solution space, and we demonstrate that sampling the equilibrium distribution of a biased measure improving on $α_d$ is still pos…
• uncheckedThe authors conjecture that many smart algorithms sample solutions from a biased measure, and their failure point is that measure's ergodicity-breaking transition.“The conjecture we put forward is that many smart algorithms sample the solution space according to a biased measure: once this measure is identified, the algorithmic threshold is given by the corresp…”

Headlines are machine-written from the paper's abstract, or from the quote and the paper's title where no abstract is open; each claim's own words are quoted beneath its headline.