DeFi & OEV Dynamics
October 25, 2026 · Version 2
Zenodo: 10.5281/zenodo.23642090
Empirical OEV and Liquidation Dynamics: Chainlink SVR Bid Recapture on Base and Builder-Payment Concentration on Ethereum L1
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Audits 105 Chainlink Smart Value Recapture (SVR) transactions containing 513 liquidations on Base (86 Morpho Blue, 19 Aave v3) alongside 1,049 MEV-Boost liquidation transactions on Ethereum L1. Proves winning solvers bid back 94.38% (incentive-weighted) of liquidation incentives to protocols, while contrasting with builder payment concentration on L1.
Metric: \( \text{Recapture}_{\text{weighted}} = 94.38\% \quad | \quad \text{Sample: } 105 \text{ SVR tx } (513 \text{ liq.}) \text{ on Base } + 1,049 \text{ L1 MEV-Boost tx} \)
Number Theory & Sieve
October 17, 2026 · Version 1
Zenodo: 10.5281/zenodo.23436283
Werr Multi-Layer Algebraic Sieve & Vélu Isogeny Engine: 100% Conductor Certification (log N) and High-Rank Elliptic Curve Records on the NSF ICARM Leaderboard
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Presents the mathematical algorithms and verification certificates for 230 high-rank elliptic curves over \(\mathbb{Q}\) certified on the official NSF ICARM Leaderboard (user/114). Combines a 4-Stage Algebraic Sieve with systematic Vélu 2- and 3-isogeny graph transport across 8 rational torsion subgroups, securing 30 #1 Gold records, 80 Podiums, and 100% Conductor Certification (curves #4308–#4537).
Achievement: 230/230 Curves Certified (100.0%) · 30 First-Place Records · 418 Top-10 Placements · NSF ICARM user/114
Lean 4 · 81 Theorems (0 Sorry)
October 16, 2026 · Release v3.0
Zenodo: 10.5281/zenodo.23425590
Machine-Certified Lean 4 Formalization of the General Divisor Theorem: Unified Density, Arbitrary-Bound Counting, and Finite Error Bounds
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Complete machine-certified formalization (Release v3.0) of the General Divisor Theorem (GDT) in Lean 4: 81 kernel-checked theorems and lemmas with 0 project axioms and 0 sorry. Formulates exact density corrections for coprime residue sets where modulus \(m\) and constraint \(N\) share prime factors, proving admissibility dichotomy, exact per-period counting \(\varphi(R)\), and \(O(1)\) arbitrary-bound counting.
Identity: \( \varphi(R) \cdot N \cdot \varphi(d) = d \cdot R \cdot \varphi(N) ımplies \delta(S) = \frac{\varphi(R)}{m R} \quad | \quad 81 \text{ Theorems, } 0 \text{ Axioms, } 0 \text{ Sorry} \)
Algebraic Geometry & Lattice
October 12, 2026 · Version 1
Zenodo: 10.5281/zenodo.23324067
Machine-Certified Formalization of the 24-Dimensional Niemeier Lattice A_8^3, K3 Hodge Duality and Umbral Moonshine
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Complete machine-certified Lean 4 formalization and Python algebraic verification oracle for the 24-dimensional even unimodular Niemeier lattice \(A_8^3\), its ternary glue code of order 27, du Val \(A_8\) singularity resolutions on complex K3 surfaces, and Umbral Moonshine lambency \(\ell = 9\). Directly eliminates algebraic sign and stabilization-trace cancellation errors with 0 sorry.
Lattice: \( A_8^3 \text{ direct sum}, \quad h = 9, \quad |G_{\text{glue}}| = 27, \quad g=(1,1,4), \quad \|g\|^2 = 4 ımplies \det(\Lambda) = 1.0 \)
Linguistics & Lean 4
October 10, 2026 · Version 1
Zenodo: 10.5281/zenodo.23273006
Güneş Dili: Deterministic Morpho-Semantic Tokenization, Machine-Checked Lean 4 Verification, and Bio-Synthetic Neural Resonance in the WERR Corpus
Authors: Volkan Dağlı, Bekirhan Dağlı, Dağhan Dağlı, Semih Salar, Dr. Zerrin Dağlı (ITouch Systems · Cukurova University Science Park)
Formulates an exact, deterministic morpho-semantic tokenization architecture inspired by phonosemantic foundations, modernized through formal language theory and verified in Lean 4. Agglutination is cast as a deterministic finite-state reduction tree with zero backtracking, guaranteeing \(O(L)\) linear time complexity, >1.2M tokens/sec throughput, and 0 Bytes VRAM overhead.
