A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations. Here I show that a single binary operator, eml(x,y)=exp(x)-ln(y), together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as $e$, $\pi$, and $i$; arithmetic operations including $+$, $-$, $\times$, $/$, and exponentiation as well as the usual transcendental and algebraic functions. For example, $e^x=\operatorname{eml}(x,1)$, $\ln x=\operatorname{eml}(1,\operatorname{eml}(\operatorname{eml}(1,x),1))$, and likewise for all other operations. That such an operator exists was not anticipated; I found it by systematic exhaustive search and established constructively that it suffices for the concrete scientific-calculator basis. In EML (Exp-Minus-Log) form, every such expression becomes a binary tree of identical nodes, yielding a grammar as simple as $S \to 1 \mid \operatorname{eml}(S,S)$. This uniform structure also enables gradient-based symbolic regression: using EML trees as trainable circuits with standard optimizers (Adam), I demonstrate the feasibility of exact recovery of closed-form elementary functions from numerical data at shallow tree depths up to 4. The same architecture can fit arbitrary data, but when the generating law is elementary, it may recover the exact formula.

The computational demands of modern AI services are increasingly shifting execution beyond centralized clouds toward a computing continuum spanning edge and end devices. However, the scale, heterogeneity, and cross-layer dependencies of these environments make resilience difficult to maintain. Existing fault-management methods are often too static, fragmented, or heavy to support timely self-healing, especially under noisy logs and edge resource constraints. To address these limitations, this paper presents NeSy-Edge, a neuro-symbolic framework for trustworthy self-healing in the computing continuum. The framework follows an edge-first design, where a resource-constrained edge node performs local perception and reasoning, while a cloud model is invoked only at the final diagnosis stage. Specifically, NeSy-Edge converts raw runtime logs into structured event representations, builds a prior-constrained sparse symbolic causal graph, and integrates causal evidence with historical troubleshooting knowledge for root-cause analysis and recovery recommendation. We evaluate our work on representative Loghub datasets under multiple levels of semantic noise, considering parsing quality, causal reasoning, end-to-end diagnosis, and edge-side resource usage. The results show that NeSy-Edge remains robust even at the highest noise level, achieving up to 75% root-cause analysis accuracy and 65% end-to-end accuracy while operating within about 1500 MB of local memory.