26 papers
Provenance and Authorization in Autobiographical Language Models
Faruk Alpay, Taylan Alpay
Autobiographical language models may draw on archives containing observations, quotations, emotional reports, and earlier model outputs. Cryptographic authentication can preserve a…
Approval Integrity and Recovery in LLM Answer Publication
Faruk Alpay, Taylan Alpay
Publication integrity in LLM systems requires binding approved content to its current authorization context. We examine exact-content binding, authorization freshness and checkpoin…
AccretionLink: On-Device Auditing of Exposure-Control Attacks on Attribute Inference
Faruk Alpay, Taylan Alpay
Exposure control lets an adversary rank authentic public posts to strengthen private-attribute inference without altering content. AccretionLink defines confidentiality and integri…
Conductance-Repair Evidence Graphs for Prospective Security Retrieval
Faruk Alpay, Taylan Alpay
Security retrieval is often evaluated as ranking over complete evidence, but operational triage is prospective: CVE descriptions, weakness metadata, fix commits, EPSS scores, KEV m…
Unprivileged Topology Certificates for Cloud GPU Attestation
Faruk Alpay, Taylan Alpay
Cloud GPU tenants receive a model name and a region, but cannot directly inspect the physical accelerator that runs their job. We present a software-only attestation primitive for…
Compute-Budgeted Exploitability Evidence Graphs for Prospective Vulnerability Triage
Faruk Alpay, Taylan Alpay
Defenders cannot patch every newly disclosed vulnerability at once, so exploitability prediction must be evaluated prospectively rather than retrospectively. We study compute-budge…
Choric Masking in Ambient Release Systems: A Finite Certificate Calculus for Trace Indistinguishability under Bounded Audiences
Faruk Alpay, Taylan Alpay
This paper develops a finite certificate calculus for ambient release systems, staged probabilistic environments in which a protected coordinate is not observed directly but can re…
Layer Order Semantics for Automata-Based Cybersecurity
Faruk Alpay, Taylan Alpay
Layered cybersecurity pipelines transform evidence before they decide on it, and the order of those transformations determines which security facts become visible to which layer. T…
Quantifying Side-Channel Leakage in Public Metrology Releases
Faruk Alpay, Taylan Alpay
Public scientific and metrology releases can leak the hidden settings that produced them. We formalize and quantify this risk as a profiled statistical side-channel audit: a releas…
AgentSecBench: Measuring Prompt Injection, Privacy Leakage, and Tool-Use Integrity in LLM Agents
Faruk Alpay, Taylan Alpay
LLM agents process trusted instructions, retrieved records, and tool observations through a common generative channel. This conflates data flow with authority: an untrusted string…
Composable Post-Quantum Security for FADEC-Coupled Dual-Spool Turbofan Cyber-Physical Systems
Faruk Alpay, Taylan Alpay
We develop a unified mathematical formulation for post-quantum authenticated telemetry and actuation in FADEC-coupled dual-spool turbofan cyber-physical systems. The formulation in…
Calibrated Counterfactual Conformal Fairness (): Post-hoc, Shift-Aware Coverage Parity via Conformal Prediction and Counterfactual Regularization
Faruk Alpay, Taylan Alpay
We present Calibrated Counterfactual Conformal Fairness (), a post-hoc procedure that targets group-conditional coverage parity under covariate shift. combines importa…
XML Prompting as Grammar-Constrained Interaction: Fixed-Point Semantics, Convergence Guarantees, and Human-AI Protocols
Faruk Alpay, Taylan Alpay
Structured prompting with XML tags has emerged as an effective way to steer large language models (LLMs) toward parseable, schema-adherent outputs in real-world systems. We develop…
Manipulating Transformer-Based Models: Controllability, Steerability, and Robust Interventions
Faruk Alpay, Taylan Alpay
Transformer-based language models excel in NLP tasks, but fine-grained control remains challenging. This paper explores methods for manipulating transformer models through principl…
Nonlinear Continuum of States and Intuitionistic Flows in a Cognitive Space
Faruk Alpay, Taylan Alpay
We construct a rigorous mathematical framework for an abstract continuous evolution of an internal state, inspired by the intuitive notion of a flowing thought sequence. Using tool…
Deterministic Coreset Construction via Adaptive Sensitivity Trimming
Faruk Alpay, Taylan Alpay
We develop a rigorous framework for deterministic coreset construction in empirical risk minimization (ERM). Our central contribution is the Adaptive Deterministic Uniform-Weight T…
Reliability, Embeddedness, and Agency: A Utility-Driven Mathematical Framework for Agent-Centric AI Adoption
Faruk Alpay, Taylan Alpay
We formalize three design axioms for sustained adoption of agent-centric AI systems executing multi-step tasks: (A1) Reliability > Novelty; (A2) Embed > Destination; (A3) Agency >…
Alpay Folded Prime Enumerator via gcd and Floors: Exact Enumeration, Record-Lift, and Non-Synonymy/Minimality Certificates
Faruk Alpay, Taylan Alpay
A single closed expression is presented which, for every integer , returns the -th prime . The construction uses only integer arithm…
Anchored Implication & Event-Indexed Fixed Points in Hilbert Spaces: Uniqueness and Quantitative Rates
Faruk Alpay, Bugra Kilictas, Taylan Alpay
We develop a synthesis of orthomodular logic (projections as propositions) with operator fixed-point theory in Hilbert spaces. First, we introduce an anchored implication connectiv…
Logically Contractive Mappings: Fixed Points and Event-Indexed Rates
Faruk Alpay, Taylan Alpay
We introduce "logically contractive mappings" nonexpansive self-maps that contract along a subsequence of iterates and prove a fixed-point theorem that extends Banach's principle.…
Transfinite Iteration of Operator Transforms and Spectral Projections in Hilbert and Banach Spaces
Faruk Alpay, Taylan Alpay, Hamdi Alakkad
We study ordinal-indexed, multi-layer iterations of bounded operator transforms and prove convergence to spectral/ergodic projections under functional-calculus hypotheses. For norm…
Transfinite Operator Fixed Points on Hilbert Spaces: An Alpay Algebra Approach
Faruk Alpay, Hamdi Alakkad, Taylan Alpay
This work develops a functional-analytic framework based on the transfinite iteration of a self-adjoint operator. Beginning with a densely defined self-adjoint operator on a Hi…
Reconstructing Trust Embeddings from Siamese Trust Scores: A Direct-Sum Approach with Fixed-Point Semantics
Faruk Alpay, Taylan Alpay, Bugra Kilictas
We study the inverse problem of reconstructing high-dimensional trust embeddings from the one-dimensional Siamese trust scores that many distributed-security frameworks expose. Sta…
Idempotent Equilibrium Analysis of Hybrid Workflow Allocation: A Mathematical Schema for Future Work
Faruk Alpay, Bugra Kilictas, Taylan Alpay +1
The rapid advance of large-scale AI systems is reshaping how work is divided between people and machines. We formalise this reallocation as an iterated task-delegation map and show…