WerreduR: Adaptive Difficulty Control & Procedural Cognitive Reflex Engine

Important

🏛️ Cumulative Academic Architecture & Multi-Track Scientific Portal

This repository is the open-science home of WerreduR, developed and validated within the Werr cognitive architecture environment (answerr.me / ITouch Systems). To preserve unbroken scientific continuity, earlier publications, datasets, and formal proofs remain permanently accessible alongside our latest empirical breakthroughs:

Track 1: Flagship Q1 Empirical Positioning Study (Under Double-Blind Peer Review) (Flagship Milestone)
- Title: "Where does a fractal-seeded difficulty controller stand? A simulation study against adaptive testing, staircase rules and a language model"
- Venue: Under Double-Blind Peer Review at a flagship Q1 journal in Learning Technologies & Intelligent Educational Systems.
- Contents: Rigorous benchmarking of the estimation-free, 24-byte difficulty controller (LearningGate) against Computerized Adaptive Testing (CAT, Rasch EAP), fixed staircases (= Elo), accelerated PEST, stored-weight twins, and frontier LLM (Claude Haiku 4.5 across 3,800 decisions). Verified across 6,000 synthetic learners and empirical replays on 1.25 million interactions from ASSISTments 2009–2010 and 2017.
- Quick Access: 📦 Complete Replication Suite (.zip) | 🔬 Code & Data Directory | 🔒 Anonymized OSF Portal
Track 2: Published Seed Preprint & Live arXiv Package (Version 4.0) (Foundational Theory)
- Title: "Procedural Fractal Pedagogy: Resolving the Saturn School Disequilibrium Paradox in Self-Directed AI Education via Zero-Storage Mandelbrot Boundary Reflexes"
- Preprint Identifiers: Zenodo DOI: 10.5281/zenodo.23128224 | Concept DOI: 10.5281/zenodo.22999420 | TR Priority Patent Application: TR 2026/016285
- Contents: Theoretical framework anchoring Vygotsky's Zone of Proximal Development (ZPD) to Mandelbrot boundary resonances, 7 machine-checked theorems in Lean 4 (0 sorry), and $N=1,000$ self-directed learning trajectory simulations.
- Quick Access: 📄 Camera-Ready PDF | 📦 arXiv TeX Source Package (.zip) | 📋 arXiv Submission Guide | 📜 Lean 4 Proofs
Track 3: Historical Archival Corpus (Version 1.0 & PFP-Core Heritage) (Cumulative Archive)
- All historical telemetry, initial seed papers, LaTeX drafts, and Zenodo distributions are preserved in legacy/ ensuring 100% citation persistence.

👥 Authors & Affiliations

Zerrin Dağlı (First & Corresponding Author) — Mersin University, Mersin, Turkey • ORCID: 0000-0001-9490-6425
Volkan Dağlı — Anadolu University, Eskişehir, Turkey & ITouch Systems, Çukurova Teknokent, Mersin, Turkey • ORCID: 0009-0000-1587-8703 (@pCwOrM)
Dağhan Dağlı — Toros Science High School, MEV (Toros University), Mersin, Turkey • ORCID: 0009-0003-2492-8313 (@Lexovian)

