Elementary differentials from multi-indices to rooted trees
Yvain Bruned; Paul Laubie · 2025 · arXiv
WASTE classifies this as Negative / Null Result Report · AI classification, approximate
The study found no significant effect — useful as a negative control or null benchmark for your own design.
Abstract (excerpt)
Rooted trees are essential for describing numerical schemes via the so-called B-series. They have also been used extensively in rough analysis for expanding solutions of singular Stochastic Partial Differential Equations (SPDEs). When one considers scalar-valued equations, the most efficient combinatorial set is multi-indices. In this paper, we investigate the existence of intermediate combinatorial sets that will lie between multi-indices and rooted trees. We provide a negative result stating that there is no combinatorial set encoding elementary differentials in dimension $d\neq 1$, and comp
Excerpt shown for reference under fair use — read the full paper at the publisher.
About to run something similar?
Run an AI Precheck on your own design to catch failure modes like this one before you spend the time. Your first desk check is free.
Related failures
Channeling Fisher: Randomization Tests and the Statistical Insignificance of Seemingly Significant Experimental Results*
Negative / Null Result ReportThe harmonic mean p -value for combining dependent tests
Negative / Null Result ReportGeneralizability of heterogeneous treatment effect estimates across samples
Negative / Null Result ReportNumerical predictors of arithmetic success in grades 1–6
Negative / Null Result ReportMethods Matter: p-Hacking and Publication Bias in Causal Analysis in Economics
Negative / Null Result ReportShould multiple imputation be the method of choice for handling missing data in randomized trials?
WASTE indexes this work — it does not host or republish it. Failure-type classification is automated and approximate.
Metadata source: arXiv