8 papers
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…
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…
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…
Fixed-Point Traps and Identity Emergence in Educational Feedback Systems
Faruk Alpay
This paper presents a formal categorical proof that exam-driven educational systems obstruct identity emergence and block creative convergence. Using the framework of Alpay Algebra…
Alpay Algebra: A Universal Structural Foundation
Faruk Alpay
Alpay Algebra is introduced as a universal, category-theoretic framework that unifies classical algebraic structures with modern needs in symbolic recursion and explainable AI. Sta…