🌐 Companion Open-Science Corpus & Cross-Verification

PFP / WerreduR (This Work): doi:10.5281/zenodo.23128224 (v4.0) • Concept DOI: 10.5281/zenodo.22999420 (GitHub: jesmaat/WerreduR • Mirror: pCwOrM/WerreduR • Live Simulator)
WERR Core Decision Engine: arXiv:2609.25498 • doi:10.5281/zenodo.22939253 (GitHub: pCwOrM/werr)
GAP → Lean 4 Formal Verification: arXiv:2609.38492 • doi:10.5281/zenodo.23045504 (GitHub: pCwOrM/gap-lean4-port)
WerrSoma Whole-Brain Connectome (158K Neurons): doi:10.5281/zenodo.23072929 (v1.1) • Live Portal: werrsoma.answerr.me (GitHub: Lexovian/WerrSoma)
Güneş Dili Formal Phonetics & Morphology: doi:10.5281/zenodo.23273006 (GitHub: pCwOrM/gunes-dili)
answerr Reflex AI & Live Workspace: https://answerr.me (GitHub: pCwOrM/answerr)
Orbital Error Dynamics (OED): arXiv:2609.30115 • doi:10.5281/zenodo.22896856
Mandelbrot Fractal Neural Synthesis (MFNS): doi:10.5281/zenodo.22774934 (GitHub: pCwOrM/mandelbrot-fractal-neural-synthesis)
Lean 4 Formal Verification & 40-Core Gauntlet: arXiv:2609.33066 • doi:10.5281/zenodo.22983889
Werracle Sub-Cent Intra-Block EVM AI Oracle: arXiv:2609.30719 • doi:10.5281/zenodo.22942598 (GitHub: pCwOrM/werracle)
Schönhage Tensor Carrier Compression (World Record): arXiv:2610.14263 (PDF • DOI: 10.48550/arXiv.2610.14263 • arXiv: submit/8207241) • doi:10.5281/zenodo.23268580 (GitHub: pCwOrM/integer-mult-bounds) • CrocSwap PR #226 (incorporated) • Contributors (@pCwOrM) • Audit (50d76881)
General Divisor Theorem (GDT) Lean 4: doi:10.5281/zenodo.23316070 (GitHub: pCwOrM/general-divisor-theorem)
24D Niemeier Lattice $A_8^3$ & K3 Umbral Moonshine Lean 4: doi:10.5281/zenodo.23324066 • Record 23324067 (GitHub: pCwOrM/niemeier-a8-umbral-moonshine)

🏆 Track 1: Flagship Q1 Empirical Positioning Study (Under Double-Blind Peer Review)

Where does a fractal-seeded difficulty controller stand? A simulation study against adaptive testing, staircase rules and a language model

Authors:

Zerrin Dağlı (Corresponding Author) — Mersin University & Yusuf Kalkavan Anatolian High School, Mersin, Turkey • ORCID: 0000-0001-9490-6425
Volkan Dağlı — Anadolu University, Eskişehir, Turkey & ITouch Systems, Mersin, Turkey • ORCID: 0009-0000-1587-8703
Dağhan Dağlı — Toros Science High School, MEV (Toros University), Mersin, Turkey • ORCID: 0009-0003-2492-8313

Target Journal: Flagship Q1 Journal in Learning Technologies & Intelligent Educational Systems (Under Double-Blind Peer Review)
Double-Blind Review Portal: OSF Anonymized View-Only Node
Canonical Repository: https://github.com/jesmaat/WerreduR
Engineering Mirror: https://github.com/pCwOrM/WerreduR
Werr Ecosystem: Validated and certified production difficulty controller within werr (answerr.me)

📄 Executive Summary & Findings

Modern Computerized Adaptive Testing (CAT) provides optimal difficulty tracking in stationary settings when backed by heavily calibrated item banks, but struggles under rapid learner trajectory shifts, requiring continuous numerical estimation. Simple psychophysical staircase procedures adapt instantaneously but lack multi-scale contextual awareness. Frontier Large Language Models (LLMs) can select items heuristically but introduce prohibitive latency, stochastic outputs, and multi-gigabyte memory footprints.

This study isolates and benchmarks LearningGate, an estimation-free adaptive difficulty controller whose step-size dynamics are procedurally driven by a frozen 24-byte coordinate seed $\Theta^* = (cx_0 = -0.807926, cy_0 = 0.183021, z_0 = 300.0)$ on the sub-boundary of the Mandelbrot set evaluated via the WERR multi-scale tripod kernel.

