Matter that pays the price of perfection
In plain wordsSome gapped, translation-invariant lattice models have entanglement growing logarithmically with region size, with a coefficient that can be any nonnegative limit of a computable sequence; a separate referee cell turns low energy into strategies for a nonlocal game, though the game-driven material remains conditional.
The result
As the paper states it, in briefGapped translation-invariant lattices whose entanglement has any prescribed limit-computable logarithmic coefficient, and a referee cell that converts low energy into strategies for a nonlocal game. The game-driven material theorem is stated conditionally.
Questionson the index
How this was checked
- Audits
- One audit by a reader who had seen summaries, so not fully blind
- Fix-checks
- A targeted fix-check.
- Verification
- Two verifications
- Lean
- None.
- Peer review
- Not yet.
Every check here is internal. How we check results.
Label checked .
Novelty and credit
- Novelty
- New, with named precedents: the gap undecidability of Cubitt, Pérez-García and Wolf and the lattice constructions after it, among them Bausch, Cubitt and Watson and Purcell, Li and Cubitt; Meyerovitch and Hochman for noncomputable growth invariants; Slofstra and Vidick for precision-dependent dimension witnesses. The paper makes no claim to the first uncomputable lattice exponent.
Versionsone, each with its own DOI
| Version | Date | DOI | Notes |
|---|---|---|---|
| 1.0.0 | 10.5281/zenodo.23771444 | PDF hosted here. |
Paper, code and links
papers/matter-v1.0.0.pdf, version 1.0.0, 550,821 bytes, 27 pages.SHA-256 414c04944d1023d4f7c9b8dce899a3be3155823ccfd69d8966459a72737237b5
Corrections
None so far.
All corrections, and what counts as one.
Cite
@misc{douglas2026matter,
author = {Douglas, Seth and Mghirbi, Nidhal},
title = {Matter that pays the price of perfection},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.23771444},
url = {https://doi.org/10.5281/zenodo.23771444}
}