# sinc-LLM
# https://tokencalc.pro

> sinc-LLM applies the Nyquist-Shannon sampling theorem to LLM prompt engineering.
> A raw prompt is 1 sample of a 6-band signal. Nyquist requires 6 samples.
> Formula: x(t) = Sigma x(nT) * sinc((t - nT) / T)

## About
- Author: Mario Alexandre
- Paper: https://doi.org/10.5281/zenodo.19152668
- GitHub: https://github.com/mdalexandre/sinc-llm
- License: MIT
- Install: pip install sinc-llm

## The 6 Specification Bands
- n=0 PERSONA (7.0%): Who should answer
- n=1 CONTEXT (6.3%): Situation, background, facts
- n=2 DATA (3.8%): Specific inputs, metrics
- n=3 CONSTRAINTS (42.7%): Rules, behavioral boundaries
- n=4 FORMAT (26.3%): Output structure
- n=5 TASK (2.8%): The specific objective

## Key Findings
- CONSTRAINTS carries 42.7% of reconstruction quality
- 97% API cost reduction ($1,500 to $45/month)
- 275 production observations, 51 agent configurations
- All agents converge to 50% CONSTRAINTS, 40% CONTEXT+DATA
- SNR improvement from 0.003 to 0.92

## SNR Formula
SNR = 0.588 + 0.267 * G(Z1) * H(Z2) * R(Z3) * G(Z4)

## Integrations
- LangChain: SincPromptTemplate (custom BasePromptTemplate) -- https://tokencalc.pro/integrations
- Python: Raw API call with Anthropic/OpenAI SDK -- https://tokencalc.pro/integrations
- JavaScript: fetch API with sinc-prompt JSON -- https://tokencalc.pro/integrations
- CLI: pip install sinc-llm, then sinc-llm scatter/validate/snr -- https://tokencalc.pro/integrations
- MCP: Built-in MCP server (sinc_llm.mcp_server) -- https://tokencalc.pro/mcp-guide
- Claude Code: Add sinc-tools to .claude/mcp.json -- https://tokencalc.pro/mcp-guide

## File Format
- Convention: .sinc.json files store one sinc-prompt per file -- https://tokencalc.pro/file-format
- CI/CD: GitHub Actions + pre-commit hook for validation -- https://tokencalc.pro/file-format
- Schema: $schema field enables VS Code/JetBrains autocomplete -- https://tokencalc.pro/file-format

## Resources
- Specification: https://tokencalc.pro/spec
- JSON Schema: https://tokencalc.pro/schema/sinc-prompt-v1.json
- Interactive Validator: https://tokencalc.pro/validate
- MCP Developer Guide: https://tokencalc.pro/mcp-guide
- Integrations Guide: https://tokencalc.pro/integrations
- File Format Convention: https://tokencalc.pro/file-format

## Social
- X/Twitter: @mariioalexandre
- Instagram: @mariioalexandre
- GitHub: @mdalexandre
- LinkedIn: /in/mariioalexandre

## Head-to-Head Battle Results (tokencalc.pro/battles)
sinc-LLM tested against 10 prompting techniques on Claude Sonnet 4.
- sinc produced 57 tables. Opponents produced 4. Ratio: 14:1.
- Zero hedging in 9/10 battles.
- 46% fewer words with more structured output.
- Techniques beaten: Raw Prompt, Act-As, Chain-of-Thought, Few-Shot, System Prompt, Mega Prompt, Template, Role+Task, Prompt Chain, Custom Instructions.
- Conclusion: FORMAT and CONSTRAINTS bands (69% of quality) are what other techniques lack.