19 papers
Repair Entropy in Dynamic Geometric Nearest-Neighbour Structures
Faruk Alpay, Bugra Kilictas
We study dynamic geometric data structures for exact nearest-neighbour maintenance under small motions. For each point we store a certificate consisting of its nearest neighbour an…
LatticeBridge: Rare-Event Sequential Inference for Faithful Structured Sequence Synthesis
Faruk Alpay, Bugra Kilictas
Structured sequence generation often requires a model to satisfy several input-derived constraints in a single output. Standard decoding methods may assign high probability to flue…
Asymptotic Semantic Collapse in Hierarchical Optimization
Faruk Alpay, Bugra Kilictas
Multi-agent language systems can exhibit a failure mode where a shared dominant context progressively absorbs individual semantics, yielding near-uniform behavior across agents. We…
Latent Object Permanence: Topological Phase Transitions, Free-Energy Principles, and Renormalization Group Flows in Deep Transformer Manifolds
Faruk Alpay, Bugra Kilictas
We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow…
Bare-Metal Tensor Virtualization: Overcoming the Memory Wall in Edge-AI Inference on ARM64
Bugra Kilictas, Faruk Alpay
The deployment of Large Language Models (LLMs) on edge devices is fundamentally constrained by the "Memory Wall" the bottleneck where data movement latency outstrips arithmetic thr…
Rate-Distortion Analysis of Compressed Query Delegation with Low-Rank Riemannian Updates
Faruk Alpay, Bugra Kilictas
Bounded-context agents fail when intermediate reasoning exceeds an effective working-memory budget. We study compressed query delegation (CQD): (i) compress a high-dimensional late…
The phi-Process: Operator-Algebraic Embeddings of Possibilities, Transfinite Stabilization, and a Quantitative Application to Sensory Depletion
Bugra Kilictas, Faruk Alpay
We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and or…
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…
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…
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…
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…
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…
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…
Alpay Algebra V: Multi-Layered Semantic Games and Transfinite Fixed-Point Simulation
Bugra Kilictas, Faruk Alpay
This paper extends the self-referential framework of Alpay Algebra into a multi-layered semantic game architecture where transfinite fixed-point convergence encompasses hierarchica…
Alpay Algebra IV: Symbiotic Semantics and the Fixed-Point Convergence of Observer Embeddings
Bugra Kilictas, Faruk Alpay
We present a theoretical framework in which a document and an AI model engage in a transfinite fixed-point interaction that leads to stable semantic alignment. Building on the foun…
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…
: Clause Purification, Embedding Realignment, and the Total Suppression of the Em Dash in Autoregressive Language Models
Bugra Kilictas, Faruk Alpay
We identify a critical vulnerability in autoregressive transformer language models where the em dash token induces recursive semantic drift, leading to clause boundary hallucinatio…
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…