6 papers
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…
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…
Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory
Faruk Alpay, Bugra Kilictas, Taylan Alpay
This paper contributes to the Alpay Algebra by demonstrating that the stable outcome of a self referential process, obtained by iterating a transformation through all ordinal stage…
A Rigorous Error Bound for the TG Kernel in Prime Counting
Bugra Kilictas, Faruk Alpay
We establish rigorous error bounds for prime counting using a truncated Gaussian (TG) kernel in the explicit formula framework. Our main theorem proves that the approximation error…
Recursive Semantic Anchoring in ISO 639:2023: A Structural Extension to ISO/TC 37 Frameworks
Bugra Kilictas, Faruk Alpay
ISO 639:2023 unifies the ISO language-code family and introduces contextual metadata, but it lacks a machine-native mechanism for handling dialectal drift and creole mixtures. We p…