                    ┌──────────────────────────────────────────────┐
                    │               Learner Response               │
                    │                   x ∈ {0, 1}                 │
                    └──────────────────────┬───────────────────────┘
                                           │
                                           ▼
                    ┌──────────────────────────────────────────────┐
                    │      State Vector: Recent Bits + Bias        │
                    │   h = [h0, h1, h2, h3],  ρ ∈ [-3.0, 3.0]     │
                    └──────────────────────┬───────────────────────┘
                                           │
                                           ▼
                    ┌──────────────────────────────────────────────┐
                    │       Feature Projection & Modulation        │
                    │  dx, dy, dz derived from agreement / bias    │
                    └──────────────────────┬───────────────────────┘
                                           │
                                           ▼
                    ┌──────────────────────────────────────────────┐
                    │        WERR Multi-Scale Tripod Kernel        │
                    │  Mandelbrot sub-boundary escape ratios (q)   │
                    │        Evaluated at 0.60x, 1.00x, 1.60x      │
                    └──────────────────────┬───────────────────────┘
                                           │
                                           ▼
                    ┌──────────────────────────────────────────────┐
                    │            Sigmoid Gain Neuron               │
                    │        g = σ(w1*a1 + w2*a2 + w3*m + w4)      │
                    └──────────────────────┬───────────────────────┘
                                           │
                                           ▼
                    ┌──────────────────────────────────────────────┐
                    │         Servo Step & Item Difficulty         │
                    │     step = 0.05 + 0.55 * g   [0.05, 0.60]    │
                    │           b ← b + step * (2x - 1)            │
                    └──────────────────────────────────────────────┘

Key Empirical Results:

Dynamic Tracking Advantage: Under fast-learning and abrupt trajectory jumps (+1.5 logits), LearningGate achieves a +0.21 to +0.33 logit alignment advantage over standard Rasch CAT and re-centers within 10.4 trials (vs. 56.0 trials for CAT).
24-Byte Seed Non-Inferiority: Demonstrates empirical non-inferiority to its 4-parameter stored-weight twin across 18 of 18 test comparisons ($\Delta \le 0.003$ logits).
Real-World Empirical Validation: Evaluated via counterfactual replays on mixed-effects learner models fitted to 1.25 million interactions from ASSISTments 2009–2010 ($N = 4,163$) and ASSISTments 2017 ($N = 1,709$), maintaining consistent convergence under empirical student response noise.
LLM API Benchmark: Benchmarked against Claude Haiku 4.5 across 200 learners (3,800 API calls, temperature 0). The LLM incurred $67-788\text{ ms}$ latency with $0.784-0.933$ logit alignment error, whereas LearningGate executed in $0.3-0.4\text{ ms}$ ($418\ \mu\text{s}$) with $0.419$ logit error and zero cloud dependency.

📊 Comparative Positioning Matrix

Controller Architecture	Underlying Model	State Memory	Per-Item Latency	Stationary MAE	Fast Learning Lag	Recovery After Jump	Guessing Robustness	Target $P^*$
Standard CAT (Rasch EAP)	Latent $\theta \sim \mathcal{N}(0, 1)$ + Calibrated Bank	121 floats (grid)	$0.008\text{ ms}$	0.257 logits	0.755 logits	56.0 trials (slow)	0.496 logits	Configurable
Fixed Staircase (Elo $K=2s$)	None	1 float	< 0.003 ms	0.356 logits	0.401 logits	14.8 trials	0.634 logits	$P^* = 0.50$
Accelerated PEST	None	3 floats	< 0.002 ms	0.412 logits	0.465 logits	11.7 trials	0.750 logits	$P^* = 0.50$
`LearningGate` (Ours, 24-Byte)	WERR Tripod Sub-Boundary	24-byte seed + 6 floats	$0.3-0.4\text{ ms}$	0.419 logits	0.380 logits	10.4 trials (fastest)	0.734 logits	$P^* = 0.50$
Stored-Weight Twin	4-Float Linear Neuron	4 floats + 6 floats	$0.001\text{ ms}$	0.418 logits	0.381 logits	10.4 trials	0.735 logits	$P^* = 0.50$
Frontier LLM (Claude Haiku 4.5)	In-context Prompt Heuristic	Multi-GB VRAM	$67 - 788\text{ ms}$	0.784 logits	Lagged	Unstable	High variance	Variable

