03 / Research
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Research published by Aletheia: explicit sources, verification the reader can repeat and stated limits. The method defines the work, not a single sector.
The areas follow the questions we take on: security of digital and defence systems, discrete mathematics, economics. Every record states its area, version, document status and sources.
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{"search":"Line-Graph Signature Beyond the 2-Core: Exact Counterexamples, Rooted Response, and Extremal Constructions at Fixed Cyclomatic Number Line-graph signature beyond the 2-core, with exact reductions, counterexamples, and extremal constructions at fixed cyclomatic number. Andrea Paone Marco Paone Graph theory and discrete mathematics Preprint; not peer reviewed line graph graph signature graph inertia spectral graph theory signless Laplacian cyclomatic number 2-core rooted response Schur complement pendant forest extremal graph theory exact computation","authors":["Andrea Paone","Marco Paone"],"area":"graph-theory","keywords":["line graph","graph signature","graph inertia","spectral graph theory","signless Laplacian","cyclomatic number","2-core","rooted response","Schur complement","pendant forest","extremal graph theory","exact computation"]}
PreprintPreprint; not peer reviewed27 July 2026
Andrea Paone, Marco Paone
Line-graph signature beyond the 2-core, with exact reductions, counterexamples, and extremal constructions at fixed cyclomatic number.
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{"search":"Unbounded Signature of Line Graphs: Counterexamples and Transfer Principles An unbounded counterexample family in planar subcubic cactus graphs, with transfer principles and exact certificates. Andrea Paone Graph theory and discrete mathematics Preprint; not peer reviewed Counterexample to the line-graph inertia conjecture Version 2 · current expanded research version line graph graph signature graph inertia inertia indices spectral graph theory cactus graph planar subcubic graph rooted module edge subdivision integral unimodular congruence Smith normal form adjacency cokernel exact residue classification","authors":["Andrea Paone"],"area":"graph-theory","keywords":["line graph","graph signature","graph inertia","inertia indices","spectral graph theory","cactus graph","planar subcubic graph","rooted module","edge subdivision","integral unimodular congruence","Smith normal form","adjacency cokernel","exact residue classification"]}
Preprint · Version 2Preprint; not peer reviewed24 July 2026
Andrea Paone
Research seriesVersion 2 · current expanded research version
An unbounded counterexample family in planar subcubic cactus graphs, with transfer principles and exact certificates.
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{"search":"A Counterexample to a Line-Graph Inertia Conjecture A finite connected simple counterexample to Conjecture 4.12 on line-graph inertia indices, accompanied by exact certificates. Andrea Paone Graph theory and discrete mathematics Preprint; not peer reviewed Counterexample to the line-graph inertia conjecture Version 1 · historical finite-counterexample record line graph graph inertia inertia indices spectral graph theory counterexample Conjecture 4.12 adjacency matrix characteristic polynomial exact arithmetic incidence congruence reproducibility certificate","authors":["Andrea Paone"],"area":"graph-theory","keywords":["line graph","graph inertia","inertia indices","spectral graph theory","counterexample","Conjecture 4.12","adjacency matrix","characteristic polynomial","exact arithmetic","incidence congruence","reproducibility certificate"]}
Preprint · Version 1Preprint; not peer reviewed22 July 2026
Andrea Paone
Research seriesVersion 1 · historical finite-counterexample record
A finite connected simple counterexample to Conjecture 4.12 on line-graph inertia indices, accompanied by exact certificates.
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Research area
Digital security, critical-infrastructure resilience, and responsible governance of artificial intelligence systems.
{"search":"From Rules to Resilience: Assessing the EU's 2026 Action Plan on Cybersecurity and Artificial Intelligence A source-audited assessment of whether the EU's 2026 Action Plan turns cyber and AI regulation into operational capability for critical infrastructure. Andrea Paone Cybersecurity and AI governance Independent research report; not peer reviewed European Union artificial intelligence AI security cybersecurity critical infrastructure cyber policy ENISA NIS2 Cyber Solidarity Act AI Act implementation readiness auditability","authors":["Andrea Paone"],"area":"cybersecurity-ai-governance","keywords":["European Union","artificial intelligence","AI security","cybersecurity","critical infrastructure","cyber policy","ENISA","NIS2","Cyber Solidarity Act","AI Act","implementation readiness","auditability"]}
Research reportIndependent research report; not peer reviewed18 July 2026
Andrea Paone
A source-audited assessment of whether the EU's 2026 Action Plan turns cyber and AI regulation into operational capability for critical infrastructure.
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