Sharp noise transitions for an adaptive single-copy stabilizer-learning process
Scott Schubr, Luminary Oddities
October 22, 2026. Archive edition 2.

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.
build_pdf.py -- portable fixed-date Tectonic build helper.
CITATION.cff and CITATION.bib -- canonical Archive citation.
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.
Signal weight and finite-dimensional stabilizer fidelity are different parameters. The critical-window mean estimate is uniform over all initial ranks, with
O(n) error and an exact leading order-n recording penalty. 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.
With Python 3 and a local Tectonic executable, run from the package root:
  python build_pdf.py --tectonic /path/to/tectonic --output-dir Build
The output directory must not already exist. The helper compiles
manuscript/main.tex with a fixed source-date epoch. Standard TeX packages
may be downloaded on first use; the bibliography is embedded. Output is
Build/main.pdf. No external bibliography, data or image file is needed.

Use Python 3.10 or later:
  python verify.py
Repeat with python -O; explicit acceptance checks remain active.
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 all-n proofs.

INTEGRITY
SHA256SUMS.txt lists all members except itself. Recompute SHA-256 with your
preferred local checksum utility to check downloaded bytes. 
