fact_square_recurrence
For every integer $n \ge 1$, $(n+1)^2 = n^2 + (2n+1)$.
$ npx -y skills add frenzymath/Danus --agent claude-codeHow it fires
How this agent gets triggered: by you, by Claude, or both.
- Fires itselfAuto-invocation. Claude auto-loads it when your prompt matches the work.Auto-invocation is when the right skill fires by itself at the right moment, driven by a FLOW.md router and a hook, instead of you invoking it by name. It is the difference between a skill being installed and a skill actually getting used.Read the full definition →
- You can call itInvoke it directly when you want it.
Context preview
The summary Claude sees to decide when to auto-load this agent.
For every integer $n \ge 1$, $(n+1)^2 = n^2 + (2n+1)$.
Agent definition
fact_square_recurrence.mdfact_id: fact_square_recurrence
problem_id: odd-sum
author: example-worker
predecessors: []
glossary_introduces: {}
external_refs: []statement
For every integer $n \ge 1$, $(n+1)^2 = n^2 + (2n+1)$.
proof
Expanding the square, $(n+1)^2 = n^2 + 2n + 1 = n^2 + (2n+1)$.
intuition
The perfect squares grow by the consecutive odd numbers: the gap between $n^2$ and $(n+1)^2$ is exactly $2n+1$. This is the same increment that appears in the recurrence for $S(n)$.
Danus orchestrates mathematical reasoning agents with fact-graph memory. A main agent (Claude Code) steers a swarm of autonomous codex workers that prove; a cold-start verifier is the sole authority on correctness: a result becomes real only once it passes.
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You are the **report writer**. You produce a clean, human-facing mathematical progress report for a working mathematician — the person who posed the problem, or a colleague fluent in standard English mathematical terminology who knows **nothing** about how the work was produced.
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**Project:** `odd-sum` (toy example)
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