Sharp noise transitions in adaptive single-copy stabilizer learning
Scott Schubr

CONTENTS
Sharp_Noise_Transitions_Adaptive_Stabilizer_Learning.pdf -- complete paper.
manuscript/main.tex -- self-contained LaTeX source, including bibliography.
verify.py -- exact finite mathematical controls; Python standard library only.
expected_checks.json -- expected output of the verification program.
SHA256SUMS.txt -- SHA-256 identities of all other members.

MATHEMATICAL SCOPE
The paper analyzes the specified Bittel et al. adaptive update under a global
depolarizing input mixture, with ideal operations and fixed prime dimension.
Its obstruction is algorithm-specific and starts at missing-diagonal rank n.
It is not a lower bound for every adaptive single-copy algorithm. Signal weight
and finite-dimensional stabilizer fidelity are different parameters. Candidate
generation and the subsequent fresh-copy validation stage are distinguished.

READING AND REPRODUCTION
Read the PDF for the full analytic proofs, definitions and attribution.
From the manuscript directory, compile with a standard LaTeX distribution providing amsmath,
amssymb, amsthm, geometry, hyperref and the other packages listed in main.tex:
  pdflatex main.tex
  pdflatex main.tex
Tectonic is an alternative compiler. Compilation may require package downloads
on a fresh TeX installation. No external bibliography or image file is needed.

Use Python 3.10 or later, with ordinary assertions enabled:
  python verify.py
Do not use Python's -O or -OO optimization flags, which remove assertions.
The JSON output should equal expected_checks.json. No third-party Python
library, input file, network connection or output-directory permission is needed.

The program exhausts all unsigned Lagrangian spaces for n=1,2 and primes
2,3,5,7, applies every sampled-difference label and every correction slope, and
checks the exact rank-transition probabilities at three rational signal-square
values. It also solves 192 exact rational hitting-time systems and 128 exact
candidate-recording systems. These finite controls supplement the analytic
proofs; neither numerical sampling nor enumeration establishes the all-n limits.

INTEGRITY
SHA256SUMS.txt lists all members except itself. Recompute SHA-256 with your
preferred local checksum utility to check downloaded bytes. A matching hash
identifies the files; it does not independently prove the mathematics.
