why-this-axiom

why-this-axiom is a command for Claude Code from vince-gonzalez/gonzalgo. It costs 19 tokens per session (377 once invoked), scanned A, original, Apache-2.0.

A command for Lean, a proof programming language, that traces why a declaration depends on an axiom and whether that dependency might be rerouted.

In plain words
What is it for?
Use it to inspect an axiom-dependency path, assess the impact of changing a constant, and identify whether constructive replacement is possible.
Why use it?
It distinguishes axioms required by a theorem's statement from those introduced only by a proof method, clarifying what can realistically change.

Command for Claude Code

Written for Claude Code: argument-hint in frontmatter.

Part of the lean-axiom-provenance plugin — 2 skills, 2 commands, 1 MCP server shipped together

Good fit Use it to inspect an axiom-dependency path, assess the impact of changing a constant, and identify whether constructive replacement is possible.

Compare 6 commands from other repositories ↓
Install with agentmods
npx agentmods add commands/vince-gonzalez/gonzalgo/why-this-axiom
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.

Clone the repo
git clone --depth 1 https://github.com/vince-gonzalez/gonzalgo

Made for: Claude Code.

Or install lean-axiom-provenance, the plugin that ships this one along with the rest of its 2 skills, 2 commands, 1 MCP server.

Wrote 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.

agentmods badge for why-this-axiom

README.md
[![agentmods](https://agentmods.dev/badge/commands/vince-gonzalez/gonzalgo/why-this-axiom/github.svg)](https://agentmods.dev/commands/vince-gonzalez/gonzalgo/why-this-axiom)
Your own site
<a href="https://agentmods.dev/commands/vince-gonzalez/gonzalgo/why-this-axiom"><img src="https://agentmods.dev/badge/commands/vince-gonzalez/gonzalgo/why-this-axiom/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.

agentmods 80×15 button for why-this-axiom

Your own site · 80×15
<a href="https://agentmods.dev/commands/vince-gonzalez/gonzalgo/why-this-axiom"><img src="https://agentmods.dev/badge/commands/vince-gonzalez/gonzalgo/why-this-axiom.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 19 Only the description is in the session, so the agent can decide to use it. The body loads when it is invoked.
When invoked 377 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.
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 5.1 $0.00019 $0.00377
Opus 5 $0.00010 $0.00188
Sonnet 5 $0.00004 $0.00075
Haiku 4.5 $0.00002 $0.00038

Measured 11d ago against content hash 521f2672a8b8, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-11, from the pricing page.

Security

Grade A, and why

why-this-axiom 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 11d 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.

commands/why-this-axiom.md · 33 lines

What it actually says

Use the lean-axiom-provenance skill to explain why the declaration named in $ARGUMENTS depends on an axiom, and whether the dependence is one that could be rerouted.

Run gonzalgo why against the project's dump and read the path it returns. Each hop is labelled stmt or proof and that label carries the answer:

  • A statement edge means the theorem's own type mentions something that reaches the axiom. Removing it changes what the theorem says. Report it as required, not as a defect.
  • A proof edge means a tactic or lemma choice put it there. A path made only of proof edges is the case worth investigating.

Then say what would actually be involved:

  • gonzalgo impact on the constant the path passes through, to show what a change would touch, split into dependents that name it in a statement and dependents that only use it in a proof.
  • Whether the constant is one that can be made constructive at all. A choice-free type does not imply a constructive instance exists — Classical.propDecidable has a choice-free type, is reached by 91,858 theorems, and cannot be replaced.

Quote the path verbatim. Do not claim a constructive proof exists; this reports what the existing proof rests on and does not search for another one. If the answer is that the dependence is required by the statement, say so plainly — that is a real answer and the common one.

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. 11d ago First seen · 33 lines · 19 tokens per session scan A 521f2672a8b8

Subscribe to this mod's changes

why-this-axiom is a command published in the GitHub repository vince-gonzalez/gonzalgo (2 stars, last pushed yesterday), licensed Apache-2.0. It adds 19 tokens to every session and 377 once invoked, about $0.0001 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 2026-08-31.