ONLINE RESOURCE 1
Journal: Numerical Algorithms
Article: Simultaneous Norm Optimality for Quadratic Regularization under
Gain and Conditioning Constraints
Authors: Nguyen Bich Van; Khong Ngoc Anh
Corresponding author: Nguyen Bich Van, nbvan@vnu.edu.vn
Affiliation: Institute for Artificial Intelligence,
VNU University of Engineering and Technology, Hanoi, Vietnam

Caption: Experiment code, recorded numerical outputs, data provenance,
environment manifests, and instructions for reproducing the computational results.

CONTENTS
software/code/: experiment and artifact-generation scripts.
software/data/scalar/: recorded scalar protocol outputs.
software/data/synthetic/: synthetic solver/noise records.
software/data/revision/: matrix, conic, rank, and timing outputs.
requirements.txt: Python dependencies.
package_checksums.json: SHA-256 hashes of all other supplied files.

RENDER RECORDED RESULTS (no experiment rerun)
From the package root, with Python 3.12 and requirements.txt installed:
  python software/code/build_artifacts.py --root .
  python software/code/format_springer_figures.py
The first generates tables and diagnostic plots from the recorded CSVs.
The second generates the final six Springer figures as PDF and EPS at 119 mm
width, using the same data. All figures use the supplied recorded numerical values. The manuscript's tables are inline and editorially
formatted. After a new experiment run, review and update these inline tables.
The manuscript and official class are separate, in Source_Numerical_Algorithms.zip.

RECOMPUTE EXPERIMENTS
  python -m pip install -r requirements.txt
  python software/code/revision_experiments.py --phase all
  python software/code/revision_timings.py
Phases synthetic, conic, and benchmark can also be run individually.
Run timings without other heavy computations. Rerunning overwrites CSVs;
retain the archived records for comparison. The scalar runs are separate
and have their own manifests and legacy experiment code.

PROVENANCE
Scalar runs were recorded on 29 September 2026; matrix/conic/timing records
on 30 September 2026. Environment manifests identify Python, libraries,
CPU, BLAS, thread settings, and split/seed information. The recorded scalar
environment uses Python 3.12.14, not the version mentioned in the earlier
conference manuscript. Source-data hashes and split indices are unchanged.
Original historical timing values are not used in the present timing tables.
Historical code hashes remain in run metadata; package_checksums.json
identifies the delivered files.

KEY RECORDS
boundary_sweep.csv: 5,625 budget combinations; Figure 1.
majorization_checks.csv: 400 feasible noncommuting competitors.
conic_checks.csv / conic_solutions.json: independent conic comparisons.
matrix_pairs.csv: 780 paired designs; matrix_all.csv: 2,340 records.
matrix_selected.csv: 360 validation-selected models.
matrix_summary.csv: predictions, ten seeds per row.
rank_sensitivity.csv: 1,200 exact-design/cutoff comparisons.
pipeline_timings.csv: 150 records for the five training policies.

INTERPRETATION
Timings depend on hardware/load. Gaps and residual bounds are nominal
floating-point diagnostics, not interval certificates. Exact-designed-rank
calculations use prescribed factors and spectra. Public data are obtained
through the cited scikit-learn and statsmodels loaders. No clinical inference
or universal predictive improvement is claimed. The theorems rely on proofs,
independently of numerical checks. No experiment was rerun for formatting.

SCALAR AND SYNTHETIC RECOMPUTATION
From the package root:
  python software/code/final_experiments.py --output rerun/scalar --seeds 10 --phase all
  python software/code/additional_checks.py --output rerun/scalar
  python software/code/legacy_experiments.py --output rerun/synthetic --seeds 10
  python software/code/verify_extension.py
The first two commands reproduce the scalar protocol and boundary/stress
follow-up. The legacy script includes the historical classification protocol
as well as the synthetic records; it is not a substitute for the current
matrix benchmark. verify_extension.py writes extension_audit.csv and
extension_summary.json next to the script.

PACKAGE MAINTENANCE
The cleanup changes explanatory docstrings and one metadata reference to an
unavailable file. Executable numerical calculations, parameters and seeds
are unchanged. All supplied CSV records, split indices and source-data hashes
are unchanged. Absolute host paths in environment manifests are reduced to
library basenames; library versions, CPU and thread settings are preserved.
Historical run code hashes identify the code used for those runs and have
not been rewritten. package_checksums.json identifies the delivered files.
Network access is needed to install dependencies. Experiment loaders use
data bundled with the installed scikit-learn and statsmodels packages.
