Vulnerability Abundance: A formal proof of infinite vulnerabilities in code

• URL: http://arxiv.org/abs/2604.07539v1
• Date: Wed, 08 Apr 2026 19:30:53 GMT
• Title: Vulnerability Abundance: A formal proof of infinite vulnerabilities in code
• Abstract summary: We present a proof that a single C program, the emphVulnerability Factory, admits a countably infinite set of distinct, independently CVE-assignable software vulnerabilities.<n>We argue that measuring vulnerability abundance, and its interaction with software deployment, has practical value for both vulnerability prevention and cyber-risk analysis.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a constructive proof that a single C program, the \emph{Vulnerability Factory}, admits a countably infinite set of distinct, independently CVE-assignable software vulnerabilities. We formalise the argument using elementary set theory, verify it against MITRE's CVE Numbering Authority counting rules, sketch a model-checking analysis that corroborates unbounded vulnerability generation, and provide a Turing-machine characterisation that situates the result within classical computability theory. We then contextualise this result within the long-running debate on whether undiscovered vulnerabilities in software are \emph{dense} or \emph{sparse}, and introduce the concept of \emph{vulnerability abundance}: a quantitative analogy to chemical elemental abundance that describes the proportional distribution of vulnerability classes across the global software corpus. Because different programming languages render different vulnerability classes possible or impossible, and because language popularity shifts over time, vulnerability abundance is neither static nor uniform. Crucially, we distinguish between infinite \emph{vulnerabilities} and the far smaller set of \emph{exploits}: empirical evidence suggests that fewer than 6\% of published CVEs are ever exploited in the wild, and that exploitation frequency depends not only on vulnerability abundance but on the market share of the affected software. We argue that measuring vulnerability abundance, and its interaction with software deployment, has practical value for both vulnerability prevention and cyber-risk analysis. We conclude that if one programme can harbour infinitely many vulnerabilities, the set of all software vulnerabilities is necessarily infinite, and we suggest the Vulnerability Factory may serve as a reusable proof artifact, a foundational `test object',for future formal results in vulnerability theory.

