Volkan Dağlı

Werr Multi-Layer Algebraic Sieve & Vélu Isogeny Engine: 100% Conductor Certification (log N) and High-Rank Elliptic Curve Records on the NSF ICARM Leaderboard

This open-science research package presents the mathematical algorithms, verification certificates, and complete dataset of 230 high-rank elliptic curves over ℚ certified and permanently recorded on the official NSF Institute for Computer-Aided Reasoning in Mathematics (ICARM) El...

Machine-Certified Lean 4 Formalization of the General Divisor Theorem: Exact Density Correction under Residue Conditioning

We present an exhaustive, machine-certified formalization of the General Divisor Theorem (GDT) in the Lean 4 interactive theorem prover. Developed originally as a discrete analytic framework by thinkthoughts (2026), the General Divisor Theorem provides exact density corrections f...

Machine-Certified Formalization of the 24-Dimensional Niemeier Lattice A_8^3, K3 Hodge Duality and Umbral Moonshine

Complete machine-certified Lean 4 formal specification and exact Python algebraic verification oracle for the 24-dimensional even unimodular Niemeier lattice A83, its ternary glue code Gglue of order 27, du Val A8 singularity resolutions on complex K3 surfaces, and Umbral Moonshi...

Machine-Checked Computational Group Theory in Lean 4: Operational Schreier-Sims Stabilizer Chains, BSGS Sifting, and Backtrack Ordered Partitions

gap-lean4-port (Release v0.2.0): Formally Machine-Checked Computational Group Theory in Lean 4 and Mathlib4 This repository and research package contains the complete, standalone formalization of foundational computational discrete algebra and permutation group algorithms verifie...

Unitary Black Hole Page Curve Reconstruction via Wormhole Error-Kernel Invariants: Non-Dissipative State Preservation, 40-Core Bare-Metal Telemetry, and Formal Verification

Version 3.0 Major Theoretical Upgrade & Extended Monograph (12 Pages, Formal Lean 4 Verification, Exact GKP Unitarity, and Kerr Polar Collimation) This monograph presents an exact, unitary, and non-dissipative resolution to the black hole information paradox and the AMPS firewall...

Universal Fractal Natural Language Decision Map: Real-Time Edge Triage Across Heterogeneous Domains

Abstract: Modern automated computing systems increasingly deploy Large Language Models (LLMs) to resolve runtime operational triage, incurring prohibitive latency (>100–500 ms), severe memory allocation (>4–8 GB VRAM), and high thermodynamic dissipation. Extending the foundationa...

Universal Fractal Natural Language Decision Map: Real-Time Edge Triage Across Heterogeneous Domains

Universal Fractal Natural Language Decision Map: Real-Time Edge Triage Across Heterogeneous Domains This open-science research package presents the complete theoretical framework, empirical replication pipeline, and bare-metal production benchmarks for the Universal Fractal Natur...

Mandelbrot Fractal Neural Synthesis: Zero-Storage Procedural Weight Derivation and Non-Linear Decision Boundaries

Mandelbrot Fractal Neural Synthesis: Zero-Storage Procedural Weight Derivation and Non-Linear Decision Boundaries What's New in Version 2.0 (Major Revision & Q1 Readiness) Systems Trade-Off Framing: Reframed the central research question from raw parameter fitting to fundamental...