20 papers
Proof-Carrying Multimodal Timelines: Finite-Trace Modal Certificates for Video-Audio Consistency
Faruk Alpay, Hamdi Alakkad
Multimodal video systems often expose clip-level scores while hiding the local temporal failure that makes a video inconsistent. We formulate video-audio consistency as finite-trac…
Finite Certificates for In-Context Determinacy and a Threshold Theory of Emergence in Language Models
Faruk Alpay, Hamdi Alakkad
This paper develops a model-theoretic framework for verifying context-conditioned language-model behavior by replacing benchmark labels with finite semantic certificates. The first…
Executable Boundary Contracts for Sound Event Traces
Faruk Alpay, Hamdi Alakkad
Sound event reports often compress timed boundary behavior into frame, segment, or event scores. This paper defines executable boundary contracts for finite sound event traces. The…
Truth-Aware Decoding: A Program-Logic Approach to Factual Language Generation
Faruk Alpay, Hamdi Alakkad
This paper introduces Truth-Aware Decoding (TAD), a verification-oriented decoding scheme that aligns neural language generation with knowledge bases. Situated in the tradition of…
A Riemannian Variational and Spectral Framework for High-Dimensional Sphere Packing: Barrier-Dynamics Reconciliation, Periodic Rigidity, and Discrete-Time Guarantees
Faruk Alpay, Hamdi Alakkad
We develop a unified framework that reconciles a barrier based geometric model of periodic sphere packings with a provably convergent discrete time dynamics. First, we introduce a…
Glass-Box Analysis for Computer Systems: Transparency Index, Shapley Attribution, and Markov Models of Branch Prediction
Faruk Alpay, Hamdi Alakkad
We formalize glass-box analysis for computer systems and introduce three principled tools. First, the Glass-Box Transparency Index (GTI) quantifies the fraction of performance vari…
On the Fixed Point Property in Reflexive Banach Spaces
Faruk Alpay, Hamdi Alakkad
Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach spac…
Quantization Errors, Human--AI Interaction, and Approximate Fixed Points in
Faruk Alpay, Hamdi Alakkad
We develop a rigorous measure-theoretic framework for the analysis of fixed points of nonexpansive maps in the space , with explicit consideration of quantization errors ar…
New Approaches to the Fixed Point Property in L^1 Spaces
Faruk Alpay, Hamdi Alakkad
This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, w…
Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment
Faruk Alpay, Hamdi Alakkad
This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-re…
Escaping Saddle Points via Curvature-Calibrated Perturbations: A Complete Analysis with Explicit Constants and Empirical Validation
Faruk Alpay, Hamdi Alakkad
We present a comprehensive theoretical analysis of first-order methods for escaping strict saddle points in smooth non-convex optimization. Our main contribution is a Perturbed Sad…
Calibrated Semantic Diffusion: A p-Laplacian Synthesis with Learnable Dissipation, Quantified Constants, and Graph-Aware Calibration
Faruk Alpay, Hamdi Alakkad
We develop a calibrated diffusion framework by synthesizing three established concepts: linear Laplacian smoothing, nonlinear graph p-Laplacian flows, and a learnable dissipation t…
Temporal Anchoring in Deepening Embedding Spaces: Event-Indexed Projections, Drift, Convergence, and an Internal Computational Architecture
Faruk Alpay, Bugra Kilictas, Hamdi Alakkad
We develop an operator-theoretic framework for temporal anchoring in embedding spaces, modeled as drift maps interleaved with event-indexed blocks culminating in affine projections…
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…
A Reproducible, Scalable Pipeline for Synthesizing Autoregressive Model Literature
Faruk Alpay, Bugra Kilictas, Hamdi Alakkad
The accelerating pace of research on autoregressive generative models has produced thousands of papers, making manual literature surveys and reproduction studies increasingly impra…
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…
Ordinal Folding Index: A Computable Metric for Self-Referential Semantics
Faruk Alpay, Hamdi Al Alakkad
The Ordinal Folding Index (OFI) is a new, fully computable yard-stick that measures how many rounds of self-reference a statement, protocol or position must unfold before its truth…
Ultracoarse Equilibria and Ordinal-Folding Dynamics in Operator-Algebraic Models of Infinite Multi-Agent Games
Faruk Alpay, Hamdi Alakkad, Bugra Kilictas +1
We develop an operator algebraic framework for infinite games with a continuum of agents and prove that regret based learning dynamics governed by a noncommutative continuity equat…
Transordinal Fixed-Point Operators and Self-Referential Games: A Categorical Framework for Reflective Semantic Convergence
Faruk Alpay, Hamdi Al Alakkad
We present a new theoretical framework that unifies category-theoretic fixed-point constructions, transfinite recursion, and game-based semantics to model how interpretations of la…