Perfect play in a binary-scoring nonlocal game requires infinite dimension but only finite energy

As the paper states it, in briefA game with ten and eleven questions and at most six answers is won perfectly by an infinite-dimensional strategy and by no finite one, with dimension profile $10{\log }_2(1/\epsilon )+O(\log \log (1/\epsilon ))$. Perfect play needs only finite energy: $275/18$ quanta per oscillator at best.

• Answered Can a game with a binary score witness the separation between finite-dimensional and spatial quantum correlations? posed by others
• Answered Can perfect play in a finite game require infinite dimension yet only finite energy?

Blind audits

One blind audit

Fix-checks

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Verification

Eight block verifications

Lean

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Peer review

Not yet.

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Label checked 30 October 2026.

Novelty

Extends named prior work: its building block is Mančinska’s flagged magic-square game, credited. Coladangelo and Stark, and Beigi, separated finite-dimensional from spatial correlations earlier for exact correlations; this game answers a possibility raised by Coladangelo and Stark. The paper makes no absolute priority claim.

PDF

papers/perfect-play-v2.0.0.pdf, version 2.0.0, 748,029 bytes, 39 pages.

SHA-256 b52cf777f273b7aa8f430986d3f15f2780e17830bed5f7ea32c956b2b2711c34

DOI

10.5281/zenodo.23772890; all versions 10.5281/zenodo.23754446

Code

github.com/Apsiape/spatial-perfection-game

1. 29 Oct 2026Version 2.0.0. Packaging: versions 1.0.0 and 1.1.0 omitted the recorded outputs of the finite checks. Version 2.0.0 includes them.doi:10.5281/zenodo.23772890

All corrections, and what counts as one.

@misc{douglas2026perfectplay,
  author  = {Douglas, Seth and Mghirbi, Nidhal},
  title   = {Perfect play in a binary-scoring nonlocal game requires infinite dimension but only finite energy},
  year    = {2026},
  version = {2.0.0},
  doi     = {10.5281/zenodo.23772890},
  url     = {https://doi.org/10.5281/zenodo.23772890}
}

perfect-play.bibAll papers as BibTeX