arXiv subjects

Aliaksandra Novik

Publications and source records attributed to Aliaksandra Novik.

5 recordsLinked to original sources

arXiv2026

On the Incompleteness of do-calculus for Universal Identifiability

We study the problem of causal effect identification from an arbitrary set of observational and/or interventional distributions, which we call Universal Identifiability (uID). The uID problem generalizes existing classical identifiability (ID) and general identifiability (gID) problems, which considered the identification problem from either mere observational distributions or a specific type of interventional distributions. Prior research has established graphical criteria to determine when a causal effect is identifiable in ID and gID problems. Moreover, algorithms that leverage do-calculus and basic probability manipulations have been proposed to compute these effects. Consequently, it has been shown that do-calculus is both sound and complete in these problems. Despite these well-established results, a formal definition of what it means for the do-calculus to be complete does not exist. We propose a rigorous formalization for the completeness of the do-calculus and show that the completeness results in previous work remain valid. However, for more general problems, such as uID, the rules of do-calculus are no longer complete. This is perhaps the reason why the uID problem has remained open thus far.

cs.CL↗

arXiv2026

Butler's conjecture for K3 curves

Butler's conjectures predict that, on a general smooth curve $C$ of genus $g\ge3$, a general coherent system $[\mathcal{O}_C\otimes V\xrightarrowφE]$ with semistable underlying bundle $E$ and $\dim V>\operatorname{rk}(E)$ has surjective evaluation map $φ$ and stable kernel. In this paper, we prove Butler's conjectures for $g\ge8$ in the two cases in which the Brill-Noether geometry of a general curve is known, namely rank one and the range $μ(E)>2g-2$. By deformation and openness, it suffices to establish the result on a single Brill-Noether-Petri general curve. We do so for curves on K3 surfaces of Picard rank one, using the wall-crossing theory of coherent systems developed by the first two authors.

math.AG↗

arXiv2026

The Harness Effect: How Orchestration Design Sets the Token Economics of Enterprise Agentic AI

Agentic AI development today runs on token maxing: buying capability with tokens -- longer reasoning traces, more turns, wider tool payloads, bigger replayed contexts -- so tokens per task grow faster than task value. Falling per-token prices mask the pattern; total spend rises anyway. We argue the decisive lever against token maxing is the harness: the orchestration layer that assembles context, exposes tools, sequences turns, delegates work, and carries enterprise observability and governance. We isolate it with a controlled swap: 22 locked evaluation tasks, six foundation models (Claude Sonnet 4.6, Gemini 3.1, Gemini Flash 3.5, Qwen 3.6, GLM 5.1, Palmyra X6), changing only the orchestration layer -- a frozen conventional production loop versus the Writer Agent Harness. Holding models constant, the harness cuts blended cost per task 41% ($0.21->$0.12), median wall-clock 44% (48s->27s), and tokens per task 38% (14.2k->8.8k), with task-completion quality at parity (0.78->0.81, directional at this sample size). Efficiency is model-invariant -- every model gets cheaper (33-61%) -- while quality gains are capability-dependent: a model's gain correlates almost perfectly with its baseline strength (r=0.99, n=6), a phenomenon we term harness leverage. Quality per dollar rises 82%; task-completions per million tokens rise from 54.9 to 92.0. On this workload the orchestration layer moved cost per task more than the full spread of the model menu did. We formalize token economics at the orchestration layer (including effective input price under prompt caching), detail the six mechanism families behind the effect -- cache-shape discipline to failure-spend governance -- compare six widely used agent systems on the same axes, and argue the harness is the one component whose efficiency multiplies across every model an organization runs -- present and future.

cs.AI↗

arXiv2026

Derived category of coherent systems on curves and stability conditions

Let $C$ be a smooth projective curve of genus $g>0$. We describe an open locus of Bridgeland stability conditions on the bounded derived category of coherent systems on $C$, and show that stability manifold detects the Brill--Noether theory of the curve.

math.AG↗

arXiv2023

Turán problems for oriented graphs

A classical Turán problem asks for the maximum possible number of edges in a graph of a given order that does not contain a particular graph $H$ as a subgraph. It is well-known that the chromatic number of $H$ is the graph parameter which describes the asymptotic behavior of this maximum. Here, we consider an analogous problem for oriented graphs, where compressibility plays the role of the chromatic number. Since any oriented graph having a directed cycle is not contained in any transitive tournament, it makes sense to consider only acyclic oriented graphs as forbidden subgraphs. We provide basic properties of the compressibility, show that the compressibility of acyclic oriented graphs with out-degree at most 2 is polynomial with respect to the maximum length of a directed path, and that the same holds for a larger out-degree bound if the Erdős-Hajnal conjecture is true. Additionally, generalizing previous results on powers of paths and arbitrary orientations of cycles, we determine the compressibility of acyclic oriented graphs with a restricted structure.

math.CO↗