derive

A reference-derivation command that finds or writes a clear proof of a selected equation or theorem from course materials. The result is saved as a markdown file with assumptions, steps, interpretation, and common mistakes.

In plain words
What is it for?
Use it to document how an equation or theorem follows from earlier results, review its meaning, and check typical derivation errors.
Why use it?
It provides a study reference without testing the user or requiring them to write a solution first. It also keeps the reasoning and source results in one reusable document.

Command

Install

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.

agentmods
npx agentmods add commands/optimeta/paideia/derive
Clone the repo
git clone --depth 1 https://github.com/OPTIMETA/PAIDEIA
Per session 34 Only the description is in the session, so the agent can decide to use it. The body loads when it is invoked.
When invoked 632 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. Scan, not verified.
Origin original No closer match found in the catalogue.
Token cost

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.

ModelPer sessionOnce invoked
Fable 5 $0.00034 $0.00632
Opus 5 $0.00017 $0.00316
Sonnet 5 $0.00007 $0.00126
Haiku 4.5 $0.00003 $0.00063

Measured 2d ago against content hash 39e7cf5d32fd, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

derive 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 2d 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.

plugins/paideia/commands/derive.md · 67 lines

How it starts

The opening of the file, as written. The whole thing — 67 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Output language

Read INTERFACE_LANG from .course-meta (default en). All user-facing prose — chat output and narrative sections of the generated derivation MD — must be in that language. Keep in English regardless: file paths, slash command names, pattern IDs, LaTeX, and any literal section anchors downstream tools regex on.

Load skills/course-builder/SKILL.md for material locations. Also read course-index/summary.md to resolve the target.

Target: $ARGUMENTS

Procedure:

  1. Locate the derivation in converted/textbook/*.md and converted/lectures/*.md. If present in both, prefer the textbook (usually cleaner).
  2. If not in materials, derive it from first principles using standard techniques for the course's domain. Cite which earlier results you're using.
  3. Format as a clean reference markdown file with:
    • Starting definitions/assumptions clearly stated
    • Each step with a one-line explanation of why
    • Boxed final result
    • Short physical / mathematical interpretation at the end
    • Typical pitfalls (common student errors) listed at bottom
  4. Save to derivations/<slug>.md. Slug is lowercase-hyphenated from the target name.
  5. Print (in $INTERFACE_LANG): "Saved derivations/<slug>.md. Open and read; ask if any step is unclear."

Do NOT quiz or prompt the user — this command is a pure reference-writer. The user explicitly set this up so they can read rather than type.

Format convention (align with existing derivations/ files if any)

The skeleton below uses English labels; if INTERFACE_LANG=ko, translate the bold labels ("Goal", "Starting point", "Step 1 — ...", "Result", "Interpretation", "Pitfalls", "Reference") to natural Korean equivalents. Keep LaTeX, file paths, and equation content unchanged.

# <Target name>

**Goal.** <statement of what we want to derive>

**Starting point.** <definition / law / axiom / earlier result>

---

### Step 1 — <step description>

$$<step equation>$$

<why this step>

### Step 2 — ...

...

---

**Result.**
$$\boxed{\;<final>\;}$$

**Interpretation.** <1-2 sentences on what this means physically/mathematically>

**Pitfalls.**
- <common error 1>
- <common error 2>

**Reference.** <source section in converted/>

Read the full file on GitHub · 67 lines

Changes

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.

  1. 2d ago First seen · 67 lines · 34 tokens per session scan A 39e7cf5d32fd

Subscribe to this mod's changes

derive is a command published in the GitHub repository OPTIMETA/PAIDEIA (91 stars, last pushed 1mo ago), licensed MIT. It adds 34 tokens to every session and 632 once invoked, about $0.0002 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 2026-08-30.