Complexity: \( O(L) \text{ worst-case latency} \quad | \quad >1,200,000 \text{ tokens/sec} \quad | \quad 0 \text{ Bytes VRAM} \quad | \quad \text{Lean 4: 0 sorry} \)
World Record · Complexity
October 9, 2026 · Version 1
Zenodo: 10.5281/zenodo.23268580
Bipartite Carrier Compression and Machine-Certified Bounds in Schönhage Trilinear Multiplication Tensors
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Discovers a non-trivial cluster-unlocking cascade in Schönhage trilinear tensors eliminating 185 carrier roles, reducing global physical wire width by 377,890 wires down to \(W = 176,906,915\). Certifies the sharpened conditional exponent \(\kappa \approx 4.1310765 \times 10^{-5}\) under exact rational arithmetic and Lean 4 verification without unproven axioms (0 sorry). Fully incorporated into CrocSwap production (PR #226).
Record: \( W = 176,906,915 \quad (\Delta W = -377,890 \text{ wires}) \quad | \quad \kappa \approx 4.1310765 \times 10^{-5} \quad | \quad \text{CrocSwap PR \#226} \)
Pedagogy · WerreduR
October 3, 2026 · Version 4.0
Zenodo: 10.5281/zenodo.23128224
Procedural Fractal Pedagogy: Resolving the Saturn School Disequilibrium Paradox in Self-Directed AI Education via Zero-Storage Mandelbrot Boundary Reflexes
Authors: Dr. Zerrin Dağlı, Volkan Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Resolves Reigeluth's Saturn School Paradox in AI education using the WerreduR zero-storage cognitive reflex engine. Formalizes Vygotsky's Zone of Proximal Development (ZPD) at sub-boundary resonance shoulder loci \(X_{\text{upper/lower}} = (0.25, \pm 0.18)\) along \(\partial M\). Synthesizes adaptive curricula from a 24-byte student seed in \(30.4\ \mu\text{s}\) with 0 Bytes VRAM, verified by 7 Lean 4 theorems (0 sorry).
Results: \( 94.19\% \text{ time-on-task} \quad | \quad 30.4\ \mu\text{s median latency} \quad | \quad 339.4\times \text{ burnout suppression} \quad | \quad \text{7 Lean 4 Theorems} \)
Connectome & BCI
October 1, 2026 · Version 1.1 Revision
Zenodo: 10.5281/zenodo.23072929
Bio-Synthetic Neuromorphic Interfacing: Integration of a Zero-Memory Fractal Decision Engine with the Whole-Brain Drosophila Melanogaster Connectome
Authors: Dağhan Dağlı, Volkan Dağlı, Dr. Zerrin Dağlı (ITouch Systems · Cukurova University Science Park)
Couples the complete 158,262-neuron, 3,990,039-synapse Drosophila connectome (Princeton FlyWire) with an implantable 1,024-pin WERR neuromorphic fractal coprocessor. Completely eliminates VRAM overhead (0 Bytes VRAM), evaluating System-1 decisions in 0.461 ms with 100.0% synaptic transmission fidelity across 300 trials and homeostatic anti-burnout clamp protection.
Biophysics: 158,262 Neurons · 3.99M Synapses · 0.461 ms Latency · 0 Bytes VRAM · \(\Delta T = +0.0012^\circ\text{C}\) · TR 2026/016633
Quantum Gravity & Lean 4
September 30, 2026 · Version 5.0 Monograph
Zenodo: 10.5281/zenodo.23072120
Unitary Black Hole Page Curve Reconstruction via Dynamical Horizon Orbifolds, GKP Modular Stabilizers, and Lean 4 Formal Verification: The Canonical Cumulative Synthesis
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Establishes a machine-verified resolution to the black hole information paradox without AMPS firewall divergence. Formalizes Schmidt bipartition from first principles, models dynamical horizons as orbifold quotients \(\mathbb{C}^2/\mathbb{Z}_9\) resolved via instantons with GKP modular stabilizers, and proves traversable ER bridges via Casimir null energy defocusing. Audited by 10 Lean 4 theorems (0 sorry).
Unitarity: \( \Phi^\dagger \Phi = \mathbb{I} \quad | \quad \mathcal{H} = \mathcal{H}_{\text{ext}} \otimes \mathcal{H}_{\text{int}} \quad | \quad 10 \text{ Machine-Verified Lean 4 Theorems (0 sorry)} \)
Group Theory & Lean 4
September 29, 2026 · Release v0.2.0
Zenodo: 10.5281/zenodo.23045504
Machine-Checked Computational Group Theory in Lean 4: Operational Schreier-Sims Stabilizer Chains, BSGS Sifting, and Backtrack Ordered Partitions
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Standalone machine-verified formalization of computational discrete algebra and permutation group algorithms in Lean 4 (v4.34.1). Formally proves Charles Sims' 1970 Schreier-Sims algorithm, transversal lookup trees, backtrack ordered partition refinement, and cyclotomic extension rings across 35 machine-checked theorems with 0 sorry.
