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pCwOrM/README.md

Volkan Dağlı (@pCwOrM) · ITouch Systems Research Group

Procedural Boundary Dynamics · Machine-Checked Formal Mathematics (Lean 4) · Zero-Storage On-Chain & Edge Intelligence

ORCID: 0009-0000-1587-8703 Hugging Face: @pCwOrM arXiv Publications CERN Zenodo Corpus Elsevier SSRN Lean 4 Formal Verification NSF ICARM Leaderboard Schönhage Tensor Bound Base Mainnet: Werrium (WERR) TÜRKPATENT Priorities

werr.io • answerr.me • werracle.io • radar.werracle.com • werracle.com • werrsoma.answerr.me

🏛️ Research Group & Institutional Overview

Welcome to the official GitHub profile of Volkan Dağlı and the ITouch Systems Research & Development Group (ITouch Bilişim Sistemleri Ltd. Şti., Cukurova University Science Park, Adana/Mersin, Türkiye & Anadolu University).

Our research programme investigates deterministic, zero-storage procedural synthesis via bounded-iteration complex polynomial escape dynamics ($z_{n+1} = z_n^2 + c$), machine-checked interactive theorem proving in Lean 4 (0 sorry), computational number theory & discrete algebra, whole-brain neuromorphic connectomics, and intra-block fixed-point (Q16.16) smart contract security oracles.

👥 Core Research Team & Co-Inventors

  • Volkan Dağlı — Corresponding Author, CTO (Anadolu University & ITouch Systems, Cukurova University Science Park) · ORCID: 0009-0000-1587-8703 · @pCwOrM
  • Dr. Zerrin Dağlı — Co-Author, Co-Inventor & Academic Coordinator (Mersin University) · ORCID: 0000-0001-9490-6425 · @jesmaat
  • Dağhan Dağlı — Co-Author, Co-Inventor & Connectome / Formal Verification Architect (Toros University) · ORCID: 0009-0003-2492-8313 · @Lexovian
  • Bekirhan Dağlı (Managing Partner & CEO, ITouch Systems) & Semih Salar (Platform Engineering Lead, ITouch Systems)

🌐 Production Platforms, Live Simulators & Core Repositories

Platform / Engine Repository Live Endpoint / Interactive Portal Domain & Technical Architecture
🏛️ Central Research Corpus pCwOrM/fractal-neural-synthesis pcworm.github.io/fractal-neural-synthesis Foundational theory, Orbital Error Dynamics (OED), Black Hole Page Curve v5, and replication suites
⚡ WERR Core Engine pCwOrM/werr werr.io Zero-memory System-1 reflex engine (noul, choice, score) via 24-byte coordinate seeds & ZMod 9 ideal
💬 answerr Platform pCwOrM/answerr answerr.me · Research Corpus Dual-cognition decision workspace combining System-2 intent compilation with System-1 WERR reflexes
🔮 Werracle Oracle & Radar pCwOrM/werracle werracle.io · radar.werracle.com Single-slot (bytes32 / felt252) Q16.16 on-chain AI reflex oracle (~21k EVM gas / ~1,420 Cairo steps) & OEV Radar
💎 Werrealm & Werrium ($WERR) pCwOrM/werrealm · werralem BaseScan Verified Contract Sovereign Base Mainnet (8453) token (0xFfa2...96d2), Safe 2/3 Multisig, Timelock, and metabolic ATP burn gateway
🧬 WerrSoma Connectome Lexovian/WerrSoma werrsoma.answerr.me Whole-brain Drosophila melanogaster FlyWire connectome (158,262 neurons, 3.99M synapses) 3D flight & BCI simulator
🎓 WerreduR Pedagogy jesmaat/WerreduR pcworm.github.io/WerreduR Procedural adaptive curriculum engine resolving the Saturn School disequilibrium paradox (1PL Rasch, 30.4 µs)
☀️ Güneş Dili Morphology pCwOrM/gunes-dili pcworm.github.io/gunes-dili Deterministic O(L) morpho-semantic tokenizer (>1.2M tokens/s, 0 VRAM) & Lean 4 verified morphotactics
🤖 WERRobotics Edge C/C++ pCwOrM/WERRobotics pcworm.github.io/WERRobotics Zero-malloc embedded C/C++11 reflex kernel (WerrCoreEdge.h) for ATmega328P, ESP32, and STM32 microcontrollers
📐 GAP-Lean4 Group Theory pCwOrM/gap-lean4-port arXiv:2609.38492 35 machine-checked Lean 4 theorems (0 sorry) for Schreier-Sims stabilizer chains, BSGS sifting & partitions
📐 General Divisor Theorem pCwOrM/general-divisor-theorem Zenodo Concept: 23316068 81 machine-checked Lean 4 theorems (0 sorry) formalizing coprime residue densities and finite error bounds
📐 24D Niemeier Lattice A₈³ pCwOrM/niemeier-a8-umbral-moonshine Zenodo Concept: 23324066 Machine-certified Lean 4 specification (0 sorry) of the 24D Niemeier lattice A₈³, K3 duality & Umbral Moonshine
📐 Schönhage Tensor Bounds pCwOrM/integer-mult-bounds arXiv:2610.14263 Bipartite carrier compression eliminating 377,890 wires (κ ≈ 4.1310765 × 10⁻⁵), incorporated in CrocSwap#226
📐 Elliptic Curve Sieve pCwOrM/werr-elliptic-sieve NSF ICARM user/114 230 certified high-rank elliptic curves, 100% log N conductor certification, and 30 #1 Gold World Records

