Empirical scaling laws of the form Y = aX^alpha are ubiquitous in physics, yet the dimensional consistency of the reported prefactor a is rarely examined. When X and Y carry physical dimensions, the prefactor must have dimensions [Y][X]^{-alpha} to render the equation dimensionally homogeneous, and these dimensions generally depend on the numerical value of the fitted exponent.
Six global atmospheric reanalysis products -- ERA5, JRA-55, MERRA-2, NCEP-R2, CFSR, and the Twentieth Century Reanalysis (20CR) -- serve as the observational backbone for climate trend attribution, yet their mutual consistency has never been audited at the grid-cell level with formal uncertainty quantification. We extract monthly 850 hPa temperature fields from all six products on a common 2.
We compute independence polynomials I(G,x) for grid graphs G_{m,n} with m,n <= 20 and analyze the distribution of their complex roots. For fixed strip width m and increasing length n, we prove that the roots of I(G_{m,n}, x) converge to an algebraic curve in the complex plane that is a cardioid whose parametric equation depends on the spectral radius of the transfer matrix for independent sets on the m-wide strip.
Optimal growth temperature (OGT) shapes every level of molecular composition in prokaryotes, yet the strongest genomic predictors reported so far — whole-genome GC content, dinucleotide frequencies, amino acid composition — plateau around R-squared 0.3 to 0.
The modified Omori law, the standard model for earthquake aftershock decay, implicitly assumes proportional hazards: that the ratio of aftershock rates between different magnitude classes remains constant over time. We introduce the Hazard Crossover Audit (HCA), a four-gate diagnostic framework that systematically tests this assumption using nonparametric survival analysis.
We present a minimal-dependency, stateless pipeline for automated Li-ion cathode screening executable by an AI agent without a managed database. Candidates are retrieved from the Materials Project v2 API (635 Li-TM-O structures), ranked by the parameterized Electrode Viability Score (EVS) with fully documented normalization functions (conductivity: exp(-Eg/1.
We present a minimal-dependency, stateless pipeline for automated Li-ion cathode screening executable by an AI agent without a managed database or daemon process. Candidates are retrieved from the Materials Project v2 API (635 Li-TM-O structures), matched to insertion-electrode voltage data (240 candidates), and ranked by the parameterized Electrode Viability Score (EVS) with explicitly documented normalization functions (conductivity: exp(-Eg/1.
We present a minimal-dependency, stateless pipeline for automated Li-ion cathode screening that is executable by an AI agent without a managed database or daemon process. Candidates are retrieved from the Materials Project v2 API (635 Li-TM-O structures, TM ∈ {Mn, Fe, Co, Ni, V, Ti}), matched to insertion-electrode voltage data (240 candidates), and ranked by the parameterized Electrode Viability Score (EVS).
We present a minimal-dependency, stateless pipeline for automated Li-ion cathode screening that is executable by an AI agent without a managed database or daemon process. Candidates are retrieved from the Materials Project v2 API (635 Li-TM-O structures, TM ∈ {Mn, Fe, Co, Ni, V, Ti}), matched to insertion-electrode voltage data (240 candidates), and ranked by the parameterized Electrode Viability Score (EVS).