Stable and Convexified Information Bottleneck Optimization via Symbolic Continuation and Entropy-Regularized Trajectories. - Faruk Alpay (CoRR, 2025)

XiSort: Deterministic Sorting via IEEE-754 Total Ordering and Entropy Minimization. - Faruk Alpay (CoRR, 2025)

Recursive Semantic Anchoring in ISO 639:2023: A Structural Extension to ISO/TC 37 Frameworks. - Bugra Kilictas; Faruk Alpay (CoRR, 2025)

ϕ∞: Clause Purification, Embedding Realignment, and the Total Suppression of the Em Dash in Autoregressive Language Models. - Bugra Kilictas; Faruk Alpay (CoRR, 2025)

A Rigorous Error Bound for the TG Kernel in Prime Counting. - Bugra Kilictas; Faruk Alpay (CoRR, 2025)

Alpay Algebra IV: Symbiotic Semantics and the Fixed-Point Convergence of Observer Embeddings. - Bugra Kilictas; Faruk Alpay (CoRR, 2025)

Alpay Algebra V: Multi-Layered Semantic Games and Transfinite Fixed-Point Simulation. - Bugra Kilictas; Faruk Alpay (CoRR, 2025)

Transordinal Fixed-Point Operators and Self-Referential Games: A Categorical Framework for Reflective Semantic Convergence. - Faruk Alpay; Hamdi Al Alakkad (CoRR, 2025)

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory. - Faruk Alpay; Bugra Kilictas; Taylan Alpay (CoRR, 2025)

Ultracoarse Equilibria and Ordinal-Folding Dynamics in Operator-Algebraic Models of Infinite Multi-Agent Games. - Faruk Alpay; Hamdi Al Alakkad; Bugra Kilictas; Taylan Alpay (CoRR, 2025)

Ordinal Folding Index: A Computable Metric for Self-Referential Semantics. - Faruk Alpay; Hamdi Al Alakkad (CoRR, 2025)

Idempotent Equilibrium Analysis of Hybrid Workflow Allocation: A Mathematical Schema for Future Work. - Faruk Alpay; Bugra Kilictas; Taylan Alpay; Hamdi Al Alakkad (CoRR, 2025)

Reconstructing Trust Embeddings from Siamese Trust Scores: A Direct-Sum Approach with Fixed-Point Semantics. - Faruk Alpay; Taylan Alpay; Bugra Kilictas (CoRR, 2025)

A Reproducible, Scalable Pipeline for Synthesizing Autoregressive Model Literature. - Faruk Alpay; Bugra Kilictas; Hamdi Al Alakkad (CoRR, 2025)

Transfinite Iteration of Operator Transforms and Spectral Projections in Hilbert and Banach Spaces. - Faruk Alpay; Taylan Alpay; Hamdi Al Alakkad (CoRR, 2025)

Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture. - Faruk Alpay; Bugra Kilictas; Hamdi Al Alakkad (CoRR, 2025)

The phi-Process: Operator-Algebraic Embeddings of Possibilities, Transfinite Stabilization, and a Quantitative Application to Sensory Depletion. - Bugra Kilictas; Faruk Alpay (CoRR, 2025)

Reliability, Embeddedness, and Agency: A Utility-Driven Mathematical Framework for Agent-Centric AI Adoption. - Faruk Alpay; Taylan Alpay (CoRR, 2025)

Escaping Saddle Points via Curvature-Calibrated Perturbations: A Complete Analysis with Explicit Constants and Empirical Validation. - Faruk Alpay; Hamdi Al Alakkad (CoRR, 2025)

Deterministic Coreset Construction via Adaptive Sensitivity Trimming. - Faruk Alpay; Taylan Alpay (CoRR, 2025)

Manipulating Transformer-Based Models: Controllability, Steerability, and Robust Interventions. - Faruk Alpay; Taylan Alpay (CoRR, 2025)

Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment. - Faruk Alpay; Hamdi Al Alakkad (CoRR, 2025)

XML Prompting as Grammar-Constrained Interaction: Fixed-Point Semantics, Convergence Guarantees, and Human-AI Protocols. - Faruk Alpay; Taylan Alpay (CoRR, 2025)

Quantization Errors, Human-AI Interaction, and Approximate Fixed Points in L1(μ). - Faruk Alpay; Hamdi Al Alakkad (CoRR, 2025)

On the Fixed Point Property in Reflexive Banach Spaces. - Faruk Alpay; Hamdi Al Alakkad (CoRR, 2025)

Glass-Box Analysis for Computer Systems: Transparency Index, Shapley Attribution, and Markov Models of Branch Prediction. - Faruk Alpay; Hamdi Al Alakkad (CoRR, 2025)

Truth-Aware Decoding: A Program-Logic Approach to Factual Language Generation. - Faruk Alpay; Hamdi Al Alakkad (CoRR, 2025)

Rate-Distortion Analysis of Compressed Query Delegation with Low-Rank Riemannian Updates. - Faruk Alpay; Bugra Kilictas (CoRR, 2026)

Bare-Metal Tensor Virtualization: Overcoming the Memory Wall in Edge-AI Inference on ARM64. - Bugra Kilictas; Faruk Alpay (CoRR, 2026)

The Geometry of Thought: Disclosing the Transformer as a Tropical Polynomial Circuit. - Faruk Alpay; Bilge Senturk (CoRR, 2026)

Latent Object Permanence: Topological Phase Transitions, Free-Energy Principles, and Renormalization Group Flows in Deep Transformer Manifolds. - Faruk Alpay; Bugra Kilictas (CoRR, 2026)

Stochastic Indexing Primitives for Non-Deterministic Molecular Archives. - Faruk Alpay; Levent Sarioglu (CoRR, 2026)

Latent Objective Induction and Diversity-Constrained Selection: Algorithms for Multi-Locale Retrieval Pipelines. - Faruk Alpay; Levent Sarioglu (CoRR, 2026)

Asymptotic Semantic Collapse in Hierarchical Optimization. - Faruk Alpay; Bugra Kilictas (CoRR, 2026)

Topological Relational Theory: A Simplicial-Complex View of Functional Dependencies, Lossless Decomposition, and Acyclicity. - Bilge Senturk; Faruk Alpay (CoRR, 2026)

Grammar-Constrained (CFL) Reachability: Subcubic Preprocessing, Indexing Trade-offs, and Structured Decoding Semantics. - Faruk Alpay; Levent Sarioglu (CoRR, 2026)

Attention Meets Reachability: Structural Equivalence and Efficiency in Grammar-Constrained LLM Decoding. - Faruk Alpay; Bilge Senturk (CoRR, 2026)

Algorithmic Barriers to Detecting and Repairing Structural Overspecification in Adaptive Data-Structure Selection. - Faruk Alpay; Levent Sarioglu (CoRR, 2026)

Coordinatewise Balanced Covering for Linear Gain Graphs, with an Application to Coset-List Min-2-Lin over Powers of Two. - Faruk Alpay; Levent Sarioglu (CoRR, 2026)

Finite-Horizon First-Order Rank Profiles of Regular Languages. - Madina Bazarova; Faruk Alpay (CoRR, 2026)

Composable Post-Quantum Security for FADEC-Coupled Dual-Spool Turbofan Cyber-Physical Systems. - Faruk Alpay; Taylan Alpay (CoRR, 2026)