https://aletheia-technologies.it/research/Aletheia Technologies research publications2026-08-05T00:00:00Zhttps://doi.org/10.5281/zenodo.21744051Line-graph inertia of roses and generalized theta graphs2026-08-01T00:00:00Z2026-08-01T00:00:00ZAndrea PaoneMarco PaoneFor two families of graphs, roses and generalized theta graphs, the work computes in closed form how many eigenvalues of the line graph are positive, zero and negative. The result depends only on the lengths of the paths, counted modulo four.https://doi.org/10.5281/zenodo.21706797Line-Graph Signature Beyond the 2-Core: Exact Counterexamples, Rooted Response, and Extremal Constructions at Fixed Cyclomatic Number2026-07-30T00:00:00Z2026-07-30T00:00:00ZAndrea PaoneMarco PaoneAn upper bound that holds for every graph, constructions that reach it, and counterexamples to a simplification that looked natural. Every case is checked with exact arithmetic, not approximation.https://doi.org/10.5281/zenodo.21737348Unbounded Signature of Line Graphs: Counterexamples and Transfer Principles2026-08-01T00:00:00Z2026-08-01T00:00:00ZAndrea PaoneNot one isolated counterexample but an infinite family, inside a class of very simple graphs, with the means to carry the result from one graph to another and exact certificates for every case.https://doi.org/10.5281/zenodo.21499790A Counterexample to a Line-Graph Inertia Conjecture2026-07-22T00:00:00Z2026-07-29T00:00:00ZAndrea PaoneA finite connected simple counterexample to Conjecture 4.12 on line-graph inertia indices, accompanied by exact certificates.https://doi.org/10.5281/zenodo.21810205From Rules to Resilience: Assessing the EU's 2026 Action Plan on Cybersecurity and Artificial Intelligence2026-08-05T00:00:00Z2026-08-05T00:00:00ZAndrea PaoneOn 2 August 2026 the Commission gained the power to compel access to an advanced AI model for evaluation. This assessment asks what it can do with it, and finds the operational side of that power still unevidenced.https://doi.org/10.5281/zenodo.21793638Response Protection for Line-Graph Equality Families: Transfer under Edge Subdivision and Rooted Attachment2026-08-04T00:00:00Z2026-08-04T00:00:00ZAndrea PaoneMarco PaoneAdding an edge to a graph can push a quantity tied to its line graph past a threshold. The paper gives a condition that prevents that jump, and proves the condition survives two ways of growing the graph: splitting an edge into four, and attaching a module at any vertex. Starting from a pentagon, this builds an infinite family of graphs sitting exactly on the bound. The condition is enough, but it is not known to be necessary, and the general bound stays open.