alphaProvenanceCert

"Extensive experiments on 3 tasks across 6 datasets demonstrate... gains of up to 4.10% and 5.65%"

"optimal learning rate follows … T^{-0.32} … magic exponent"

"We present early results for 1-loop lattice perturbation theory improvement of the Wilson loop and show how it improves the α_s extraction. We present a preliminary reanalysis of the TUMQCD (2+1)-flavor QCD data."

"ibDET provides accurate spectral properties with much reduced cost... errors... around 0.1 eV"

"Theorem 1.1... α > 11/40 for n ≥ n_α... asymptotic solution to 2(12α−3)ln(3α)=(1−3α)(3ln3−4)"

"sideband amplitudes a± = i χ a0 a1* a2 ... χ = sqrt(π/2) ξ K F / |sin θ| ... SNR formula (23) with integration time τ"

"A TFNO ensemble reaches a held-out root-mean-square error of 198.2 keV"

"best fit model ... C/O ratios of 0.5-0.7 ... chemical ages ... 0.6 and 5 Myr"

"α_s = 0.7, σ = 0.1 GeV² (as used in description of quarkonia), and m = 0.33 GeV. ... the eigenvalues ε_n are proportional to √n; assuming that n equals the integer part of A^(2/3), the cavity radii r* then scale as R_0 A^(1/3), with R_0 ≈ 1 fm"

"Both the kernel bandwidth σ and the complex parameter ω are selected via grid search."

"M0 = 9.02 meV, M1 vx vy = −1.58 eV·nm², Mz = 13.1 meV·nm², Dz = −4.58 meV·nm², carrier density n0 = 1.7×10^17 cm⁻³"

"Estimations based on quantum field theory suggest the vacuum energy should be ∼10^113 joules per cubic meter, whereas observations indicate ∼10^−9 joules per cubic meter. This discrepancy of ∼10^120 is the 'cosmological constant problem'."

"√σ ≈ 0.412136 GeV, mu ≈ 0.134247 GeV, ms ≈ 0.221086 GeV, mc ≈ 1.44844 GeV, mb ≈ 4.78122 GeV (five fitted parameters)"

"Current challenges, e.g., U-parameter sensitivity, realistic surface chemistry, spin-lattice coupling, and large-scale integration are discussed."

"Spearman rank correlation coefficients between final success rate and KER... ρ = 0.37 (Chemical), ρ = 0.70 (Fire)."

"The colibre model is calibrated by adjusting up to four subgrid parameters ... that control the strengths of stellar and AGN feedback in order to reproduce simple observed galaxy scaling relations at z=0: the galaxy stellar mass function (GSMF) and the galaxy size-stellar mass relation (SSMR)."

"We take the fine structure constant α=e²/(ℏc)=0.0072973525643≃1/137.035999177."

"Safeness Score = λ₁ S_perclos − λ₂ S_mouth − λ₃(1−S_head) − λ₄(1−S_action) ... where λᵢ denotes the weight assigned to each contribution."

"graphene ... displays ... a frequency independent absorption/layer of απ ≈ 2.3 %, being α the fine constant"

"L ≈ A(p/p_th)^{d_e} with A ≈ 2.09·10^-1 and p_th ≈ 7.33·10^-2 fit empirically from path counting"

"We introduce for convenience the dimensionless quantities ... E, L, S, and magnetic parameter B ... The radius of ISCO decreases with the increase of the magnetic field B or spin S."

"Using parameterization of the deceleration parameter q(z) and the corresponding H(z) expression, we constrain the model parameters with the recent Hubble parameter and BAO data through a Markov Chain Monte Carlo (MCMC) approach."

"AdamW (lr=1e-4), 300 epochs, batch size 32, λ_SNR=50, η₀=0.5, σ_PSF=2"

"4√π/√3 gΛ^{3/2} ≤ E^{g,Λ}_G ≤ 4√(3π) gΛ^{3/2} for all g>0 and Λ > (3/(8π)) g^{-2}."

"Mittag-Leffler kernels K_i defined through their Laplace transform: cKᵢ(z) = 1/(1 + δ̃ᵢ z^αᵢ), with αᵢ ∈ (1/2, 1) free parameters fitted to empirical equity microstructure (H ≈ 0.1)."

"We conclude by studying the models' tunability and identifying the best-fit parameters for each... αs(mZ) ∈ [0.106, 0.130], p²T,min ∈ [0.5, 1.5], Clmax ∈ [2.5, 4.5]."

"δ = π(1 − √(2/(2−K))) + (2m/b)(1 + 1/(1 − (ω_h/ω_∞)²))"

"The framework is operationalized via a learned diagonal mass matrix M(q), step size η, evolution length T=4, regularization weights λ, λ_geo, λ_photo, and a hinge margin γ — all tuned hyperparameters with no closed-form derivation."

"We adopt the rise-fall star-formation history... allow the following to vary: t_start, τ1, τ2, SFE, and the outflow mass-loading factor η."

"Threshold parameters τ_commit, τ_reject, τ_degraded, δ, d_min, b_min, ε_trust ... All thresholds are frozen before evaluation."