Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add deciqAI/knowledge-skills --skill power-law-distributiongit clone --depth 1 https://github.com/deciqAI/knowledge-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/deciqai/knowledge-skills/power-law-distribution)<a href="https://agentmods.dev/skills/deciqai/knowledge-skills/power-law-distribution"><img src="https://agentmods.dev/badge/skills/deciqai/knowledge-skills/power-law-distribution/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/deciqai/knowledge-skills/power-law-distribution"><img src="https://agentmods.dev/badge/skills/deciqai/knowledge-skills/power-law-distribution.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector pass
What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00132 | $0.01992 |
| Opus 5 | $0.00066 | $0.00996 |
| Sonnet 5 | $0.00026 | $0.00398 |
| Haiku 4.5 | $0.00013 | $0.00199 |
Grade A, and why
power-law-distribution scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 9d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 120 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Power-Law Distribution
Overview
A power-law distribution is a statistical distribution where probability of size x is proportional to x^(−α): large events are rare but far more probable than a Gaussian model predicts, and the largest events dominate the total — there is no "typical" case.
First quantified by Pareto (1896) in wealth; formalized by Mandelbrot (1963) for financial returns; surveyed universally by Newman (2005) across cities, earthquakes, citations, and web traffic.
Composes with pareto-principle (80-20 is the most famous application; this skill provides the math foundation), black-swan (black swans are the extreme upper-tail events power laws make far more probable), expected-value-and-kelly (Kelly sizing breaks under infinite-variance power laws), and antifragile (antifragile strategies exploit the upper tail).
When to Use
- Allocating capital or resources across a portfolio — power-law returns mean design must prioritize outliers
- Prioritizing customers, channels, content, or features where a small number account for most value
- Assessing business risk — Gaussian risk models (VaR, std dev) systematically underestimate extreme risk
- Any domain where "average" is the planning assumption and extreme outcomes are possible
- Evaluating AI/compute concentration — AI capex, chip export controls, frontier-lab funding, or "AI bubble" questions where value is capturing into a thin tail of companies
Not when: distribution is demonstrably Gaussian; stakes are low enough that shape doesn't affect the decision; audience will misuse power-law framing as nihilism.
Coaching Novices (Adaptive Front Door)
- Engine mode: user has a concrete portfolio, risk, or allocation decision → run The Process directly.
- Coach mode: user is new to the concept → guide step by step.
In Coach mode, respond one step at a time. Each [WAIT] is a hard stop — output only that step's question, then stop.
What ships with it
3 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 9d ago First seen · 120 lines · 132 tokens per session scan A d7345cfd6748
power-law-distribution is a skill published in the GitHub repository deciqAI/knowledge-skills (10 stars, last pushed 10d ago), licensed MIT. It adds 132 tokens to every session and 1,992 once invoked, about $0.0007 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.
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