Scientific Resource Catalog
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We prove that the Fourier coefficients of the three weight-4 newforms of levels 6, 8, 12 are governed by a rigid algebraic framework centred on the even subalgebra Cl⁰(2,2) of the real Clifford algebra of signature (2,2). The coefficients are assembled into a single Clifford element A(n) = a(n)X +…
AbstractA representation resolves some perturbations of a system and leaves others undetected, and the orbit-stabiliser relation makes that division an exact two-term conservation law. Between the perturbations that move nothing and those that move the output without law lies a third class, moving…
Separating a theorem's statement dependencies from its proof dependencies bounds how much classical dependence a formal library could shed. Across Mathlib, 13.1% of theorems have a choice-free statement and a choice-dependent proof; nothing outside that band can be removed under any argument. The m…
Combining noble metal nanoparticles with electron acceptors, such as semiconductors or non-plasmonic metals, significantly enhances photocatalytic performance. However, optimizing multi-material combinations for superior catalytic efficiency remains challenging. In this study, we present a method f…
Abstract Van der Waals (vdW) materials have garnered ample interest as next-generation sensors and catalysts, owing to high surface-to-volume ratio, defect tunability, easy modulation of active sites, and convenience in device fabrication. However, one major drawback delimiting surface activity of…
Empirical Validation of Phase Stability via 50-Day Continuous Operation of Autonomous Laminar Water-Cooling Ⅳ Total Pipeline Length: Approximately 6 meters (The explicit combination sequence is strictly confidential; it will never be disclosed under any circumstances).Trend Observation: The system…
Framework for Next-Generation Infrastructure Investment under EU MiCA To facilitate the immediate, compliant reallocation of global institutional capital from failing legacy computational networks to the sub-millimeter geometric pure-water architecture, the Sovereign Asset Tokenization framework op…
Pt-Mn catalysts exhibit high performance for propane dehydrogenation (PDH), yet the influence of the support on active site formation remains debated. This study investigates Pt and bimetallic Pt-Mn species on SiO2 and θ-Al₂O₃. Combined TPR, XPS, and XRD analyses reveal accelerated MnOx reduction o…
Epoxy coatings are widely used to protect steel structures; however, industrial substrates often retain residual corrosion products and organic contaminants after surface preparation. Waterborne (WB) epoxy coatings are generally considered less surface-tolerant than solventborne (SB) systems, altho…
Abstract Machine learning has emerged as a powerful approach for molecular property prediction and drug discovery. However, the black-box nature of many machine learning models limits their interpretability, trustworthiness, and adoption in interdisciplinary research settings. This is especially th…
The O-series defines a canonical pair-level capacity observable and establishes that vertical non-injectivity does not change its observable rank. The further prescription ${\beta^{*}}=1/({\delta_{\mathrm{pair}}}+\tfrac12)$, however, imports the changing-degree LPS growth equation into a fixed-degr…
The O12–O18 sequence identifies the pair-level quantity ${\sigma_{\mathrm{pair}}}(n) = \sigma_{c}(n)\,\sigma_{q-c}(n)$ as the structurally motivated candidate observable on ${\mathrm{Heis}_{3}(\mathbb{Z}/q\mathbb{Z})}$, with capacity exponent ${\delta_{\mathrm{pair}}} \approx 7.44$ consistent with…
Crystallographic texture in polycrystalline materials, such as in Hexagonal Close-Packed metals, strongly influences their mechanical and physical performance. Texture commonly develops during thermomechanical deformations that engineering metal components undergo during manufacturing, yet accurate…
Abstract The precise synthesis of helical graphene nanoribbons (GNRs) with a controlled handedness has a transformative potential as the promising chiral carbon materials. We now report the first synthesis of a dynamic helical poly[4]helicene nanoribbon, a novel class of helical GNRs, entirely comp…
The emergence of biological membranes was a fundamental step in the origin of cellular life because compartmentalization enabled molecular concentration, selective interactions, and increasingly complex chemical evolution. Although fatty acids have traditionally been regarded as the principal const…
Abstract We present OMOL-1k-MD, a new dataset for the benchmark and training of universal machine-learning interatomic potentials (uMLIPs). It contains three independent ab initio molecular dynamics (AIMD) trajectories of 10 ps each for 1000 arbitrarily chosen neutral closed shell molecular systems…
We present a computational framework that integrates machine learning with high-throughput ab initio calculations to screen over 2.8 million compounds for metallic transport. We identify several intermetallic candidates with predicted high conductivities comparable to that of aluminum (36.59 x $10^…
The development of accurate strength prediction models for titanium alloys is critical for advanced materials design. This study systematically examines how the mechanical properties of $α$-Ti are affected by substitutional (X = Al, V, Mo) and interstitial (Y = H, C, N, O) alloying elements, with a…
Rare-earth iron garnets, such as yttrium iron garnet (YIG) and thulium iron garnet (TmIG), are the benchmark magnetic insulators for spintronic and magnonic devices, but achieving usable perpendicular magnetic anisotropy (PMA) in these materials typically relies on substrate strain- engineering, re…
This work presents a machine learning-symbolic regression (ML-SR) strategy to develop a physically interpretable formula for predicting low pressure CO2 adsorption capacity in hypothetical metal-organic frameworks (hMOFs). Four ML models were trained on a small dataset of 1,000 samples, and five ke…