📥 Track 1 Replication Package & Double-Blind Review Assets

Manuscript Status: Currently under double-blind peer review at a leading Q1 journal in Learning Technologies & Intelligent Educational Systems. In strict compliance with double-anonymized peer review policies and to protect against pre-publication web indexing (iThenticate / Turnitin / Crossref), raw manuscript drafts and submission documents are maintained under confidential academic embargo until formal acceptance. Independent peer reviewers can access and inspect the complete anonymized replication suite via the OSF View-Only Node.
📦 Supplementary_Code_and_Data_v2.zip — Complete, self-contained, byte-exact replication archive (7.4 MB).
🔬 v2/ Replication Suite Directory:
- v2/pfpw/: C++ kernel (werr_kernel.cpp), R wrappers, simulation runs, finite bank tests, guessing remedies, sensitivity sweeps, and vector publication figures (Figure 1, Figure 2, Figure S1).
- v2/replay/: ASSISTments 2009–2010 and 2017 mixed models and counterfactual replay scripts.
- v2/llm_api/: Claude Haiku 4.5 API decision traces across 200 learners (3,800 calls).
- v2/llm_pilot_runs/: Pilot benchmark runtime (llm_kontrolcu_deneyi.html) and raw telemetry.
- v2/data/: ASSISTments dataset provenance and automated retrieval instructions.

🚀 Track 2: Published Seed Preprint & arXiv Package (Version 4.0)

Procedural Fractal Pedagogy: Resolving the Saturn School Disequilibrium Paradox in Self-Directed AI Education via Zero-Storage Mandelbrot Boundary Reflexes

Preprint Identifiers:

Version 4.0 DOI: 10.5281/zenodo.23128224 (October 4, 2026)
Concept DOI: 10.5281/zenodo.22999420
Patent Application: TÜRKPATENT National Priority Application No. TR 2026/016285
Related Preprints: arXiv:2609.25498 • arXiv:2609.30115

📄 Abstract

In this foundational paper, we formalize Vygotsky’s Zone of Proximal Development (ZPD) and Reigeluth’s disequilibrium corridor as an explicit Observer Horizon Corridor anchored at sub-boundary resonance shoulder loci $X_{\text{upper}} = (0.25, +0.18)$ and $X_{\text{lower}} = (0.25, -0.18)$ along the boundary of the Mandelbrot set ($\partial\mathcal{M}$, $z_{n+1} = z_n^2 + c$). Across $N = 1,000$ simulated self-directed learner trajectories ($T = 120$ cycles), the zero-storage reflex engine achieved $94.19% \pm 0.14%$ time-on-task retention and $89.24% \pm 0.13%$ ZPD residence, mitigating off-task learner drift without cloud LLM dependencies. Student assessment is formalized as a non-dissipative error-kernel invariant ($\mathcal{K}_{\text{error}} \cong \mathcal{I}_3 \subset \mathbb{Z}/9\mathbb{Z}$) governed by the TAMAMe Horizon Complementarity law $B(t) + S(t) = 1$, machine-verified in Lean 4 with zero sorry axioms.

📥 Track 2 Resources

📄 Download Camera-Ready PDF — 2-column preprint PDF.
📦 Download arXiv v4.0 Package — Complete self-contained TeX source, BibTeX, and 4 PNG figures.
📋 arXiv Yükleme Rehberi (Step-by-Step Guide) — Copy-paste submission guide.
📜 Lean 4 Machine Proofs — 7 theorems machine-checked with zero sorry axioms.
🎮 Interactive Web Simulator — In-browser visualization of the Mandelbrot Observer Horizon.

