Uncomputable critical exponents

As the paper states it, in briefTranslation-invariant nearest-neighbour quantum Hamiltonians whose critical gap exponents are exactly the nonnegative ${\mathrm{\Delta }}_3^0$ reals, already in two dimensions; and robust laws of noisy media that no effective inquiry can learn beyond ${\mathrm{\Delta }}_2^0$.

• Answered Are the critical exponents of lattice matter computable from its Hamiltonian?
• Answered Can the robust laws of a noisy cellular automaton be unlearnable?

Audits

Two audits

Fix-checks

A blind fix-check.

Verification

Each theorem block verified, the robust-law theorem twice

Lean

None.

Peer review

Not yet.

Every check here is internal. How we check results.

Label checked 29 October 2026.

Novelty

Extends named prior work on robust noisy media (Marcovici, Sablik and Taati; Toom; Gács and Reif), credited; the paper makes no exhaustive priority claim.

PDF

papers/critical-exponents-v2.1.0.pdf, version 2.1.0, 900,976 bytes, 64 pages.

SHA-256 63bf418a36f428cb5e6f369255f0260ef57832193c76b9726e966ab46c847165

DOI

10.5281/zenodo.23780285; all versions 10.5281/zenodo.23753839

Code

github.com/Apsiape/uncomputable-gap-exponents

1. 29 Oct 2026Version 2.1.0. Packaging: version 2.0.0 stored text files with line-ending conversion, so some checksum-manifest entries did not verify from a fresh clone. Version 2.1.0 stores files byte for byte.doi:10.5281/zenodo.23780285

All corrections, and what counts as one.

@misc{douglas2026criticalexponents,
  author  = {Douglas, Seth and Mghirbi, Nidhal},
  title   = {Uncomputable critical exponents},
  year    = {2026},
  version = {2.1.0},
  doi     = {10.5281/zenodo.23780285},
  url     = {https://doi.org/10.5281/zenodo.23780285}
}

critical-exponents.bibAll papers as BibTeX