Related papers

• GraftyVul: Synthesising Insecure Programs Through Real-World Vulnerability Grafting [8.596028166822489]
  GraftyVul constructs vulnerable programs by grafting real-world vulnerabilities into open-source projects.<n>We generate 212 verified and exploitable vulnerable programs spanning five programming languages.
  arXiv  Detail & Related papers  (2026-08-28T05:10:49Z)
• AI Slop and Hallucinations in Vulnerability Assessment: A Survey on Reasoning Failures and Trustworthy Mitigation [48.55515767840701]
  "AI slop" is artifacts, hallucinated vulnerabilities, plausible but incorrect patches, and semantically repackaged bug reports.<n>This paper surveys the empirical evidence, identifies a unifying mechanism, and traces a path toward trustworthy triage.
  arXiv  Detail & Related papers  (2026-08-26T11:48:38Z)
• The Illusion of High Utility in Safety Alignment of Text-to-Image Diffusion Models [49.67749928542536]
  Safety alignment of text-to-image (T2I) diffusion models aims to suppress harmful generations while preserving utility on benign prompts.<n>Recent methods often appear to deliver high safety with high utility, but this conclusion rests largely on coarse global utility metrics.<n>We show that when utility is measured with structured evaluation, this illusion breaks: onA (Text-to-Image Faithfulness evaluation with Question Answering)<n>We propose StructureAware Geometric Regularization (SAGE), a safety alignment objective that explicitly preserves embedding spread and inter-prompt relational structure.
  arXiv  Detail & Related papers  (2026-07-01T04:00:27Z)
• Provably Secure Agent Guardrail [89.79561918065122]
  Existing defense architectures rely on empirical semantic guardrails and probabilistic large model adjudicators.<n>This paper proposes a new security paradigm for agents based on the fundamental limitations of logical reasoning.
  arXiv  Detail & Related papers  (2026-05-28T02:12:41Z)
• An Empirical Evaluation of LLM-Generated Code Security Across Prompting Methods [11.454777386934632]
  Large Language Models (LLMs) for automated code generation has enhanced software development efficiency, but often at the cost of security.<n>We present a comprehensive empirical evaluation of the security quality of LLM-generated code across five LLMs and four programming languages.<n>We introduce a weaknesses-aware zero-shot chain-of-thought (WA-0CoT) prompting strategy that enriches prompts with security context using CWE mappings to guide model reasoning.
  arXiv  Detail & Related papers  (2026-05-22T23:52:33Z)
• ExploitGym: Can AI Agents Turn Security Vulnerabilities into Real Attacks? [92.21756459993695]
  Exploitation is a challenging task because it requires low-level program reasoning.<n>Despite its importance and diagnostic value, exploitation remains under-evaluated.<n>We introduce ExploitGym, a large-scale, diverse, realistic benchmark on the exploitation capabilities of AI agents.
  arXiv  Detail & Related papers  (2026-05-11T18:00:14Z)
• SecureForge: Finding and Preventing Vulnerabilities in LLM-Generated Code via Prompt Optimization [61.91729298584227]
  We introduce SecureForge, an automated pipeline that audits security risks of frontier models and produces auditing-informed secure system prompts.<n>SecureForge first identifies benign prompts that produce statically detectable vulnerabilities, and then amplifies them into a large synthetic prompt corpus of diverse scenarios.<n>On frontier models, SecureForge yields a statistically significant improvement in both unit test success and output security, with output vulnerabilities reduced by up to 48%.
  arXiv  Detail & Related papers  (2026-05-08T18:40:47Z)
• Towards Predicting Multi-Vulnerability Attack Chains in Software Supply Chains from Software Bill of Materials Graphs [1.628589561701473]
  We propose a new research direction based on learning multi-vulnerability attack chains through a novel SBOM-driven graph-learning approach.<n>This treats SBOM structure and scanner outputs as a dependency-constrained evidence graph rather than a flat list of vulnerabilities.<n>We train a Heterogeneous Graph Attention Network (HGAT) to predict whether a component is associated with at least one known vulnerability.<n>We frame the discovery of vulnerabilities as CVE-pair link prediction using a lightweight Multi-Layer Perceptron (MLP) neural network trained on documented multi-vulnerability chains.
  arXiv  Detail & Related papers  (2026-04-04T17:29:39Z)
• Cascaded Vulnerability Attacks in Software Supply Chains [1.628589561701473]
  We propose a novel approach to SBOM-driven security analysis methods and tools.<n>We model vulnerability relationships over dependency structure rather than treating scanner outputs as independent records.<n>We then train a Heterogeneous Graph Attention Network (HGAT) to predict whether a component is associated with at least one known vulnerability.
  arXiv  Detail & Related papers  (2026-01-28T01:31:09Z)
• What Do They Fix? LLM-Aided Categorization of Security Patches for Critical Memory Bugs [46.325755802511026]
  We developLM, a dual-method pipeline that integrates two approaches based on a Large Language Model (LLM) and a fine-tuned small language model.<n>LM successfully identified 111 of 5,140 recent Linux kernel patches addressing OOB or UAF vulnerabilities, with 90 true positives confirmed by manual verification.
  arXiv  Detail & Related papers  (2025-09-26T18:06:36Z)
• CyberGym: Evaluating AI Agents' Real-World Cybersecurity Capabilities at Scale [45.97598662617568]
  We introduce CyberGym, a large-scale benchmark featuring 1,507 real-world vulnerabilities across 188 software projects.<n>We show that CyberGym leads to the discovery of 35 zero-day vulnerabilities and 17 historically incomplete patches.<n>These results underscore that CyberGym is not only a robust benchmark for measuring AI's progress in cybersecurity but also a platform for creating direct, real-world security impact.
  arXiv  Detail & Related papers  (2025-06-03T07:35:14Z)
• Reformulation is All You Need: Addressing Malicious Text Features in DNNs [53.45564571192014]
  We propose a unified and adaptive defense framework that is effective against both adversarial and backdoor attacks.<n>Our framework outperforms existing sample-oriented defense baselines across a diverse range of malicious textual features.
  arXiv  Detail & Related papers  (2025-02-02T03:39:43Z)
• The Impact of SBOM Generators on Vulnerability Assessment in Python: A Comparison and a Novel Approach [56.4040698609393]
  Software Bill of Materials (SBOM) has been promoted as a tool to increase transparency and verifiability in software composition. Current SBOM generation tools often suffer from inaccuracies in identifying components and dependencies. We propose PIP-sbom, a novel pip-inspired solution that addresses their shortcomings.
  arXiv  Detail & Related papers  (2024-09-10T10:12:37Z)
• SecureFalcon: Are We There Yet in Automated Software Vulnerability Detection with LLMs? [3.566250952750758]
  We introduce SecureFalcon, an innovative model architecture with only 121 million parameters derived from the Falcon-40B model.<n>SecureFalcon achieves 94% accuracy in binary classification and up to 92% in multiclassification, with instant CPU inference times.
  arXiv  Detail & Related papers  (2023-07-13T08:34:09Z)
• Learning to Quantize Vulnerability Patterns and Match to Locate Statement-Level Vulnerabilities [19.6975205650411]
  A vulnerability codebook is learned, which consists of quantized vectors representing various vulnerability patterns. During inference, the codebook is iterated to match all learned patterns and predict the presence of potential vulnerabilities. Our approach was extensively evaluated on a real-world dataset comprising more than 188,000 C/C++ functions.
  arXiv  Detail & Related papers  (2023-05-26T04:13:31Z)
• DRSM: De-Randomized Smoothing on Malware Classifier Providing Certified Robustness [58.23214712926585]
  We develop a certified defense, DRSM (De-Randomized Smoothed MalConv), by redesigning the de-randomized smoothing technique for the domain of malware detection. Specifically, we propose a window ablation scheme to provably limit the impact of adversarial bytes while maximally preserving local structures of the executables. We are the first to offer certified robustness in the realm of static detection of malware executables.
  arXiv  Detail & Related papers  (2023-03-20T17:25:22Z)
• Multi-context Attention Fusion Neural Network for Software Vulnerability Identification [4.05739885420409]
  We propose a deep learning model that learns to detect some of the common categories of security vulnerabilities in source code efficiently. The model builds an accurate understanding of code semantics with a lot less learnable parameters. The proposed AI achieves 98.40% F1-score on specific CWEs from the benchmarked NIST SARD dataset.
  arXiv  Detail & Related papers  (2021-04-19T11:50:36Z)
• Autosploit: A Fully Automated Framework for Evaluating the Exploitability of Security Vulnerabilities [47.748732208602355]
  Autosploit is an automated framework for evaluating the exploitability of vulnerabilities. It automatically tests the exploits on different configurations of the environment. It is able to identify the system properties that affect the ability to exploit a vulnerability in both noiseless and noisy environments.
  arXiv  Detail & Related papers  (2020-06-30T18:49:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.