Preprint Publications
The NASA Paper & Small Falcon Algebra by EDM
Introduces N/U Algebra, a conservative and reproducible framework for propagating uncertainty in science and engineering. Each quantity is represented as a pair (n,u) of nominal value and uncertainty, with algebraic rules designed to ensure transparency, monotonicity, and closure on nonnegative uncertainty. The framework provides a consistent extension of arithmetic that preserves invariants and maintains associativity under multiplication.
The NASA Paper and Small Falcon Algebra Numerical Validation Dataset
Provides the official reference implementation and numerical validation dataset for N/U Algebra. Includes complete Python source code, reproducible validation experiments, and example scripts. Contains over 70,000 test cases confirming closure, associativity, and conservatism within machine precision, with all results stored as CSV files under deterministic RNG seed.
Conservative Framework for Bounded Uncertainty Propagation with O(1) Computational Complexity & Provable Coverage Guarantees
Presents the first mathematically defined uncertainty propagation system that maintains provably constant time and space complexity per operation (O(1)), remains enclosure-preserving under arithmetic composition, and is algebraically closed under addition, scalar multiplication, and product. Achieves deterministic, conservative, and auditable uncertainty propagation suitable for real-time and governance-critical systems by enforcing a bounded epistemic horizon.
Key Innovation: First system to achieve constant-time uncertainty propagation across arbitrary arithmetic computations
Performance: 0.8 seconds (single core) vs. 47 hours (512-core cluster) for 1000 time steps
Performance: 0.8 seconds (single core) vs. 47 hours (512-core cluster) for 1000 time steps
Independent Reproducibility Test of Hubble Constant (H₀) Calculation Achieving 0.966σ Concordance with Planck CMB
Documents independent verification of computational reproducibility for Hubble constant calculations. Achieves H₀ = 68.518 ± 1.292 km/s/Mpc with 0.966σ concordance with Planck CMB measurements. Includes RENT Validation Framework with adversarial testing, cryptographic verification, and automated reproducibility proof. All result files are byte-for-byte identical when regenerated on independent machines, demonstrating complete computational reproducibility.
Result: H₀ = 68.518 ± 1.292 km/s/Mpc
Validation: 9/9 result files byte-for-byte identical on independent machines
Validation: 9/9 result files byte-for-byte identical on independent machines
All preprints are available on Zenodo with open access. Code and data are publicly archived for full reproducibility.