Computational Verifications
Independent computational analyses testing MAGELLAN hypotheses against real data. Each verification runs reproducible code on published datasets to confirm, refute, or qualify the AI-generated predictions.
Kerr QNM Level Spacing Statistics
Verifying: Near-Extremal Kerr QNM Pair Correlation Matches the Montgomery-Odlyzko Sine Kernel (Prime numbers (number theory, prime distribution, Riemann zeta function, prime gaps) x Black holes (general relativity, Hawking radiation, information paradox, singularities, event horizons))
Data falls between GUE and Poisson. Clear level repulsion rules out pure Poisson. W increases monotonically with spin, crossing GUE at a/M~0.9 -- not near-extremal as H3 predicted. GUE-like statistics appear at moderate spin, a novel computational observation not found in prior literature.
Data: qnm package (Stein 2019, JOSS 4:1683) -- Leaver continued fraction method, s=-2 gravitational perturbations
Competing Risk Theorem for Protein Design
Verifying: The Dominant Competing Risk Theorem -- Optimizing One Failure Mode Provably Accelerates Another (Competing risks survival analysis (Fine & Gray 1999, actuarial roots >200y) x De novo protein design for therapeutics (RFdiffusion 2023, ProteinMPNN 2022, <4y))
Original broad claim falsified (GPT-5.4 found valid counterexample: global stabilization). Ceteris-paribus version proven analytically and validated with Monte Carlo (N=10,000). Gap formula confirmed across 100 random parameter combinations (max error 1.44e-15).
Data: Analytical proof + Monte Carlo simulation (N=10,000); realistic protein failure mode parameters from literature
Nelson-Aalen Cumulative Hazard Decomposition for Accelerated Stability Studies
Verifying: Nelson-Aalen Cumulative Hazard Decomposition Reveals Hidden Failure Modes in Accelerated Stability Studies (Competing risks survival analysis (Fine & Gray 1999, actuarial roots >200y) x De novo protein design for therapeutics (RFdiffusion 2023, ProteinMPNN 2022, <4y))
7/7 checks passed. Jensen's Inequality confirmed analytically and numerically. Single-Ea Arrhenius overestimates shelf-life by 1.77-2.29x for real proteins. Nelson-Aalen decomposition reduces bias from 1.93x to 1.10x.
Data: Literature Ea values: Sanchez-Ruiz 1992, Wakankar & Borchardt 2006; ICH Q5C standard
GEV Tail Index Analysis of the Meltome Atlas
Verifying: GEV Tail Index (xi) as Phylogenomic Signature of Thermal Adaptation Strategy (Extreme value statistics (GEV distributions, tail index analysis, return level estimation, peaks-over-threshold) x Proteome-wide thermal stability distributions (thermal proteome profiling, Meltome Atlas))
No significant Spearman rank correlation detected (rho=-0.136, p=0.658) across 13 species. Pearson r=-0.628 (p=0.022) suggests a linear trend driven by extremes. Possible explanations: measurement censoring, phylogenetic confounds, or effect too weak to detect with 13 species.
Data: Jarzab et al. 2020, Nature Methods 17:495-503 (PRIDE: PXD011929)
Cramer-Rao Bound for Plant Gravitropic Sensing
Verifying: Cross-Species CRB Landscape Predicts Gravitropic Precision Hierarchy Across Statolith-Based Plant Organs (Statistical estimation theory / information geometry (Cramer-Rao bound, Fisher information) x Plant gravitropism / statolith-based gravity sensing)
The CRB (0.79-2.36 deg) is a valid, non-trivial lower bound on plant angular resolution (1.0-5.0 deg). Plants operate 1x-6x above the fundamental physical limit -- comparable to photoreceptors (5-10x above shot noise). First application of statistical estimation theory to plant gravitropism.
Data: Berut et al. 2018, PNAS 115:5123; Chauvet et al. 2016, Sci. Rep. 6:35431