Reproducibility

All decisive calculations use exact rational arithmetic. No numerical tolerance, random point sample, or remote service is required.

One-command checks

From the repository root:

make verify
make book

Or run each layer separately:

python3 artifacts/sympy/verify.py
python3 artifacts/sympy/verify_plane_attack.py
python3 artifacts/sympy/verify_resultant_route.py
python3 research/n2/certify_pseudoplane_poisson.py
python3 research/n2/search_resultant_poisson.py --poisson-degree 3
DOT_SAGE=/tmp/jacobian-sage sage artifacts/sage/verify.sage
DOT_SAGE=/tmp/jacobian-sage sage research/n2/low_degree_collision.sage
cd artifacts/magma
MAGMA_STARTUP_FILE=/dev/null /Applications/Magma/magma run_all.m

The DOT_SAGE and MAGMA_STARTUP_FILE settings only isolate user-specific cache/startup behavior. They do not change the coefficient field or algorithms.

What each implementation checks

Artifact	Threefold map	Plane descent	Near-models	Resultant route
SymPy scripts	full	identities	yes	full identities/search
Sage scripts	full	degree-3 collision ideal	no	no
Magma suite	full	structural identities	yes	core identities
Jupyter notebook	full core	documentation	documentation	documentation

Jupyter Book

Build the book with

jupyter-book build knowledge

and open knowledge/_build/html/index.html. The notebook is stored with exact outputs but book builds do not re-execute it by default, so documentation builds remain deterministic. Re-execute explicitly with:

jupyter nbconvert --to notebook --execute --inplace \
  knowledge/notebooks/sympy-verification.ipynb

Obsidian

Open the knowledge/ directory as an Obsidian vault. It already contains a minimal .obsidian/ configuration. Ordinary relative Markdown links are used so the same source works in Obsidian, GitHub, and Jupyter Book.

Expected outputs

The command-line certificates terminate on any failed assertion. Successful runs end with messages of the form:

PASS: all SymPy certificates verified exactly over Q.
PASS: all exact plane-attack certificates verified over Q.
PASS: all exact factorization/resultant route certificates verified over Q.
PASS: pseudo-plane Poisson identities and quadratic no-go certified over Q.
PASS: all SageMath certificates verified exactly over Q.
PASS: all Magma certificates completed.