🏛️ Track 3: Historical Archival Corpus (Legacy)

All assets prior to Version 2.0 are preserved in legacy/ for continuous verification of past citations:

legacy/zenodo_dist/: Zenodo v1/v4 distribution bundles and SHA-256 seal manifests.
legacy/sim/ & legacy/data/: Raw telemetry and simulation scripts for early PFP-Core studies.
legacy/lean4/: Machine-checked Lean 4 formal proofs.
legacy/README_LEGACY.md: Original documentation and historical benchmarks.

📁 Repository Directory Structure

WerreduR/
├── README.md                                    # 📖 Ana bilimsel portal ve kümülatif yol haritası
├── CHANGELOG.md                                 # 📜 Sürüm günlüğü (v1.0 -> v4.0 -> v2.0 -> v2.1 Q1)
├── CITATION.cff                                 # 📑 Akademik atıf künyesi
├── .zenodo.json                                 # 🌐 Zenodo metadata yapılandırması
├── LICENSE                                      # ⚖️ Business Source License 1.1 (BSL 1.1)
├── index.html                                   # 🌐 Canlı GitHub Pages web simülatörü
│
├── v2/                                          # 🔬 Track 1: Q1 Ampirik Replikasyon ve Veri Paketi
│   ├── README.md                                # Replikasyon rehberi ve çalıştırma talimatları
│   ├── pfpw/                                    # C++ çekirdeği, R wrapperları, 6 sentetik koşul
│   │   ├── src/werr_kernel.cpp                  # C++11 optimize WERR tripod Mandelbrot çekirdeği
│   │   ├── R/                                   # 00_seed_search.R ... 07_seed_sensitivity.R
│   │   ├── tests/                               # test_parity.R, test_js_parity.js, referans csv'ler
│   │   └── out/                                 # RDS verileri, CSV tabloları, Figure 1, 2, S1
│   ├── replay/                                  # ASSISTments ampirik karma modelleri & replay
│   │   ├── 01_fit_learner_model.R ... 07_second_dataset_replay.R
│   │   └── out/                                 # Model ağırlıkları, AUC kalibrasyonu, replay tabloları
│   ├── llm_api/                                 # Claude Haiku 4.5 API deneyi (200 öğrenci, 3.800 çağrı)
│   │   ├── kararlar_claude_claude-haiku-4-5-20251001.csv
│   │   ├── llm_api_deneyi.R
│   │   └── ozet_claude_claude-haiku-4-5-20251001.txt
│   ├── llm_pilot_runs/                          # Destekleyici pilot çalıştırmalar (Tablo S12)
│   ├── llm/                                     # Pilot çalışma test uyumluluk köprüsü
│   └── data/                                    # ASSISTments veri indirme talimatları ve provenance
│
├── werr/                                        # 🧠 WERR Ekosisteminde Doğrulanmış Üretim Çekirdeği
│   ├── learning_gate.py                         # Üretim sınıfı LearningGate kontrolcüsü
│   ├── engine.py                                # Kognitif refleks motoru
│   ├── fractal.py                               # Mandelbrot & Tripod çekirdeği
│   └── ...
│
├── tests/                                       # 🧪 Otomasyonlu Test Paketi
│   └── test_learning_gate_parity.py             # 9/9 Geçen Parite ve Değişmezlik Testleri (C++, R, JS, Python)
│
├── releases/                                    # 📦 Dağıtım Paketleri ve İndirmeler
│   ├── Supplementary_Code_and_Data_v2.zip       # Q1 eksiksiz replikasyon arşivi (7.4 MB)
│   ├── arxiv_submission_pfp_v4.zip              # Track 2: arXiv v4.0 TeX/PNG paketi
│   └── Procedural_Fractal_Pedagogy_Seed_Paper_v1.pdf # Track 2: Kamera hazır önbaskı PDF
│
├── arxiv_pfp_v4/                                # 📄 Track 2: Açık TeX & BibTeX Kaynakları
│
└── legacy/                                      # 🏛️ Track 3: Önceki Yayınların Tüm Arşiv Verileri
    ├── lean4/PFP_HorizonProof.lean              # Lean 4 Biçimsel Doğrulama (7 teorem, 0 sorry)
    ├── zenodo_dist/                             # Zenodo v1/v4 dağıtım paketleri & manifestolar
    ├── sim/ & data/                             # İlk yayın simülasyon ve veri kaynakları
    └── README_LEGACY.md                         # Tarihsel dokümantasyon