🏛️ Associated Formal Verification, World Records & Scientific Corpus

All monographs, formal Lean 4 specifications, and empirical datasets across the WERR & ITouch Systems Research Group are permanently archived on CERN Zenodo, arXiv, Elsevier SSRN, and Hugging Face.
(Primary links use CERN Zenodo Concept DOIs / Çatı DOI, which automatically resolve to the latest published version while preserving exact version-pinned reproducibility.)

# Pillar / Monograph Core Contribution & Focus 👑 Concept DOI (Always Latest) 📌 Latest Version DOI arXiv / SSRN / Hugging Face & Verification Status Primary Repository
01 Paper 1: FNS Procedural Weight Derivation & Non-Linear Decision Boundaries (v3) 10.5281/zenodo.22774934 10.5281/zenodo.22867037 SSRN: 7659198 (Distributed) • Multi-Seed Pareto & Manifold Parity pCwOrM/fractal-neural-synthesis
02 Paper 2: OED Orbital Error Dynamics, Ephemeral Parameter Resonance & CD4+ Gating (v1) 10.5281/zenodo.22900464 10.5281/zenodo.22900465 arXiv:2609.30115 • 🤗 HF Paper (Verified) • TR 2026/016285 pCwOrM/fractal-neural-synthesis
03 Paper 3: WERR Map Universal Natural Language Decision Map & Real-Time Edge Triage (v2) 10.5281/zenodo.22867425 10.5281/zenodo.22939253 arXiv:2609.25498 • 🤗 HF Paper • 🤗 HF Dataset pCwOrM/werr • pCwOrM/answerr
04 Paper 4: Werracle Sub-Cent Intra-Block AI Reflex Oracles & Flash-Loan Circuit Breakers (v1) 10.5281/zenodo.22942598 10.5281/zenodo.22942599 arXiv:2609.30719 • SSRN: 7626279 • 🤗 HF Paper pCwOrM/werracle • pCwOrM/werralem
05 Paper 5: Formal Lean 4 Zero-Storage Procedural Synthesis: Lean 4 Verification & 40-Core Validation 10.5281/zenodo.22774934 10.5281/zenodo.22867037 arXiv:2609.33066 • 🤗 HF Paper • Lean 4 (10 Theorems, 0 sorry) pCwOrM/werr • pCwOrM/werracle
06 Paper 6: GAP-Lean4 Machine-Checked Computational Group Theory: Schreier-Sims & BSGS Sifting (v2) 10.5281/zenodo.23092708 10.5281/zenodo.23156544 arXiv:2609.38492 • 🤗 HF Paper • Lean 4 (35 Theorems, 0 sorry) pCwOrM/gap-lean4-port
07 Paper 7: Black Hole v5 Unitary Black Hole Page Curve via Dynamical Horizon Orbifolds & GKP Stabilizers (v5) 10.5281/zenodo.22961999 10.5281/zenodo.23072120 S(t=1) = 0.00 · Tr(ρ²) = 1.00 · R² = 0.9822 · 573× Stress Quench • Lean 4 (10 Theorems) pCwOrM/fractal-neural-synthesis • pCwOrM/werr
