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 raja21068/AutoResearch --skill formula-derivationgit clone --depth 1 https://github.com/raja21068/AutoResearchWrote 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/raja21068/autoresearch/formula-derivation)<a href="https://agentmods.dev/skills/raja21068/autoresearch/formula-derivation"><img src="https://agentmods.dev/badge/skills/raja21068/autoresearch/formula-derivation/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/raja21068/autoresearch/formula-derivation"><img src="https://agentmods.dev/badge/skills/raja21068/autoresearch/formula-derivation.svg" alt="Reviewed on agentmods" width="80" height="20"></a>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 | $0.00084 | $0.02000 |
| Opus 5 | $0.00042 | $0.01000 |
| Sonnet 5 | $0.00017 | $0.00400 |
| Haiku 4.5 | $0.00008 | $0.00200 |
Grade A, and why
formula-derivation 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 6d 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.
This is a copy
100% identical to formula-derivation — 2 lines differ, which has more behind it and is treated as the original. This page carries a canonical link to it rather than competing with it.
How it starts
The opening of the file, as written. The whole thing — 281 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Formula Derivation: Research Theory Line Construction
Build an honest derivation package, not a fake polished theorem story.
Constants
- DEFAULT_DERIVATION_DOC =
DERIVATION_PACKAGE.mdin project root - STATUS =
COHERENT AS STATED | COHERENT AFTER REFRAMING / EXTRA ASSUMPTION | NOT YET COHERENT
Context: $ARGUMENTS
Goal
Produce exactly one of:
- a coherent derivation package for the original target
- a reframed derivation package with corrected object / assumptions / scope
- a blocker report explaining why the current notes cannot yet support a coherent derivation
Inputs
Extract and normalize:
- the target phenomenon, formula, relation, or theory line
- the intended role of the derivation:
- exact identity / algebra
- proposition / local theorem
- approximation
- mechanism interpretation
- explicit assumptions
- notation and definitions
- any user-provided formula chain, sketch, messy notes, or current draft
- nearby local theory files if the request points to them
- desired output style if specified:
- internal alignment note
- paper-style theory draft
- blocker report
If the target, object, notation, or assumptions are ambiguous, state the exact interpretation you are using before deriving anything.
Workflow
Step 1: Gather Derivation Context
Determine the target derivation file with this priority:
- a file path explicitly specified by the user
- a derivation draft already referenced in local notes
DERIVATION_PACKAGE.mdin project root as the default target
Read the relevant local context:
- the chosen target derivation file, if it already exists
- any local theory notes, formula drafts, appendix notes, or files explicitly mentioned by the user
Extract:
- target formula / theory goal
- current formula chain
- assumptions
- notation
- known blockers
- desired output mode
Step 2: Freeze the Target
State explicitly:
- what is being explained, derived, or supported
- whether the immediate goal is:
- identity / algebra
- proposition
- approximation
- interpretation
- what the derivation is expected to output in the end
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.
- 6d ago First seen · 281 lines · 84 tokens per session scan A 3f1ce5b87c4b
formula-derivation is a skill published in the GitHub repository raja21068/AutoResearch (2 stars, last pushed 3mo ago), licensed MIT. It adds 84 tokens to every session and 2,000 once invoked, about $0.0004 per session on Opus 5. A static security scan graded it A with 0 findings. It is 100% identical to formula-derivation, differing in 2 lines, and is treated as a copy.
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