🛠️ Verification & Testing

Verify cross-language parity, exact mathematical invariants, and benchmark consistency:

# Verify LearningGate Parity (C++, R, JS, Python, Elo identity, analytical bounds)
python tests/test_learning_gate_parity.py

Output: 9/9 tests pass with $\Delta < 10^{-9}$ floating-point precision.

To run the full R simulation suite:

cd v2/pfpw
Rscript tests/test_parity.R
Rscript R/01_run_simulation.R 1000 120
Rscript R/02_report.R

🏛️ Associated Formal Verification & Scientific Corpus

WerreduR represents Paper 3 in the unified open-science corpus spanning fractal neural synthesis, formal verification, biophysical modeling, and decentralized reflex intelligence:

Makale / Sütun	Başlık / Katkı	En Son Sürüm DOI	Çatı / Konsept DOI	arXiv / Doğrulama Durumu	Birincil Depo
Paper 1: MFNS	Mandelbrot Fractal Neural Synthesis	`10.5281/zenodo.22867037`	`10.5281/zenodo.22774934`	Açık Bilim Önbaskısı (Revizyonda)	`pCwOrM/mandelbrot-fractal-neural-synthesis`
Paper 2: OED	Orbital Error Dynamics (OED v3)	`10.5281/zenodo.22900465`	`10.5281/zenodo.22896855`	`arXiv:2609.30115` • HF Paper	`pCwOrM/mandelbrot-fractal-neural-synthesis`
Paper 3: WerreduR	Procedural Fractal Pedagogy (v4.0)	`10.5281/zenodo.23128224`	`10.5281/zenodo.22999420`	Hedef: Q1 Learning Technologies (Hakemde) • Canlı Simülatör	`jesmaat/WerreduR` (Mirror: `pCwOrM/WerreduR`)
Paper 4: BH Page	Black Hole Page Curve & Quantum Gravity (v5)	`10.5281/zenodo.23072120`	`10.5281/zenodo.22961999`	CERN Record 22978460 • Stabilizer Kodları	`pCwOrM/mandelbrot-fractal-neural-synthesis`
Paper 5: Formal	Lean 4 40-Core Gauntlet (v2)	`10.5281/zenodo.22983889`	`10.5281/zenodo.22974543`	`arXiv:2609.33066` • HF Paper	`pCwOrM/werr` & `werracle`
Paper 6: WerrSoma	Drosophila Connectome (158K Nöron, v1.1)	`10.5281/zenodo.23072929`	`10.5281/zenodo.22996625`	`arXiv:submit/8161759` [on hold] • 3D Portal	`Lexovian/WerrSoma` (Mirror: `pCwOrM/WerrSoma`)
Paper 7: Werracle	Sub-Cent Intra-Block EVM AI Oracle (v1)	`10.5281/zenodo.22942599`	`10.5281/zenodo.22942598`	`arXiv:2609.30719` • HF Paper	`pCwOrM/werracle` & `werralem`
Paper 8: Schönhage	Tensor Taşıyıcı Sıkıştırma ($W=176M$)	`10.5281/zenodo.23268580`	`10.5281/zenodo.23268579`	`arXiv:2610.14263` (PDF • DOI: `10.48550/arXiv.2610.14263` • `submit/8207241` [published]) • CrocSwap #226 (Incorporated) • Contributors • Audit `50d76881`	`pCwOrM/integer-mult-bounds`
Paper 9: Güneş Dili	Deterministik Morfoloji & 53 Koma	`10.5281/zenodo.23273006`	`10.5281/zenodo.23273005`	Lean 4 Doğrulanmış • Canlı Portal	`pCwOrM/gunes-dili`
Paper 10: GDT	Genel Bölen Teoremi & Kalan Koşullanması	`10.5281/zenodo.23316070`	`10.5281/zenodo.23316070`	Lean 4 Doğrulanmış (2.287 Kontrol PASS)	`pCwOrM/general-divisor-theorem`
Paper 11: Niemeier	24D Niemeier $A_8^3$ & K3 Umbral Moonshine	`10.5281/zenodo.23324066`	`10.5281/zenodo.23324066`	Lean 4 Sertifikalı (0 sorry, 0 aksiyom) • Kayıt 23324067	`pCwOrM/niemeier-a8-umbral-moonshine`
Motor: WERR	Zero-VRAM Gauntlet & JevBench Intake	`10.5281/zenodo.22939253`	`10.5281/zenodo.22867425`	`arXiv:2609.25498` • HF Paper • HF Dataset	`pCwOrM/werr`
Platform: answerr	Reflex AI & Canlı Çalışma Alanı	Canlı: `answerr.me`	-	Çift Bilişsel Refleks Platformu & API	`pCwOrM/answerr`
Ayrık Alg	GAP-Lean4 Biçimsel Doğrulanmış Port (35 Teorem)	`10.5281/zenodo.23045504`	`10.5281/zenodo.23045503`	`arXiv:2609.38492` • HF Paper	`pCwOrM/gap-lean4-port`
Robotik: WERRobotics	Sıfır-Bellek Arduino & Gömülü Edge AI Çekirdeği (`v0.5.1`)	`10.5281/zenodo.22939253`	`10.5281/zenodo.22867425`	ATmega328P / ESP32 / STM32 (`0 Byte Heap`, `TR 2026/016633`)	`pCwOrM/WERRobotics`

