DOI: 10.5281/zenodo.17221863
title: The NASA Paper and Small Falcon Algebra Numerical Validation Dataset

description: The NASA Paper and Small Falcon Algebra Numerical Validation Dataset

Updated Citation



Martin, E. D. (2025). The NASA Paper & Small Falcon Algebra – Reference Implementation and Validation Dataset (v3.0.0). Zenodo. https://doi.org/10.5281/zenodo.17221863 


Releasing GitHub Repo

https://github.com/abba-01/nualgebra

This dataset provides the full numerical validation results underlying The NASA Paper & Small Falcon Algebra study. It contains reproducible experiments confirming the mathematical properties of N/U Algebra, a conservative linear framework for uncertainty propagation.

The dataset includes:





Addition sweeps (8,000 cases): N/U vs. Gaussian root-sum-square uncertainties, showing strict conservatism (median ratio ≈1.74).




Product tests (30,000 cases): N/U vs. first-order Gaussian propagation, capped by the theoretical √2 bound (≈1.414).




Interval relations (30,000 cases): Half-width consistency between N/U products and exact intervals, with only floating-point deviations (<0.015%).




Chain multiplications (3–20 factors): No explosion; N/U matches interval growth within machine precision.




Monte Carlo comparisons (24 distributions × parameter sets): Empirical standard deviations never exceed N/U uncertainty.




Invariant grid (54 points): Conservation law M = |n|+u holds exactly.




Associativity checks (30,000 trials): Nominal associativity preserved up to machine precision.



All results are stored in CSV form with a machine-readable summary.json. Random number generation is fully deterministic (seed = 20250926). Floating-point tolerances are set at abs_tol = 1e−9, rel_tol = 1e−12.

UPDATED VERSION HIGHLIGHTS

What’s New in v3.0.0 Click Here for V3.0.0





Rewritten and verified Python module (nu_algebra.py) implementing all algebraic definitions from the 2025 NASA Paper revision:





Addition/Subtraction → (n₁ ± n₂, u₁ + u₂)




Multiplication → (n₁n₂, |n₁|u₂ + |n₂|u₁)




Scalar/Affine → (an + b, |a|u)




Catch → (0, |n| + u) Flip → (u, |n|) (Invariant M = |n| + u preserved)






Full worked examples from Section 7 reproduced in examples/basic_operations.py.




Regenerated validation data (70 000 + cases) confirming closure, associativity, and conservatism within machine precision.




Added cumulative and weighted-mean operators for statistical aggregation.




All prior datasets recomputed under deterministic RNG seed = 20250926 with absolute tolerance 1 × 10⁻⁹ and relative tolerance 1 × 10⁻¹².



Dataset Highlights





Addition (8 000 cases): N/U ≥ Gaussian RSS — median ratio ≈ 1.74




Products (30 000 cases): N/U ≥ First-order Gaussian — max ≈ √2 (1.414)




Interval Relations (30 000 cases): Half-width match ≤ 0.014 % relative error




Chain Multiplications (3–20 factors): Stable, no growth beyond interval bounds




Monte Carlo (24 distributions): Empirical σ never exceeds N/U uncertainty




Invariant Grid (54 points): M = |n| + u preserved exactly




Associativity (20 000 trials): Nominal and uncertainty parts agree within floating-point precision



All results are stored as CSV files with a machine-readable summary.json. The entire workflow is deterministic and reproducible under Python ≥ 3.9.

Citation



Martin, E. D. (2025). The NASA Paper & Small Falcon Algebra – Reference Implementation and Validation Dataset (v3.0.0). Zenodo. https://doi.org/10.5281/zenodo.17221863


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