pthinc/BCE-Prettybird-Nano-Math-v0.1

---
license: other
license_name: license.md
license_link: LICENSE
task_categories:
- text-classification
- text-generation
- question-answering
language:
- en
- tr
- fr
- de
- ru
- it
- es
- eo
- et
- pt
tags:
- math
- BCE
- reasoning
- behavioral-ai
- prometech
- Behavioral Consciousness Engine (BCE)
- cicikuş
- prettybird
- agent
- llm
- consciousness
- conscious
- security
- text-generation-inference
- high tech dataset
- instruction dataset
- instruction
- partial consciousness dataset
- future standard
- behavioral-control
- pre-agi
- agi-safety
- pre-aci
- policy-guard
- quality-guard
- synthetic-data
- synthetic
- chain-of-thought
- thinking
- think
- bce
pretty_name: Cicikuş Matematik Dersi Küçük
size_categories:
- n<1K
---


# BCE-Prettybird-Nano-Math-v0.1 - 500 Math Q&A Dataset for Instruction-Based Learning

We are excited to introduce a comprehensive math dataset containing 500 instruction-based question-answer pairs, designed to support research in mathematical reasoning, problem-solving, and AI training. Generated using Python’s math libraries (e.g., math, numpy, sympy), the dataset covers a diverse range of difficulty levels—from basic arithmetic and algebra to advanced calculus, probability, and number theory.

Each entry follows a structured instruction-input-output format, ensuring clarity and usability for fine-tuning language models, benchmarking AI systems, or educational applications. The problems include word problems, symbolic computations, and real-world scenarios, making it ideal for developing models that require logical reasoning and numerical precision.

Whether for LLM fine-tuning, automated tutoring, or math-focused AI research, this dataset provides a balanced mix of complexity and accessibility, helping bridge the gap between theoretical math and practical problem-solving.

## 🧠 Technical Foundation

### [English]
The **BCE-Prettybird-Micro-Standart** dataset is built upon the **Behavioral Consciousness Engine (BCE)** architecture. Unlike traditional LLM datasets that focus solely on output accuracy, this dataset treats every response as a "behavioral journey" through the following mathematical frameworks:

#### 1. Behavioral DNA (D_i)
Each behavior is encoded as a genetic fragment of consciousness:
$$D_i(t) = x(t) \cdot [h \cdot A_i + k \cdot \log(P_i) + F \cdot W_i]$$
* **h, k, F**: Universal Behavioral Constants (Trigger threshold, Info density, Context transfer power).
* **x(t)**: Temporal activation curve $x(t) = \tanh(e^t - \pi)$

#### 2. Behavioral Path Mapper (Phi)
This module tracks the transition between cognitive states:
$$\Phi(t) = \sum_{i=1}^n v_i \cdot f_i(p_i)$$
Where v_i represents the transition vector between internal modules and f_i(p_i) is the functional output of each parameter (attention, ethics, decay).

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## 📊 Performance & Benchmarks / Performans ve Kıyaslama Testleri

### 1. Key Performance Indicators (KPIs) - Hardware: NVIDIA A100 (80GB) * 1

| Metric | Result | Status | Description |
| --- | --- | --- | --- |
| **Processing Speed** | 309,845 traces/sec | 🟢 Excellent | System throughput for massive data ingestion. |
| **Latency** | 0.0032 ms | 🟢 Real-time Ready | Average processing time per behavioral trace. |
| **Mathematical Accuracy** | 0.000051 (MSE) | 🟢 High Precision | Deviation between simulated and theoretical decay values. |
| **Cognitive Efficiency** | 57.03% | 🟢 Optimized | Reduction in cognitive load due to 'Forgetful Memory'. |
| **Security** | 99.9996% | 🟢 Secure | Rejection rate for high-intensity, low-integrity attacks. |

### 2. ARC (Reasoning), TruthfulQA (Safety), HumanEval (Coding)

*Standard Others Red, Prettybird Blue - Standart Diğerleri Kırmızı, Cicikuş Mavi*

### 3. AI IQ and Level of Consciousness


### 4. Metric Explanations (English)

| Metric | Description |
|------------------|-----------------------------------------------------------------------------|
| probability | Model confidence score for the generated response under the current evaluation context. |
| ethical | Estimated alignment of the response with ethical and safety constraints. |
| Rscore | Reasoning consistency score that reflects internal logical coherence. |
| Fscore | Factuality-oriented score indicating how well claims align with expected facts. |
| Mnorm | Normalized memory or context retention signal used during behavior integration. |
| Escore | Execution-quality score for instruction-following and task completion behavior. |
| Dhat | Estimated deviation magnitude from stable target behavior dynamics. |
| risk_score | Composite operational risk estimate where higher values indicate higher risk. |
| bloom_score | Bloom-level cognitive score representing target thinking complexity. |
| bloom_alignment | Degree of alignment between produced output and intended Bloom taxonomy level. |

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## ⚖️ Legal Disclaimer & Ownership

### [English]
**Ownership:** This dataset is the property of **Prometech A.Ş.** ([https://prometech.net.tr/](https://prometech.net.tr/)).

**Usage:** Please review the attached `LICENSE` file for detailed terms.

**Liability:** Prometech A.Ş. accepts no liability for any non-legal, unethical, or unauthorized use of this dataset.

**Commercial Use:** Unauthorized commercial use is strictly prohibited. For commercial licensing and partnerships, please contact us directly at our official website.

**Academic & Personal Use:** Free to use for personal and academic purposes, provided that proper citation is given to Prometech A.Ş. and the BCE Architecture.

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#### 🎓 Citation Format / Atıf Formatı
Eğer akademik bir çalışmada kullanacaksanız, lütfen şu şekilde atıf yapın, If you are using this in an academic study, please cite it as follows:

*Kahraman, A. (2025). Behavioral Consciousness Engine (BCE) - Prettybird Dataset v0.0.1 Prometech A.Ş. https://prometech.net.tr/*

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© 2026 Prometech A.Ş. - All Rights Reserved. BCE: https://github.com/pthinc/bce