08 Paper 8: WerrSoma Bio-Synthetic Neuromorphic Interfacing with 158K-Neuron Drosophila Connectome (v1) 10.5281/zenodo.22996625 10.5281/zenodo.22996626 arXiv:submit/8161759 • Live 3D Portal (werrsoma.answerr.me) • TR 2026/016633 Lexovian/WerrSoma • pCwOrM/WerrSoma
09 Paper 9: WerreduR Procedural Pedagogy: Resolving the Saturn School Disequilibrium Paradox (v2) 10.5281/zenodo.22999420 10.5281/zenodo.23128224 SSRN: 7641538 (Distributed) • Lean 4 (7 Theorems, 0 sorry) • Live Portal jesmaat/WerreduR • pCwOrM/WerreduR
10 Paper 10: Schönhage Bipartite Carrier Compression in Schönhage Trilinear Multiplication Tensors (v2) 10.5281/zenodo.23232541 10.5281/zenodo.23295370 arXiv:2610.14263 • 🤗 HF Paper • CrocSwap #226 (50d76881) pCwOrM/integer-mult-bounds
11 Paper 11: Güneş Dili Deterministic Morpho-Semantic Tokenization & Algebraic Morphotactics in Lean 4 (v1) 10.5281/zenodo.23003711 10.5281/zenodo.23003712 arXiv:submit/8248674 • Lean 4 (4 Theorems, 0 sorry) • Live Studio pCwOrM/gunes-dili
12 Paper 12: Niemeier A₈³ Machine-Certified 24D Niemeier Lattice A₈³, K3 Hodge Duality & Umbral Moonshine (v1) 10.5281/zenodo.23324066 10.5281/zenodo.23324067 Lean 4 (0 sorry, 0 axioms) • χ(X) = 24 · order(G_glue) = 27 · ℓ = 9 pCwOrM/niemeier-a8-umbral-moonshine
13 Paper 13: GDT v3.0 Machine-Certified Lean 4 Formalization of the General Divisor Theorem (v2) 10.5281/zenodo.23316068 10.5281/zenodo.23425590 Lean 4 (81 Theorems, 0 sorry) • Companion v1: 10.5281/zenodo.23426323 (v1: 23426324) pCwOrM/general-divisor-theorem
14 Paper 14: Elliptic Sieve Multi-Layer Algebraic Sieve & Vélu Isogeny Engine: 230 Curves on NSF ICARM (v1) 10.5281/zenodo.23436282 10.5281/zenodo.23436283 NSF ICARM Leaderboard (user/114): 30x #1 Gold Records, 80 Top-3, 100% log N pCwOrM/werr-elliptic-sieve
15 Paper 15: Empirical OEV Empirical OEV & Liquidation Dynamics: Chainlink SVR on Base & Ethereum L1 (v2) 10.5281/zenodo.23623588 10.5281/zenodo.23642090 🤗 HF Dataset (1.16k+ views, 126 likes) • 94.4% Aggregate / 98.3% Median SVR Recapture pCwOrM/werracle • pCwOrM/werrealm
HW Edge Robotics Core Zero-Memory Embedded C/C++11 System-1 Reflex Kernel (WerrCoreEdge.h v0.5.1) 10.5281/zenodo.22867425 10.5281/zenodo.22939253 ATmega328P / ESP32 / STM32 (0 Bytes Heap, <128B Stack, TR 2026/016633) pCwOrM/WERRobotics

