“This article summarizes practical knowledge gained from the actual operation of Claude Code Skills.”

“The article uses the power of LLMs to provide a theoretical explanation for optimizing F1 score.”

“The article is aimed at readers familiar with Python basics and seeking to speed up machine learning model inference.”

“By converting history to Markdown and feeding the same prompt to multiple LLMs, you can see your own 'core issues' and the strengths of each model.”

“Our approach relies on a unified formulation of the distance from a point to a hyperplane on the considered spaces.”

“Compact, interpretable rules are distilled from failure traces and injected into the prompt during inference to improve task performance.”

“"A 50-message thread uses 5x more processing power than five 10-message chats because Claude re-reads the entire history every single time."”

“They got me good with the extended usage limits over the last week.. Signed up for Pro. Extended usage ended, decided Pro wasn't enough.. Here I am now on 5x Max. How long until I end up on 20x? Definitely worth every cent spent so far.”

“The article itself does not contain any direct quotes. The content is derived from the linked X posts.”

“The paper proposes local approximations to the global Minkowski Hamiltonian in quantum field theory (QFT) motivated by the operator-algebraic property of nuclearity.”

“The paper identifies physical theories as least fixed points of admissibility constraints derived from Galois connections.”

“The paper derives bilinear tau forms of the canonically quantized Painlevé equations, relating them to those previously obtained from the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations.”

“The paper derives sufficient conditions on a compact self adjoint perturbation to guarantee that the perturbed system stays exactly observable.”

“The paper identifies universal polar dual pairs of spherical codes C and D such that for a large class of potential functions h the minima of the discrete h-potential of C on the sphere occur at the points of D and vice versa.”

“The paper derives explicit expressions for the joint Laplace-Stieltjes transform, probability density function, and governing differential equations of the multivariate gamma subordinator.”

“Model-derived metrics such as arterial stiffness, pulse wave velocity, resistance, and compliance were found to align with clinical indicators of disease severity and progression.”

“The paper derives the counting DRM, the effective area, and the flash effective area from the counting DRF.”

“The paper derives the graphicality of infinite sequences for double power-laws, uncovering a rich phase-diagram and pointing out the existence of five qualitatively distinct ways graphicality can be violated.”

“The paper derives fundamental estimation limits for a wide-band near-field sensing systems employing orthogonal frequency-division multiplexing signaling over a coherent processing interval.”

“The paper derives closed-form Cram'er--Rao bounds (CRBs) for joint estimation of target position, velocity, and radar cross-section (RCS).”

“The paper proves a fully nonlinear, saturable lower bound valid for arbitrary current vectors Δq: D_bath ≥ B(Δq,V,V'), where the bound depends only on the transported-charge signal Δq and the pre/post collision covariance matrices V and V'.”

“The paper derives a Pontryagin maximum principle on the belief space, providing necessary conditions for optimality in this hybrid setting.”

“The paper establishes a correspondence between solutions of the Liouville equation and the Weierstrass representations of spacelike and timelike minimal surfaces.”

“The paper derives an exact identity for overdamped Langevin dynamics that equates the total EP rate to the mutual-information rate.”

“The entanglement entropy naturally emerges from the normalization condition of the Husimi distribution within this framework.”

“The paper shows that its restricted holonomy group is SU(2), implying universal single-qubit control by closed loops in shape space.”

“The paper establishes the consistency of the QMLE and derives its asymptotic distribution, and proposes a bias-corrected estimator.”

“The paper finds novel non-supersymmetric domain walls interpolating between different pairs of AdS extrema.”

“The paper obtains mean-field analogues of momentum distribution formulas for electron gas in high density and metallic density limits, and applies to a general class of singular potentials.”

“The paper establishes error bounds for the reconstructed solution and the source term without requiring classical source conditions, and derives an expected convergence rate for the source error in a weaker topology.”

“The paper derives a third-order linear differential equation for the partition function, a key result.”

“The paper derives a symmetry that relates expectation values of Pauli strings, allowing for the reduction in the number of measurements needed when simulating fermionic systems.”

“The paper derives closed-form BF structures and develops an efficient first-order algorithm to achieve high-quality local solutions.”

“The paper derives explicit conditions that determine when certain values of N are valid for the encryption scheme.”

“The paper derives a novel recursion relationship across depth which extends the eligibility traces of E-prop to deeper layers.”

“Nuclei located in neurogenic regions consistently exhibited significantly higher phase values (optical path difference) compared to nuclei elsewhere, suggesting cell-type-specific biophysical signatures.”

“The paper derives necessary and sufficient conditions for the existence of such residual generators and provides explicit design formulas.”

“An excess is observed with respect to the standard model expectation with a local significance of 2.4 standard deviations for a signal with an H$^\pm$ boson mass ($m_{\mathrm{H}^\pm}$) of 600 GeV.”

“The construction makes it possible to design infinite families of graphs on which exact and stable completion is possible for every fixed rank matrix through the sum-of-squares hierarchy.”

“The dispersive shift and vacuum Rabi splitting emerge from the transcendental eigenvalue equation, with the residues determined by matching to the splitting: $δ_{ge} = 2Lg^2ω_q^2/v^4$, where $g$ is the vacuum Rabi coupling.”

“The paper derives a generalized Heisenberg-Robertson uncertainty inequality valid across all spectral regimes.”

“The resulting equations take the form of Regge-Wheeler equations modified by expectation values of the quantum black hole geometry, providing a clear characterization of quantum corrections to the classical description of the black hole interior.”

“Necessary and sufficient conditions for complete positivity and trace preservation are derived and the canonical decomposition describing DU-covariant superchannels is provided.”

“The paper provides an expression of the optimal terminal wealth for complete markets using max-plus decomposition and derives explicit forms for the Black-Scholes-Merton model.”

“The result shows significant differences with the use of THM rates, which in some cases goes in the direction of improving the agreement with the observations with respect to the use of only reaction rates from direct data, especially for the $^7$Li and deuterium abundances.”

“The paper derives the polynomial rate of decay of ruin probabilities in insurance portfolios where insolvency is driven by a single extreme claim.”

“The paper identifies the tangent map with the dual HKR map and proves liftability along square-zero extensions to be a derived invariant.”

“The paper constructs a general class of unique solutions to certain matrix equations and derives several equivalent properties of W-weighted DMP and MPD inverses.”

“The paper reveals the structure of superconducting Berry curvatures and derives the superconducting Berry curvature induced thermal Edelstein effect and spin Nernst effect.”

“The backreaction introduces spacetime dependent mass and increases the UV divergence of the equal position correlation function.”