📜 Citation & Open Science

1. Citing the Flagship Q1 Empirical Positioning Study (Under Review)

@article{dagli2026learninggate,
  author    = {Da{\u{g}}l{\i}, Zerrin and Da{\u{g}}l{\i}, Volkan and Da{\u{g}}l{\i}, Da{\u{g}}han},
  title     = {Where does a fractal-seeded difficulty controller stand? A simulation study against adaptive testing, staircase rules and a language model},
  journal   = {Under Peer Review},
  year      = {2026},
  note      = {Flagship Empirical Study; Replication package: \url{https://github.com/jesmaat/WerreduR}}
}

2. Citing the Foundational Seed Paper (Version 4.0 Archive)

@article{dagli2026pfpv4,
  author    = {Da{\u{g}}l{\i}, Zerrin and Da{\u{g}}l{\i}, Volkan and Da{\u{g}}l{\i}, Da{\u{g}}han},
  title     = {Procedural Fractal Pedagogy: Resolving the Saturn School Disequilibrium Paradox in Self-Directed {AI} Education via Zero-Storage Mandelbrot Boundary Reflexes},
  journal   = {Zenodo Open Science Archive},
  year      = {2026},
  month     = {October},
  doi       = {10.5281/zenodo.23128224},
  note      = {Version 4.0; Concept DOI: 10.5281/zenodo.22999420; \url{https://zenodo.org/records/23128224}}
}

⚖️ License & Intellectual Property

Software Code & Verification Modules: Licensed under the Business Source License 1.1 (BSL 1.1).
- Free Academic, Educational & Research Use: You may freely run, compile, inspect, benchmark, test, fork, and reproduce the Licensed Work for non-commercial research, academic study, and educational evaluations.
- Commercial Restrictions: Production commercial deployment, hosted software-as-a-service (SaaS), paid APIs, or cloud-based decision services require an express written Commercial Enterprise License from ITouch Bilişim Sistemleri Ltd. Şti. (answerr.me).
Preprint & Data Telemetry: Open-access research data licensed under Creative Commons Attribution 4.0 International (CC-BY 4.0).
Patent Disclosure: Procedural coordinate seed routing, boundary modulation, and zero-storage difficulty control architectures are protected under Turkish Patent and Trademark Office (TÜRKPATENT) National Priority Application No. TR 2026/016285.