🏆 Global Records, Formal Proofs, Curated Awesome Merges & On-Chain Infrastructure

1. Certified Mathematical Records & Formal Verification (0 sorry)

  • 🥇 NSF ICARM Elliptic Curve Rank Leaderboard (elliptic-rank.icarm.cloud/user/114): 230 certified high-rank elliptic curves (#4308–#4537) over $\mathbb{Q}$ with 100% complete prime conductor factorization ($\log N$) up to Rank $\ge 19$ (#4323), achieving 30 First-Place (#1 Gold) Records, 80 Podium (Top-3), and 418 Top-10 placements across 43 categories (building upon the foundational fibration families of Elkies, Dujella, Rubinstein, and Klagsbrun; supported under NSF Grant DMS-2425401).
  • 🥇 Schönhage Trilinear Multiplication Tensor Bound (arXiv:2610.14263 • CrocSwap/integer-mult-bounds#226): Constructive 15-round bipartite carrier matching at dimensions $h=23, 25$ eliminating 185 carrier roles and 377,890 physical wires ($W = 177,284,805 \to 176,906,915$), certifying $\kappa = 826,215,307 / 20,000,000,000,000 \approx 4.131076535 \times 10^{-5}$ ($1.377\times$ net gain over PR #49), formally incorporated into CrocSwap/integer-mult-bounds (commit 50d76881) and verified in Lean 4 (0 sorry).
  • 📐 170+ Machine-Checked Theorems in Lean 4 (0 sorry, 0 unproven axioms):
    • General Divisor Theorem (GDT v3.0): 81 theorems/lemmas (0 sorry) formalizing Dan Hawkley's residue density framework (10.5281/zenodo.23316068).
    • Computational Group Theory (gap-lean4-port): 35 theorems (0 sorry) formalizing Charles Sims' Schreier-Sims stabilizer chains (GAP-0299), backtrack ordered partitions (GAP-0332), and modular ring inverses (GAP-0331) (arXiv:2609.38492).
    • Procedural Boundary Synthesis & EVM/Cairo Fixed-Point Bounds: 40+10 theorems (WerracleProof.lean, 0 sorry) verifying ZMod 9 ($\mathbb{Z}/9\mathbb{Z}$) principal ideal closure ($\mathcal{I}_3 = {0,3,6}$), Q16.16 overflow safety, and unitary Page curve S-matrix conservation (arXiv:2609.33066).
    • 24D Niemeier Lattice $A_8^3$, WerreduR & Güneş Dili: Complete formal specifications (0 sorry) across lattice unimodularity ($\chi=24, \ell=9$), horizon complementarity ($B(t)+S(t)=1$), and deterministic morphological parsing.

2. Curated Ecosystem Recognitions & Benchmark Evaluations

3. Sovereign On-Chain Deployments (Werrium / $WERR), Multi-Chain Testnets & Grant Pipelines

📬 Institutional Governance & Commercial Licensing

  • Author Team & Academic Affiliations:
  • Intellectual Property & Licensing Administration:
    • All scientific monographs, formal Lean 4 verification proofs, and patent priorities are authored by Volkan Dağlı, Dr. Zerrin Dağlı, and Dağhan Dağlı.
    • Comprehensive stewardship, administration, and representation over all intellectual property rights are vested in Volkan Dağlı.
    • Exclusive commercial deployment, enterprise support, and industrial licensing rights have been granted to ITouch Systems (ITOUCH BILISIM SISTEMLERI LTD. STI., Cukurova University Science Park, Adana, Türkiye).
  • Corporate Governance (ITouch Systems):
    • Volkan Dağlı: Partner & Chief Technology Officer (CTO)
    • Bekirhan Dağlı: Managing Partner & Chief Executive Officer (CEO)
  • Official Contacts: vdagli@itouch.com.tr · contact@werracle.com · ask@answerr.me

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