BCE-Prettybird-Middle-Math-v0.1 110,500 Math Q&A Dataset for Instruction-Based Learning

We are excited to introduce a comprehensive math dataset containing 110,500 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: $$D_i(t)=x(t)\cdot [h\cdot A_i+k\cdot \log (P_i)+F\cdot W_i]D\_i(t)\; =\; x(t)\; \backslash cdot\; [h\; \backslash cdot\; A\_i\; +\; k\; \backslash cdot\; \backslash log(P\_i)\; +\; F\; \backslash cdot\; W\_i]$$

• 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: $$\mathrm{\Phi }(t)=\sum _{i=1}^n{v}_i\cdot f_i(p_i)\backslash Phi(t)\; =\; \backslash sum\_\{i=1\}^n\; v\_i\; \backslash cdot\; f\_i(p\_i)$$ 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).

---

📊 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.

---

⚖️ Legal Disclaimer & Ownership

[English]

Ownership: This dataset is the property of Prometech A.Ş. (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.

---

🎓 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/

---

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