Reproduction and data contracts
Run commands from the package directory. The exact programs require Python 3 and its standard library. They use fractions.Fraction for all rank, kernel, inversion, and decoding equalities. No account, token, external service, or network call is needed.
Full verification
python code/reproduce_all.py
The runner executes the new robust, bridge, and resource-selection suites. It then extracts the preserved original archive into a private temporary directory and reruns its original verifier. It records results/verification_summary.json and copies the original executed report into results/legacy_results.json. Repeated runs may change descriptive runtime fields; exact results and theorem statements should agree.
Planner
python code/plan_robust_calibration.py examples/dense_complete_four.json --output results/planning.json
Input fields are n, edges, trusted_rows, sensor_spaces, and optional nonnegative integer erasures, errors, and seed. A sensor space is a list of allowed ambient row basis vectors. Its rows are independently configurable from the rows of other sensors. Fractions should be quoted strings, e.g. "1/3". Vertex indices are zero based. Every matrix width equals n.
The planner is limited to 16 candidate channels because it transparently enumerates all subsets. This is a deliberate implementation limit. The mathematical theorem applies to arbitrary finite catalogue sizes.
requested_tolerance_possible is determined by the exact cut formula. The numerical coefficient search separately returns certified, already_identified, or search_exhausted_not_infeasible. A returned certified matrix has been checked against all theoretical subset ranks; its kernel witnesses and deletion profiles are computed directly. A failed bounded search is not a proof of infeasibility.
Measurement model
The decoder's input is the aligned discrepancy Y = D B0 - C = C Q, not raw observational data. The graph, latent coordinate labels and units, reference B0, trusted constraints, and aligned new mixing response D are explicit prerequisites. A corruption is an arbitrary entire sensor row; an erasure has a known location. Installed rows in trusted_rows are treated as exact and uncorrupted.
Optional plots and PDF
python code/plot_results.py
This optional script needs NumPy and Matplotlib. Two figures use exact recorded integer results; the conditioning figure is explicitly a floating-point illustration.
cd source
latexmk -pdf manuscript.tex
A standard TeX Live installation with the packages declared in the preamble is sufficient. The PDF can be rebuilt from the supplied sources and included figure PDFs. The original archive remains unchanged by the new runner.
Verification meaning
Finite tests validate implementations and examples. Universal statements rely on the written proofs; complexity claims rely on the supplied reductions and the cited rational spark theorem. No external certification, formal proof-assistant verification, or empirical sensor experiment is claimed.