Theorems: Schreier-Sims Invariance · BSGS Sifting Completeness · Cell Refinement · 35 Theorems (0 Sorry)
Formal Verification & Gauntlet
September 26, 2026 · Version 2
Zenodo: 10.5281/zenodo.22983889
Zero-Storage Procedural Neural Synthesis via Boundary Dynamics: Formal Verification in Lean 4 and Bare-Metal Gauntlet Validation
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Formal verification and 40-core bare-metal empirical validation of WERR and Phase III Orbital Error Dynamics (OED). Contains 10 machine-verified Lean 4 theorems in WerracleProof.lean establishing ZMod 9 algebraic closure, Q16.16 fixed-point overflow safety below \(2^{63}-1\), and an EVM gas model bounding worst-case execution to 22,557 gas.
Formal Proof: \( \mathbb{Z}/9\mathbb{Z} \text{ closure} \quad | \quad \text{Gas} \le 22,557 \le 24,000 \quad | \quad \text{40-Core Gauntlet Seal SHA-256 Verified} \)
On-Chain EVM Oracle
September 24, 2026 · Version 1
Zenodo: 10.5281/zenodo.22942599
Werracle: Sub-Cent Intra-Block AI Reflex Oracles and Flash-Loan Circuit Breakers for EVM Smart Contracts
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Production-grade, zero-storage on-chain AI decision oracle capable of sub-millisecond, intra-block execution inside standard EVM smart contracts. Replaces multi-gigabyte weight tensors with a 24-byte fractal coordinate triplet packed into a single 32-byte storage slot (bytes32). Evaluates a 16-point Pareto micro-grid in ~21,438 gas (< $0.0005 on L2s).
EVM Footprint: 1 Word (32 Bytes Storage) · ~21,438 Gas · Atomic Flash-Loan Circuit Breaker · Pure Fixed-Point Q16.16
Edge Reflex & NLP
September 24, 2026 · Version 2.0
Zenodo: 10.5281/zenodo.22939253
Universal Fractal Natural Language Decision Map: Real-Time Edge Triage Across Heterogeneous Domains
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Presents the Universal Fractal Natural Language Decision Map realized via the WERR edge reflex runtime and production platform answerr.me. Synthesizes deterministic strongly-typed decisions without stored weight tensors (0 Bytes VRAM) via Auto-Seed Router (\(\Phi_D\)), semantic token damping filter (\(T_{\text{desc}} = 0.045\)), and \(\mathbb{Z}/9\mathbb{Z}\) cyclic modular discretization.
Triage: 0 Bytes VRAM · Median 3.31 ms Latency · 0.0% Empirical Bypass on Injection · JevBench v1.4+ 100% Wire Compliance
Theory & Biological Ontologies
September 22, 2026 · Version 3.0
Zenodo: 10.5281/zenodo.22900465
Orbital Error Dynamics: Self-Organized Criticality, Ephemeral Parameter Resonance, and Non-Linear Biological Ontologies in Zero-Storage Neural Synthesis
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Proposes that intelligence is ongoing non-equilibrium resistance against dynamic attractor collapse. Formulates Orbital Error Dynamics (OED), introducing the Bent Sine Wave Hypothesis, Observer Horizon geometry with sub-boundary resonance shoulder loci \(X_{\text{upper/lower}} = (0.25, \pm 0.18)\), biomimetic Cauchy jump operator (zinc sparks), and 4-quadrant genetic nucleotide basis mapping.
Principle: \( z_{n+1} = z_n^2 + c \quad | \quad \text{Homeostatic Cardioid Surfing } (c = 1/4) \quad | \quad \text{Patent: TR 2026/016285} \)
Foundational Monograph
September 21, 2026 · Version 3.0
Zenodo: 10.5281/zenodo.22867037
Mandelbrot Fractal Neural Synthesis: Zero-Storage Procedural Weight Derivation and Non-Linear Decision Boundaries
Authors: Volkan Dağlı, Dr. Zerrin Dağlı, Dağhan Dağlı (ITouch Systems · Cukurova University Science Park)
Foundational research paper establishing procedural fractal neural synthesis. Eliminates linear \(O(W)\) parameter retention by deriving synaptic weights and threshold biases from the non-linear visual morphology of the Mandelbrot set (\(\partial M\)) using a 24-byte coordinate seed \(\Theta = (c_x, c_y, \text{zoom})\). Solves all boolean gates and non-linear XOR, Two-Moons (99.30%), and Two-Spirals (98.50%).
Recurrence: \( z_{n+1} = z_n^2 + c \quad | \quad \Theta = (c_x, c_y, \text{zoom}) ın \mathbb{R}^3 \quad (24 \text{ Bytes } O(1)) \quad | \quad \text{Two-Moons: } 99.30\% \)