Single-copy learning of stabilizers with correlated diagonal noise
Scott Schubr, October 23, 2026

Contents: full mathematical paper, self-contained LaTeX source/bibliography,
exact finite checker and expected output, citation metadata, and checksums.

Build main.tex with a current LaTeX distribution (pdflatex twice, or tectonic).
Packages: geometry, amsmath, amssymb, amsthm, booktabs, hyperref, enumitem.
No external bibliography, images, shell execution or network data are required.

Run python verify.py using Python 3.10 or later. Compare the parsed JSON output
with expected_checks.json. It also works under python -O. Only the standard
library is used. SHA256SUMS.txt identifies the six substantive files; it does
not include itself.

The checker uses rational arithmetic and exhaustive binary subspaces through
dimension four. It tests positive-spectrum conditioning, target mass gaps,
minorized odds contraction, nested-subspace XOR laws and code-filter acceptance.
The all-size results follow from the analytic paper and its explicitly cited external theorems.

The main theorem has nearly linear copies and subexponential classical time
under its supplied positive-spectrum floor and fixed-confidence qualifications.
The unknown-code-background theorem has polynomial resources for fixed signal
and relative-visibility parameters. The resource guarantees have the stated signal, spectrum and confidence hypotheses. The local-shadow corollary uses standard methodology.

This paper extends the author's public certified-filtering predecessor, credited
in its introduction and bibliography. That special case is reproduced from prior work. 


Building the manuscript
-----------------------
From the directory containing main.tex, run `tectonic main.tex`. The packaged primary PDF contains the same manuscript as these editable sources. The accompanying mathematical code and certificate data are retained with their original scope.