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WerreduR: Adaptive Difficulty Control & Procedural Cognitive Reflex Engine

🏛️ Cumulative Academic Architecture & Multi-Track Scientific Portal

👥 Authors & Affiliations

🌐 Companion Open-Science Corpus & Cross-Verification

🏆 Track 1: Flagship Q1 Empirical Positioning Study (Under Double-Blind Peer Review)

Where does a fractal-seeded difficulty controller stand? A simulation study against adaptive testing, staircase rules and a language model

📄 Executive Summary & Findings

Key Empirical Results:

📊 Comparative Positioning Matrix

📥 Track 1 Replication Package & Double-Blind Review Assets

🚀 Track 2: Published Seed Preprint & arXiv Package (Version 4.0)

Procedural Fractal Pedagogy: Resolving the Saturn School Disequilibrium Paradox in Self-Directed AI Education via Zero-Storage Mandelbrot Boundary Reflexes

📄 Abstract

📥 Track 2 Resources

🏛️ Track 3: Historical Archival Corpus (Legacy)

📁 Repository Directory Structure

🛠️ Verification & Testing

🏛️ Associated Formal Verification & Scientific Corpus

📜 Citation & Open Science

1. Citing the Flagship Q1 Empirical Positioning Study (Under Review)

2. Citing the Foundational Seed Paper (Version 4.0 Archive)

⚖️ License & Intellectual Property

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arxiv_pfp_v4		arxiv_pfp_v4
assets		assets
embargo		embargo
extras		extras
legacy		legacy
releases		releases
tests		tests
tools		tools
v2		v2
werr		werr
.gitignore		.gitignore
.zenodo.json		.zenodo.json
ARXIV_V4_YUKLEME_REHBERI.md		ARXIV_V4_YUKLEME_REHBERI.md
CHANGELOG.md		CHANGELOG.md
CITATION.cff		CITATION.cff
LICENSE		LICENSE
README.md		README.md
index.html		index.html

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WerreduR: Adaptive Difficulty Control & Procedural Cognitive Reflex Engine

🏛️ Cumulative Academic Architecture & Multi-Track Scientific Portal

👥 Authors & Affiliations

🌐 Companion Open-Science Corpus & Cross-Verification

🏆 Track 1: Flagship Q1 Empirical Positioning Study (Under Double-Blind Peer Review)

Where does a fractal-seeded difficulty controller stand? A simulation study against adaptive testing, staircase rules and a language model

📄 Executive Summary & Findings

Key Empirical Results:

📊 Comparative Positioning Matrix

📥 Track 1 Replication Package & Double-Blind Review Assets

🚀 Track 2: Published Seed Preprint & arXiv Package (Version 4.0)

Procedural Fractal Pedagogy: Resolving the Saturn School Disequilibrium Paradox in Self-Directed AI Education via Zero-Storage Mandelbrot Boundary Reflexes

📄 Abstract

📥 Track 2 Resources

🏛️ Track 3: Historical Archival Corpus (Legacy)

📁 Repository Directory Structure

🛠️ Verification & Testing

🏛️ Associated Formal Verification & Scientific Corpus

📜 Citation & Open Science

1. Citing the Flagship Q1 Empirical Positioning Study (Under Review)

2. Citing the Foundational Seed Paper (Version 4.0 Archive)

⚖️ License & Intellectual Property

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