tables/DATA_DICTIONARY.md

Viewer data dictionary

These CSV files are packaging derivatives of recorded LHF v3.0.0 results. They add no experiments, recomputed outcomes, proof verification, or independent review. The original JSON, experiment code, saved arrays and manuscript remain the authoritative records.

Numbers are written with Python's CSV writer without rounding or percentage conversion. Validation reads the CSV values back with their stated types and compares them to the original JSON-decoded scalar values. This preserves scalar numeric values, rather than the original JSON text formatting. Fractions such as 0.935 are accuracy proportions, not percentages.

The neural study uses one fixed optical-digits split (1,257 training / 540 test samples), three training seeds, eight-dimensional frozen learned features, eight constructed observation scenarios, and six paired noise norms. Its transport comparison does not demonstrate general AI intelligence improvement or state-of-the-art superiority. Latent coordinates have no physical SI unit.

Source mappings:

CSV	Original JSON field	Rows
neural_results.csv	data/neural_digits_results.json → records (scalar fields only)	36
neural_aggregates.csv	data/neural_digits_results.json → aggregates	12
verification_groups.csv	data/mathematical_verification.json → groups	14
frontier_curve.csv	data/mathematical_verification.json → frontier_curve	61
exact_checks.csv	data/exact_certificates.json → identities, overall status and scope	20

The nested scenario_accuracies list is deliberately omitted from neural_results.csv; all original per-scenario values remain in data/neural_digits_results.json. The aggregate table copies the source aggregates; it does not recalculate them.

The exact-check JSON records one overall PASS and twenty identity labels. Its recorded_status is therefore copied from the overall run to all twenty rows. These rows are not twenty independently rerun checks and do not supply proof-assistant verification.

neural_results.csv

Field	Type	Units	Definition
seed	int64	none	Training random seed; one of 7, 23, 61.
noise_norm	float64	latent-observation Euclidean norm	Fixed norm of paired post-observation noise for each test sample and scenario.
method	string	none	Transport contraction: uniform or optimized.
mean_scenario_accuracy	float64	fraction [0, 1]	Mean test-label accuracy across eight observation scenarios.
worst_scenario_accuracy	float64	fraction [0, 1]	Minimum test-label accuracy among the eight scenarios.
mean_reconstruction_RMSE	float64	latent-state Euclidean norm	Mean across scenarios of sqrt(mean squared Euclidean state error across test samples); not per-coordinate RMSE.
maximum_state_error	float64	latent-state Euclidean norm	Largest Euclidean state-reconstruction error across all tested samples and scenarios.
deterministic_error_radius	float64	latent-state Euclidean norm	Recorded deterministic reconstruction bound noise_norm / sqrt(spectral information floor).
certified_prediction_stability_fraction	float64	fraction [0, 1]	Fraction of clean predictions certified unchanged under the prescribed radius; does not certify label correctness.
mean_prediction_stability	float64	fraction [0, 1]	Mean across scenarios of the fraction of reconstructed predictions equal to clean predictions.

neural_aggregates.csv

Field	Type	Units	Definition
noise_norm	float64	latent-observation Euclidean norm	Fixed norm of paired post-observation noise.
method	string	none	Transport contraction: uniform or optimized.
mean_accuracy	float64	fraction [0, 1]	Mean of mean_scenario_accuracy across the three training seeds.
seed_std	float64	accuracy fraction	Sample standard deviation (ddof=1) of the three seeds' mean_scenario_accuracy.
mean_worst_scenario_accuracy	float64	fraction [0, 1]	Mean across seeds of each seed's minimum scenario accuracy.
mean_reconstruction_RMSE	float64	latent-state Euclidean norm	Mean across seeds of scenario-mean root-mean-squared Euclidean state error.
mean_certified_stability	float64	fraction [0, 1]	Mean across seeds of certified_prediction_stability_fraction; does not certify label correctness.

verification_groups.csv

Field	Type	Units	Definition
name	string	none	Recorded numerical-check group identifier.
status	string	none	Status recorded in the original verification JSON; not a newly executed verification status.
cases	int64	cases	Number of seeded cases recorded for the group.
max_residual	float64	group-dependent mathematical residual	Largest residual recorded for this group; residual definitions differ by group and must not be compared as a common metric.
interpretation	string	none	Original group interpretation, including empty strings when no interpretation was recorded.

frontier_curve.csv

Field	Type	Units	Definition
B	float64	dimensionless natural-log determinant budget	Budget in |det(C)| = exp(-B) for the fixed two-dimensional noncommuting example.
exact	float64	spectral information floor in model coordinates	Recorded float evaluation of the exact closed-form optimum; CSV contains the evaluation, not a symbolic expression.
computed	float64	spectral information floor in model coordinates	Recorded numerical solver value for the same budget and example.
uniform	float64	spectral information floor in model coordinates	Recorded uniform-contraction floor at the matched determinant budget.

exact_checks.csv

Field	Type	Units	Definition
identity	string	none	Identifier from the original exact-certificate identities array.
recorded_status	string	none	Original JSON's overall certificate-run status copied to each identity row. Individual identity statuses are not separately stored and were not independently rerun during packaging.
scope	string	none	Scope statement copied verbatim from the original exact-certificate JSON.