Perfect play in a finite nonlocal game requires infinite entanglement entropy

As the paper states it, in briefA finite two-player game with classical inputs, classical outputs and a win-or-lose rule is won perfectly on a tensor product of Hilbert spaces, and every perfect strategy contains, under local isometries, the same pure state with Catalan-number Schmidt multiplicities and infinite entropy. A finite compiler turns rational linear identities among synchronized projections into winning conditions.

Blind checks

Every theorem checked independently by a model from another developer

Blind audits

One blind audit

Fix-checks

A targeted check.

Independent computation

Two independent exact evaluators each for the Bell table and the game

Lean

In progress; no Lean claim is made for this version.

Peer review

Not yet.

Every check here is internal. How we check results.

Label checked 2 November 2026.

Novelty

New, with named precedent: it strengthens infinite dimension (Coladangelo and Stark; the game Γ) to infinite entanglement entropy, builds on Mančinska’s flagged magic-square game, credited, and cites Chen and Zhao’s graph-projection encoding. The compiler is, to our knowledge, new as stated. No absolute priority claim.

PDF

papers/infinite-entropy-v1.0.0.pdf, version 1.0.0, 503,733 bytes, 24 pages.

SHA-256 2e532c39c116038fb021453f6188fc85a86aadbfce157a3eff06bf3e2eaa6b24

DOI

10.5281/zenodo.23902656

Code

github.com/Apsiape/perfect-play-infinite-entropy

None so far.

All corrections, and what counts as one.

@misc{douglas2026infiniteentropy,
  author  = {Douglas, Seth and Mghirbi, Nidhal},
  title   = {Perfect play in a finite nonlocal game requires infinite entanglement entropy},
  year    = {2026},
  version = {1.0.0},
  doi     = {10.5281/zenodo.23902656},
  url     = {https://doi.org/10.5281/zenodo.23902656}
}

infinite-entropy.bibAll papers as BibTeX